Works  of  Prof.  Robt.  H.  Thurston. 

Published  by  JOHN  WILEY  &  SONS,  53   E.  Tenth 
Street,  New  York. 


The  Publishers  and  the  Author  will  be  grateful  to 
any  of  the  readers  of  this  volume  who  will  kindly  call 
their  attention  to  any  errors  of  omission  or  of  commission 
that  they  may  find  therein.  It  is  intended  to  make 
our  publications  standard  works  of  study  and  reference, 
and,  to  that  end,  the  greatest  accuracy  is  sought.  It 
rarely  happens  that  the  early  editions  of  works  of  any 
size  are  free  from  errors  ;  but  it  is  the  endeavor  of  the 
Publishers  to  see  them  removed  immediately  upon  being 
discovered,  and  it  is  therefore  desired  that  the  Author 
may  be  aided  in  his  task  of  revision,  from  time  to  time, 
by  the  kindly  criticism  of  his  readers. 

JOHN  WILEY  &  SONS. 
53  EAST  TEXTH  STREET, 


Works  of  Prof.  Robt.  H.  Thnrston. 

Published  by  JOHN   WILEY  &  SONS,  53  E.  Tenth 
Street,  New  York. 


MATERIALS  OF  ENGINEERING. 

A  work  designed  for  Engineers,  Students,  and  Artisans  in  wood, 
metal,  and  stone.  Also  as  a  TEXT-BOOK  in  Scientific  Schools,  show- 
ing the  properties  of  the  subjects  treated.  By  Prof.  R,  H.  Thurston. 
Well  illustrated.  In  three  parts. 

Part  I.    THE  NON-METALLIC  MATERIALS  OF  ENGINEER 

ING  AND  METALLURGY. 

With  Measures  in  British  and  Metric  Units,  and  Metric  and  Reduction 
Tables 8vo,  cloth,  $2  00 

Part  H.    IRON  AND   STEEL. 

The  Ores  of  Iron :  Methods  of  Reduction ;  Manufacturing  Processes; 
Chemical  and  Physical  Properties  of  Iron  and  Steel :  Strength,  Duc- 
tility. Elasticity  and  Resistance ;  Effects  of  Time,  Temperature,  and 
repeated  Strain ;  Methods  of  Test ;  Specifications  ...  8vo,  cloth,  3  .50 

Part  HI.    THE  ALLOYS  AND  THEIR  CONSTITUENTS. 

Copper,  Tin,  Zinc,  Lead,  Antimony.  Bismuth,  Xickel,  Aluminum,  etc.: 
The  Brasses.  Bronzes;  Copper-Tin-Zinc  Alloys:  Other  Valuable 
Alloys:  Their  Qualities,  Peculiar  Characteristics:  Uses  and  Special 
Adaptations:  Thurston's  "Maximum  Alloys":  Strength  of  the 
Alloys  as  Commonly  Made,  and  as  Affected  by  Special  Conditions: 

The  Mechanical  Treatment  of  Metals 8vo,  ctoth,    2  30 

"  AB  intimated  above,  this  work  will  form  one  of  the  most  con 
well  as  modern  treatises  upon  the  Materials  wed  in  all  torts  at 
Constructions.    As  a  whole  it  forms  a  very  comprehensive  and  pract 
book  for  Engineers,  both  Civil  and  Mechanical."— America*  MacMimitt. 

'•  We  regard  this  as  a  most  useful  book  for  reference  in  its  departments  : 
it  should  be  in  every  Engineer's  Horary."— Jfetna»ifal  Krujinetr. 

MATERIALS  OF  CONSTRUCTION. 

A  Text-book  for  Technical  Schools,  condensed  from  Thurston's 
"Materials  of  Engineering."  Treating  of  Iron  and  Steel,  their  ores, 
•Miiifm  Inn  .  properties  and  uses:  the  useful  metals  and  their  alloys, 
especially  brasses  and  bronzes,  and  their  "  kalchoids " :  strength, 
ductility,  resistance,  and  elasticity,  effects  of  prolonged  and  oft- 
repeated  loading,  crystallization  and  granulation :  peculiar  metals : 
Thurston's  "  maximum  alloys";  stone:  timber;  preservative  pro- 
cesses, etc.,  etc.  By  Prof.  Robt.  H.  Thurston,  of  Cornell  University. 

Many  illustrations Thick  8vo,  cloth,    500 

"Prof.  Thursion  has  rendered  a  great  service  to  the  profession  by  the 
publication  of  this  thorough,  yet  comprehensive,  text-book.  .  .  .  The 
book  meets  a  long-fe'.t  want,  and  the  well-known  reputation  of  its  author 
is  a  sufficient  guarantee  for  its  accuracy  and  thoroughness."—  Building. 

TREATISE   ON  FRICTION  AND  LOST  WORK  IN  MACHIN- 
ERY AND  MTT.T.  WORK. 
Containing  an 
of  the  variou: 

experiments  to  deduce  the  laws  of  Friction  and  Lubricated  Surfaces, 
etc.  By  Prof.  Robt.  H.  Thurston-  Copiously  illustrated.. £vo.  cloth,  3  00 

•'I;,  is  not  too  high  praise  to  say  that  the  present  treatise  is  exhaustive 
and  a  complete  renew  of  the  whole  subject-"— American  Engineer. 

STATIONARY   STEAM  ENGINES. 

Especially  adapted  to  Electric  Lighting  Purposes.  Treating  of  the 
Development  of  Steam-en  srines—  the  principles  of  Construction  and 
Economy,  with  description  of  Moderate  Speed  and  High  Speed  En- 
gines. By  Prof.  R.  H.  Thurston ..12mo.  ctotb.  1  ."At 

"  This  work  must  prove  to  be  of  great  interest  to  both  manufacturers  and 
users  of  steam-engines  "—Snider  and  TVomf-trarter. 


explanation  of  the  Theory  of  Friction,  and  an  account 
i  Lubricants  in  general  use,  with  a  record  of  various 


DEVELOPMENT    OF   THE   PHILOSOPHY  OF   THE   STEAM- 
ENGINE. 

By  Prof.  R.  H.  Thurston 12mo,  cloth,  $0  75 

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DESIQNS>  CON- 

For  Technical  Schools  and  Engineers.    By  Prof.  R.  H.  Thurston.    (183 

engravings  in  text.)    Second  edition 8vo.  cloth,    5  00 

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and  fresh  work,  based  on  the  most  recent  data  and  cognizant  of  the  latest 
discoveries  and  devices  in  steam  boiler  construction."— Mechanical  Neics. 

STEAM-BOILER  EXPLOSIONS  IN  THEORY  AND  IN  PRAC- 
TICE. 

Containing  Causes  of — Preventives — Emergencies — Low  Water — Con- 
sequences— Management —  Safety —  Incrustation  —  Experimental  In- 
vestigations, etc.,  etc.,  etc.  By  H.  H.  Thurston,  LL.D.,  Dr.  Eng., 
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trations  12mo,  cloth,  150 

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matter  of  peculiar  interest  to  practical  men."— American  Machinist. 

"  It  is  a  work  that  might  well  be  in  the  hands  of  every  one  having  to  do 
with  st<-am  boilers,  either  in  design  or  use." — Kngineering  Newt. 

A  HAND  BOOK  OF  ENGINE   AND   BOILER    TRIALS,    AND 

THE  USE  OF  THE  INDICATOR  AND  THE  BRAKE. 
By  R.  H.  Thurston,  Director  of  Sibley  College,  Cornell  University. 

Second  edition  revised 5  09 

"Taken  altogether,  this  book  is  one  which  every  Engineer  will  find  of 
value,  containing,  as  it  does,  much  information  in  regard  to  Engine  and 
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tered paper*  in  the  transactions  of  engineering  societies,  pamphlet  reports, 
note-books,  etc."—  Railroad  Gazette. 

CONVERSION  TABLES. 

Of  the  Metric  and  British,  or  United  States  WEIGHTS  AXD  MEAS- 
URES. With  an  Introduction  by  Robt.  H.  Thurston,  A.M.,  C.E. 

8vo,  cloth,    1  00 

"  Mr.  Thnrston's  book  is  an  admirably  useful  one,  and  the  very  difficulty 
and  unfamiliarity  of  the  Metric  System  renders  such  a  volume  as  this  almost 
indispensable  to  Mechanics,  Engineers,  Students,  and  in  fact  all  classes  of 
people." — Mechanical  News. 

REFLECTIONS  ON  THE  MOTIVE  POWER  OF  HEAT. 

And  on  Machines  fitted  to  develop  that  Power.  From  the  original 
French  of  N.  L.  S.  Carnot.  By  Prof.  R.  H.  Thurston ....  12mo,  cloth,  2  00 

From  Mons.  Haton  de  la  Goupilliere,  Director  of  the  Ecole  Nationale 
Superieure  da  Mints  de  France,  and  President  of  La  Sociite  d'  Encourage- 
ment Jtour  V Industrie  Nntionule: 

•'  I  have  received  the  volume  so  kindly  sent  me.  which  contains  the  trans- 
lation of  the  work  of  Carnot.  Yon  have  rendered  tribute  to  the  founder  of 
the  science  of  thermodynamics  in  a  manner  that  will  be  appreciated  by  the 
whole  French  people." 

A  MANUAL  OF  THE  STEAM  ENGINE. 

A  companion  to   the  Manual  of   Steam  Boilers.     By   Prof.  Robt. 

H.  Thurston.    2  vols 8vo,  cloth,  12  00 

Part  I.    HISTORY,  STRUCTURE  AND  THEORY. 

For  Engineers  and  Technical  Schools.    (Advanced  courses.)    Nearly 

900  pages 8vo,  cloth,    730 

Part  II.    DESIGN,  CONSTRUCTION  AND  OPERATION. 

For  Engineers  and  Technical  Schools.  (Special  courses  in  Steam 
Engineering.)  8vo,  cloth,  750 

TEXT  BOOK  OF  THE  PRIME  MOTORS. 

For  the  Senior  Year  in  Schools  of  Engineering.  By  Prof.  R.  H. 
Thurston.  Ready,  Fall  of  '98. 


PART  I, 
HISTORY,  STRUCTURE,  AND  THEORY 

OF    THE 

STEAM-ENGINE. 


A  MANUAL 


STEAM-ENGINE 


FOR  ENGINEERS  AND  TECHNICAL  SCHOOLS; 

ADVANCED  COURSES. 


PART   I. 
STRUCTURE  AND   THEORY. 


BY 

ROBERT   H.  THURSTON,  A.M.,    LL.D.,   DR.  ENG'G; 

DIRECTOR    OF   SIBLEY   COIJ.EGE,    CORNELL    UNIVERSITY  ;     FORMERLY   OF  THE   U.    S.    N.    ENGINEERS  ; 

PAST  PRESIDENT  AM.   SOCIETY    MECH.    ENGRS.  ;    AITHOR   OF   "  A   HISTORY   OF 

THE  STEAM-ENGINE,"    "  MANUAL   OF   STEAM- 

"MATERIALS   OF   ENGINEERING/' 

ETC.,  ETC.,  ETC. 


NEW  YORK: 

JOHN     WILEY    &     SONS, 

53  EAST  TENTH  STREET. 

1891. 


COPYRIGHT,  1891, 

BY 
ROBERT   H.  THURSTON 


ROBERT  DRUMMOTO, 

Elfctrot\rper, 

444  &  W,  Pearl  Street, 

New  York. 


FEMUS  BROS.. 

Printers, 

.328  Pearl  Street, 

New  York 


or 


PREFACE. 


In  the  work  of  which  this  is  the  first  volume,  the  endeavor 
has  been  to  condense  the  essential  facts  and  principles  consti- 
tuting the  theory'  of  the  steam-engine,  both  in  the  ideal  form 
usually  assumed  by  older  writers  and  in  the  actual  form  famil- 
iar to  the  practitioner,  and  also  to  give  the  more  important 
facts  and  methods  of  its  design,  construction,  maintenance, 
operation  and  trial.     The  first  part  contains  the  salient  points 
i    of  theory  and  an  account  of  the  gradual  development  of  the 
%}  engine  from  the  crude  forms  of  earlier  times  to  the  elegant 
t"*   and  efficient  types  familiar  to  the  engineer  of  to-day,  and  also 
a  description  of  the  general  structure  and  the  various  special 
v  forms  of  the  modern  engine.     The  second  volume  gives  the 
t  principles  of  general  design,  of  the  construction  of  the  details 
0  of  the  machine,  and  the  methods  of  operation  and  repair  found 
satisfactory  in  recent  practice. 

In  the  construction  of  this  work,  it  has  been  assumed  that 
the  reader  is  familiar  with  the  higher  mathematics  and  the 
principles  of  thermal  physics,  and  generally  well-read  in  those 
subjects  which  constitute  the  essential  scientific  basis  of  the 
professional  training  of  the  engineer.  This  assumption,  which, 
a  generation  ago,  would  have  been  unjustifiable,  is  to-day  per- 
fectly reasonable.  The  profession  of  engineering  has  become 
one  of  the  learned  professions  in  a  single  generation,  a  conse- 
quence of  the  rapid  development  of  the  system  of  technical 
education  now  forming  an  essential  and,  often,  the  most  exten- 
sive department  of  modern  education  in  all  civilized  countries. 
The  book  is  intended  especially  for  the  use  of  educated,  prac- 
tising engineers  and  of  students,  undergraduate  and  graduate, 


334    210995 


VI  PREFACE. 

in  those  technical  schools  which  are  sufficiently  extensive  in 
curriculum,  and  which  have  so  large  a  student  body  as  to  jus- 
tify specialization  and  the  offering  of  advanced  courses  of 
instruction  ;  institutions  which  include  graduate  schools  of  pro- 
fessional, specialized,  work ;  for  example,  in  the  mechanical 
engineering  of  railways,  of  naval  construction,  of  steam-engine 
building. 

In  the  introduction  of  the  reference  to  the  use  of  this  work 
in  technical  schools,  in  its  title,  it  is  not  assumed  that  many 
such  schools  can  find  time  or  place  for  such  a  treatise.  It  is 
considered  that  possibly  a  few  may  find  in  it  work  for  the  sen- 
ior year  of  their  undergraduate  course,  and  that  still  fewer 
among  existing  schools  may  find  the  two  volumes  and  appro- 
priate collateral  reading  suitable  work  for  a  year  in  graduate 
schools  of  steam-engineering.  It  is  only  in  the  highest  class  of 
such  undergraduate  schools  and  in  a  few  special  graduate 
schools  that  it  would  be  justifiable  to  attempt  such  an  ex- 
tended course  of  instruction  in  this  department.  It  is  in  part 
for  such  cases  in  Sibley  College  and  elsewhere  that  it  has  been 
prepared. 

Referring  to  the  general  plan  and  to  the  special  and  char- 
acteristic matter  of  the  work,  it  will  be  observed  that  it  differs 
greatly  from  other  treatises  on  the  subject,  and  that  an  at- 
tempt is  here  made  to  construct  a  theory  of  application  for  the 
real  engine.  In  earlier  works,  no  such  attempt  was  made. 
The  thermodynamic  theory,  that  of  the  ideal  engine,  was  long 
since  completed  ;  but  the  same  statement  could  not  be  made 
in  regard  to  the  real  engine.  It  has  seemed  to  the  Author 
that  the  subject  has  now  reached  such  a  stage,  in  its  develop- 
ment, though  still  by  no  means  complete  or  wholly  satisfac- 
tory, that  some  advance  might  be  made  toward  that  end  which 
only  would  be  accepted  by  the  practitioner  as  the  true  purpose 
of  applied  theory.  In  this  belief,  he  has  planned  and  worked 
out  this  scheme,  in  which  he  has  endeavored  to  embody  the 
most  recent  and  useful  results  of  the  later  researches  of  engi- 
neers and  physicists  looking  toward  this  reduction  of  the 
theory  of  the  steam-engine  to  a  practically  applicable  form. 


PREFACE.  Vll 

The  work  will,  ere  long,  undoubtedly,  seem,  in  view  of  further 
progress,  crude  and  unsatisfactory  ;  but  we  may  at  least  hope 
that  it  cannot  be  long  before  some  later  writer  will  achieve  full 
success. 

In  the  construction  of  the  theory  of  the  engine — ideal  and 
real — the  purely  thermodynamic  theory  is  first  given  form,  and  in 
this  the  general  methods  of  Rankine  and  Clausius,  substantially 
identical,  and,  after  a  generation,  entirely  unchanged  by  their 
successors,  are  adhered  to.  In  detail,  the  work  of  Clausius, 
and  his  methods,  are  mainly  followed  in  the  production  of  the 
principal  equations  of  thermodynamics ;  then,  in  application, 
the  course  taken  by  Rankine  is  adopted.  Rankine's  initial 
processes  are  too  obscure  for  the  first  part  of  the  work,  but 
those  of  application  are  admirably  simple  and  convenient. 
Clausius.  developing  his  equations  with  beautiful  precision, 
and  in  simple,  logical,  and  exact  mathematical  ways,  is  less 
satisfactory  when  we  come  to  deal  with  the  practical  problems 
of  the  engineer.  Combining  the  two,  we  obtain  what  has 
seemed  to  the  Author  a  much  more  satisfactory  system  than 
either,  as  originally  presented.  The  theory  of  the  Real 
Engine,  the  "  experimental  theory  "  as  Him  called  it,  is  neces- 
sarily still  incomplete  and  imperfect.  The  facts  and  laws  of 
internal  wastes  of  heat  in  the  engine  are  as  yet  too  imperfectly 
understood  to  permit  the  framing  of  an  exact  theory  of  this 
part  of  the  subject ;  but,  fortunately,  so  much  work  has  been 
done  that  we  are  now  come  to  a  point  which  permits  us  to  for- 
mulate a  provisional  theory,  and  to  adopt  processes  of  compu- 
tation sufficiently  accurate,  in  many  cases,  to  at  least  afford 
the  engineer  some  assistance  in  his  endeavor  to  anticipate 
what  may  be  hoped  for  in  the  performance  of  the  machine, 
the  design  of  which  he  may  have  taken  in  hand. 

The  treatise  of  Professor  Rankine,  now  ranked  among  the 
noblest  of  the  engineer's  classics,  was  published  in  1859.  The 
Author,  then  just  out  of  college  and  engaged  in  steam-engine 
design  as  a  special  line  of  professional  work,  in  the  old  firm  of 
Thurston,  Green  &  Co.,  probably  like  many  other  young  en- 
gineers, read  the  work  with  avidity,  anticipating  that  it  might 


Vlii  PREFACE. 

give  him  an  applied  theory  of  the  heat-engines,  and  a  guide  in 
their  design  and  proportioning.  But  the  results  of  thermo- 
dynamic  computation  were  in  such  evident  disaccord  with  the 
practice  of  the  time  that  he  threw  it  aside  as  disappointing  and 
misleading.  Later,  during  ten  years  and  more  of  service  in 
the  U.  S.  N.  Engineer  Corps,  a  considerable  part  of  the  time 
in  active  service  at  sea,  during  the  civil  war  and  later,  and  dur- 
ing a  half-dozen  years  of  duty  at  the  Naval  Academy,  detailed 
to  give  instruction  in  the  departments  of  physics,  chemistry,  and 
applied  mechanics,  the  works  of  Rankine,  of  Clausius,  and  of 
their  numerous  successors  and  imitators,  were  in  constant  use 
by  the  Author,  and  he  still  found  that  the  same  broad  gulf 
between  the  pure  and  the  applied  theory,  or  rather  the  same 
deficiency  of  an  applied  science  of  the  heat-engines,  rendered  it 
impossible  for  the  engineer  to  make  practical  use  of  works  on 
thermodynamics  in  his  work  of  constructing  engines  for  speci- 
fied conditions.  Practical  experience  was  the  only  guide — a  light 
only  from  the  past.  It  was  only  when  Professor  Cotteriil  made 
the  experimental  work  of  Clark,  of  Hirn,  of  Isherwood,  and  of 
Emery  a  basis  for  his  beautiful  treatise  on  "  The  Steam-engine 
considered  as  a  Heat-engine"  that  engineers  began  to  find  the 
thermodynamic  theory,  now  supplemented  by  something  ap- 
proximating a  satisfactory  study  of  losses  of  heat  and  of  work, 
really  useful  in  office-work. 

In  the  course  of,  now,  twenty-five  years  of  unintermitted 
employment  as  a  specialist  in  technical  college  work,  of  thirty 
years  of  practical  experience  and  work  in  the  design,  the  con- 
struction, the  management,  and  the  scientific  investigation  of 
the  principles  of  the  steam-engine,  the  Author  has  been  much 
interested  in  watching  the  gradual  closing  of  this  gap  between 
the  ideal  and  the  real  case,  and  the  slow  but  steady  growth  of 
a  philosophy  of  the  real  heat-engine  competent  to  at  least 
direct  and  aid,  if  not  to  form  an  exact  science  of  the  subject. 
In  this  development  of  an  applied  science,  the  honors  are  won 
by  the  engineers  who  have  undertaken — however  crudely, 
judged  by  the  refined  methods  o-f  modern  science — to  ascertain 
by  experimental  investigation  precisely  how  heat-energy  en- 


PREFACE.  IX 

tering  the  engine  is  distributed  by  transfer  and  transformation 
into  useful  and  useless  work,  and  to  what  extent  it  is  subject  to 
waste  as  heat.  The  mathematical  physicists  gave  us  the 
thermodynamic  theory ;  but  the  engineers  have  been  com- 
pelled to  supply  the  essential  complement,  in  order  that  we 
might  make  the  science  useful  in  engineering.  When  it  be- 
came possible  to  write  out  a  correct  balance-sheet  of  itemized 
receipts  and  expenditures,  it  was  possible  for  the  engineer 
to  make  the  science  of  the  steam-engine  the  basis  of  the  most 
refined  operations  of  his  art  in  the  design  and  construction  of 
the  engine  and  its  adjustment  to  its  purposes  with  maximum 
economical  result. 

The  long-established  thermodynamic  theory  of  the  heat- 
engines,  supplemented  by  what  is  rapidly  coming  to  be  a  well- 
understood  extra-thermodynamic  theory  of  wastes,  constitutes 
the  complete  theory  of  the  machine,  its  operation,  and  its 
efficiency. 

The  attention  of  scientific  men  and  engineers,  throughout 
the  world,  has  now*  become  so  earnestly  drawn  toward  this 
matter,  and  researches  are  so  generally  in  progress,  under  the 
direction  of  so  many  skilled  investigators,  that  it  cannot  be 
long  before  this  thermal  division  of  the  theory  of  the  engine 
will  be  as  well  developed  and  as  well  understood  as  is  now  the 
thermodynamic.  That  it  will  ever  be  possible  to  secure  as 
simple  expression  of  the  physical  laws  involved  can  perhaps 
hardly  be  hoped,  still  less  expected.  The  simple  expressions 
adopted  by  the  Author  seem  to  him  likely  to  prove  representa- 
tive of  a  class  which  will  always  supply  the  engineer  with  his 
working  equations.  As  far  as  accuracy  is  concerned,  the  best 
that  can  ever  be  said  of  them,  probably,  is  that  they  enable  us 
to  predict,  more  closely  than  the  pure  thermodynamic  theory, 
the  probable  performance  of  the  engine.  In  other  words,  they 
give  the  engineer  processes  of  application,  where,  formerly, 
theoryr  was  often  useless  and  sometimes  even  misleading. 
The  supplementing  of  the  pure  theory  of  the  ideal  engine  by 
the  physical  theory  of  the  real  engine  gives  us  a  theory  of 
application  that  enables  us  to  ascertain,  in  a  general  way,  the 


X  PREFACE. 

effects  of  variation  of  the  conditions  of  operation,  to  approxi- 
mately compute  the  demand  for  steam  and  fuel,  and  to  deter- 
mine the  most  economical  proportions  and  method  of  use  of 
the  machine,  as  affected  by  the  commercial  conditions  of  its 
environment.  It  is  only  now  that  the  true  problem  of  the 
engineer  in  this  field  can  be  solved,  the  problem  :  How  may  a 
given  quantity  of  mechanical  energy  and  power  be  obtained, 
by  transformation  from  its  potential  form  in  fuel  at  minimum 
total  cost  ?  The  fact  that  this  is  the  first  attempt  to  give  some 
consistency  and  unity  to  the  theory  of  the  real  engine  will  be 
possibly  accepted  as  a  justification  of  the  perhaps  somewhat 
over-liberal  introduction  of  illustrative  examples,  and  of  the 
occasional  repetition  of  statements  of  the  more  essential  facts 
and  principles. 

The  concluding  chapter  in  the  first  part  of*  the  work  repre- 
sents an  attempt  to  make  the  later  facts  and  recent  theory  of 
the  engine  a  basis  for  an  investigation  impossible  of  completion 
earlier.  The  beautiful  method  of  Rankine,  modified  by  the 
introduction  of  the  theory  of  the  thermal  wastes  of  the  real 
engine,  becomes  applicable  to  the  solution  of  a  great  variety 
of  problems  which  were,  formerly,  entirely  beyond  the  reach 
of  the  designer  or  of  the  operator  of  the  machine.  They  are 
problems,  nevertheless,  of  extreme  importance,  and,  in  fact, 
constitute  the  first  step  in  the  logical  series  of  processes  which 
lead  to  the  final  perfection  of  the  design  of  an  engine  precisely 
adapted  to  its  place  and  purpose,  mechanically  and  commer- 
cially. As  now  applicable  to  the  case  of  the  real  engine,  they 
permit  the  substitution  of  a  more  accurate  and  correct  method 
for  that  unscientific  "  guesswork  "  of  earlier  practice  which  is 
responsible  for  so  many  and  such  unfortunate  failures  of  the 
designing  engineer  in  the  adaptation  of  the  machine  to  its 
work.  The  Author  is  convinced  that  here,  as  in  the  further 
investigation  of  the  internal  wastes  of  the  engine,  the  highest 
talent  of  the  skilled  in  research  may  for  a  long  time  find 
profitable  employment  in  effecting  closer  approximations  and 
in  finding  better  and  more  exact  systems  of  development. 

The  now  familiar  distinction   between  the    ideal    and   the 


PREFACE.  XI 

real  engine  also  makes  it  easy  to  bring  into  strong  relief  the 
principles  controlling  the  reduction  of  the  wastes  which  con- 
stitute the  distinctive  feature  of  the  latter,  and  to  show  how 
the  various  familiar  expedients  for  narrowing  the  range  be- 
tween the  two  cases  operate.  The  theory  of  the  compound 
engine,  of  jacketing,  of  superheating,  can  to-day  be  readily 
constructed  and  the  influence  of  these  and  other  expedients 
looking  toward  the  same  end  may  be  clearly  seen.  It  thus 
becomes  now  possible  to  intelligently  employ  them  and  to 
judge  when  and  to  what  extent,  their  use  is  desirable  and  justi- 
fiable on  the  ground  of  ultimate  economy.  The  designer  is 
beginning  to  find  use  for  his  theory,  as  now  made  an  applied 
theory,  in  every  direction.  This  will  be  further  illustrated  in 
the  second  part  of  this  work  when  the  proportioning  of  the 
compound  engine  is  taken  in  hand.  The  general  principles 
are  exhibited  in  Chapter  VI  of  the  first  part ;  while  the  com- 
putation of  dimensions  comes  properly  into  the  second,  which 
includes  the  designing  of  parts  in  detail.  The  computations  of 
efficiencies  for  the  single  and  multiple-cylinder  engines,  intro- 
duced into  Chapter  VI  in  Part  I,  as  in  all  other  cases,  must  be 
taken  as  illustrative  only.  The  engineer  must,  in  every  case 
in  his  own  practice,  satisfy  himself  as  to  the  exact  conditions 
involved  and  determine  for  himself  the  precise  values  of  the 
quantities  to  be  employed  in  his  own  computations.  No  two 
cases  are  likely  to  involve  the  same  conditions  or  give  the  same 
figures. 

Part  II  deals  with  the  designing,  the  construction,  the 
operation  and  maintenance,  and  the  determination  of  the 
power  and  efficiency  of  the  engine.  The  principles  of  both 
parts  of  the  work  are  summarized  by  a  chapter  on  specifications 
and  contracts.  The  discussion  of  the  principles  of  regulation, 
of  governor-construction,  of  the  action  of  reciprocating  parts, 
of  the  designing  and  proportioning  of  valve-motions,  also  fall 
into  this  division  of  the  work. 

In  the  preparation  of  the  whole,  every  known  available  source 
of  information  has  been  resorted  to,  and.  in  many  instances,  in 
the  absence  of  such  records  of  fact,  the  Author  has,  as  in  the 


Xll  PREFACE. 

preparation  of  his  work  on  the  Materials  of  Engineering,  at  an 
earlier  date,  been  compelled  to  resort  to  experiment  and  to 
secure  by  direct  investigation  the  facts  considered  by  him 
essential  to  the  completion  of  his  task.  Fortunately,  the 
rapid  progress  of  technical  schools,  and  the  general  introduc- 
tion of  research  as  a  feature  of  their  higher  work,  are  making 
this  part  of  the  work  vastly  easier  and  more  satisfactory  by 
constantly  bringing  into  light  new  areas  of  the  previously 
unexplored  field.  It  has  been  the  intention  of  the  Author  to 
give  every  essential  reference  to  such  authorities  as  he  has  con- 
sulted ;  their  number  and  variety  may  give  some  idea  of  the 
magnitude  of  the  task  which  has  been  here  assumed,  and  justify, 
in  some  small  measure,  its  imperfections. 


A  MANUAL  OF  THE  STEAM-ENGINE. 


PLAN. 
PART   I.     STRUCTURE  AND  THEORY. 

CHAPTER  I.  HISTORY  OF  THE  STEAM-ENGINE. 
II.  STRUCTURE  OF  MODERN  ENGINES. 

III.  PHILOSOPHY  OF  THE  STEAM-ENGINE- 

IV.  THERMODYNAMICS  OF  GASES  AND  VAPORS. 
V.  THEORY  OF  THE  STEAM-ENGINE. 

VI.  COMPOUNDING  ;  JACKETING  ;  SUPERHEATING. 
VII.  EFFICIENCIES  OF  THE  STEAM-ENGINE. 
APPENDIX. 

PART   II.     DESIGN,  CONSTRUCTION,  OPERATION. 

CHAPTER  I.  DESIGN  OF  THE  STEAM-ENGINE. 
II.  VALVES  AND  VALTE-MOTIONS. 

III.  REGULATION;  GOVERNORS;  FLY-WHEELS;  INERTIA-EFFECTS. 

IV.  CONSTRUCTION  AND  ERECTION. 

V.  OPERATION  ;  CARE  AND  MANAGEMENT. 
VI.  ENGINE  AND  BOILER  TRIALS. 
VII.  SPECIFICATIONS  AND  CONTRACTS. 
VIIL  FINANCE;  COSTS  AND  ESTIMATES. 


CONTENTS. 


CHAPTER  I. 

THE   HISTORY   OF   THE   STEAM-ENGINE. 

ART.  PAGE 

1.  The  Purpose  of  the  Heat-engine i 

2.  General  Methods  of  Energy-transformation I 

3.  Heat  Engines  classified 2 

4.  Steam-engines  classified , 2 

5.  Origin  of  the  Steam-engine 3 

6.  Hero's  Engine 3 

7.  Early  Knowledge  of  Steam * 5 

S.  Steam  in  the  Middle  Ages 5 

9.  The  Marquis  of  Worcester's  Engine 5 

10.  Savery's  "Fire-engine" 8 

n.  Performance  of  Savery's  Engine n 

12.  Newcomen's  Engine 12 

13.  Its  Merits  and  Demerits 16 

14.  James  Watt iS 

15.  The  Newcomen  Model 19 

16.  Watt's  Single-acting  Engine 22 

17.  Watt's  Double-acting  Engine 23 

1 8.  Later  Pumping  Engines 2; 

19.  Early  Compound  Engines 27 

20.  The  Stationary  Engine 33 

21.  The  Locomotive  Engine.     Steam  Fire-engines 34 

22.  Early  Marine  Engines  45 

23.  Later  Marine  Engines 57 

24.  Recent  Use  of  Multiple-cylinder  Engines -  68 

25.  Process  of  Development  of  the  Steam-engine 73 

26.  The  Philosophical  Study  of  this  Development. 77 


XVI  CONTENTS 

CHAPTER    I 

THE   STRUCTURE    OF    THE    MODERN    STEAM-ENGINE. 
ART.  ''AGE 

27.  Structure  and  Uses  of  the  Steam-engine 82 

28.  Classification  of  Engines  into  Types ' .  .  82 

29.  Steam-engines  classed 83 

30.  The  Designer's  Aim ;  Principles  of  Design 85 

31.  General  Principles  of  Construction 86 

32.  Exigencies  of  Operation 36 

33.  The  Stationary  Engine;  Older  Forms 87 

34.  The  Mill  or  Factory  Engine;  Corliss  and  Greene  Engines;  Simple  and 

Compound  Forms 9; 

35.  High-speed  and  Low-speed  Engines;  Simple  and  Compound  Forms. ..  116 

36.  Single-acting  and  H igh-speed  Engines 1 50 

37.  Pumping-engines 163 

38.  Portable  Engines;  Agricultural  Engines 1 79 

39.  Road  Locomotives  and  Rollers 187 

40.  The  Locomotive-engines 193 

41.  Marine  Engines 211 

42.  Standard  Forms;  Compound  Screw-engine 217 

43.  Adaptation  of  Structure  to  increasing  Steam-pressure 229 

44.  Peculiar  Types  of  Steam-engine;  Experimental  Engines 231 

CHAPTER    III. 

THE   PHILOSOPHY   OF   THE   STEAM-ENGINE. 

45.  The  Scope  of  the  Philosophy  of  Heat-engines 2^3 

46.  Nature  of  the  Processes  studied „ . . .  243 

47.  Character,  Source,  and  Transformations  of  Energy 245 

48.  Chemical  Principles  involved 245 

49.  Physical  Principles  ;  Thermodynamics 246 

50.  Mechanical  Principles 247 

51.  Energetics  and  Thermodynamics 249 

52.  The  Ideal  and  the  Real  Engine  250 

53.  Nature  of  the  Scientific  Problem 251 

54.  Outline  of  the  Progress  of  this  Philosophy 251 

55.  Origin  and  Form  of  the  Mechanical  Theory  of  Heat 253 

56.  The  Science  of  Thermodynamics 256 

57.  General  Theory  of  Steam-engines 257 

58.  Carnot's  Work  ;  De  Pambour  ;  Tate 258 

59.  Clausius's  Labors 261 

60.  Rankine  and  his  Work  ;  Thomson 263 

61.  The  Thermodynamics  of  To-day 267 

62.  Limitations  of  Thermodynamic  Theory 267 


COA'TEJTTSi  xvil 

ART.  f-AGE 

63.  Watt's  and  Smeaton's  Discoveries ,..,, 268 

1 64.  The  Best  Ratio  of  Expansion 271 

65.  Cylinder-condensation ;  Clark's  Researches 271 

66.  Hirn's  Investigations;  Dwelsoauvers-Dery. . . .- 274 

67.  Isfaerwood's  Experiments;  Cotterill 275 

65.  Status  of  the  Theory  of  1850 277 

t-j.  The  Three  Periods  of  this  Philosophy 279 

70.  Work  still  to  be  done:  Outlook 221 

71.  Plan  of  Succeeding  Portion  of  this  Work 2=2 


CHAPTER   IV. 

THERMODYNAMICS  OF   THE  GASES   AND   VAPORS.      HEAT-UTILIZATION   BY 
TRANSFORMATION. 

72.  Thennodynamics  of  the  Steam-engine 290 

73.  Definition  of  Thennodynamics 291 

74.  Thermodynamics  as  a  Branch  of  Energetics 297 

7;.  Energetics  denned  and  discussed :  The  Fundamental  Law 298 

76.  Matter;  Force;  Work;  and  Energy 299 

77.  Law  of  Energetics 304 

78.  Newton's  Laws  and  Energetics 305 

79.  Algebraic  Expressions  in  Energetics 307 

50.  Thermodynamics  a  Restricted  Case  of  Energetics;  Thermodynamics 

deaned 309 

51.  Basis  and  Laws  of  Thermodynamics 310 

£2.  Expressions  of  the  First  Law;  The  Mechanical  Equivalent  of  Heat. ..  312 

53.  The  First  Law  and  the  Heat-engines 315 

24.  The  Second  Law  of  Thermodynamics 315 

85.  The  Steam-engine  and  the  Second  Law 319 

56.  The  General  Fundamental  Thennodynamic  Equations 319 

87.  The  Relations  of  the  two  Laws 321 

55.  Thermodynamics  and  the  Constitution  of  Matter 322 

89.  Solids;  Liquids;  Gases;  Fusing  and  Boiling  Points;  The  Kinetic  Theory.  322 

90.  External  and  Internal  Work 327 

91.  Heat  and  Temperature;  Absolute  Scale 328 

92.  Quantities  of  Heat;  Calorimetry 333 

93.  Specific,  Latent,  and  Total  Heats:  Computation  of  Latent  and  Total 

Heat  of  Steam 336 

94.  The  Critical  Physical  Conditions  and  Temperature 350 

95.  The  Perfect  Gas;  Definition;  Equation 354 

96.  Thermodynamics  of  the  Perfect  Gas 355 

97.  Thermodynamics  of  Work  and  Energy 36$ 

98.  Thermodynamics  of  Imperfect  Gases  and  of  Vapors 373 

99.  Thermodynamics  of  Steam  ;  Factors  of  Evaporation  :  Tables 376 


CONTENTS. 


100.  Regnault's  Work;  Stored  Energy  in  Steam;  Steam  Power 383 

101.  General  Thermodynamic  Equation  for  Steam;  Thermodynamic  Func- 

tion.  - 389 

102.  Expansion  ;  Thermal  Lines  for  Steam  and  Vapors 594 

103.  Construction  of  the  Thermal  Lines 400 

104.  Cyclical  Thermodynamic  Operations 410 


CHAPTER  V. 

THERMODYNAMICS   OF  THE   STEAM-ENGINE.      WASTES  OF    ENERGY  ;    EFFICIENCY. 

105.  Thermodynamics  of  the  Steam-engine 421 

106.  The  Steam-engine  as  a  Heat-engine , . .  j .  422 

107.  The  Real  distinguished  from  the  Ideal  Engine 423 

loS.  The  Wastes  of  the  Steam-engine 426 

109.  The  Thermodynamic  Wastes 427 

no.  The  Physical  or  Thermal  Wastes 429 

in.  The  Mechanical  or  Dynamic  Wastes;  Back-pressure  and  Clearance..  430 

112.  The  Ideal  Cases  ;  Heat  transformed  ;  Adiabatic  Condensation 431 

113.  Special  Cases  ;  Use  of  Saturated  Steam  ;  Jacketed  Engines 444 

114.  Efficiency  of  Cyclical  Operations 447 

115.  Conditions  of  Maximum  Efficiency. . .    449 

116.  Theory  of  Efficiency  of  Ideal  Engines 450 

117.  Computations  of  Ideal  Engine  Efficiencies.     Examples  of  Application  454 

118.  Limit  of  Actual  Engine  Efficiency ..  466 

119.  Real  Engines  and  their  Cycles 467 

120.  Distribution  of  Energy  in  Real  Steam-engines 467 

121.  Method  of  Operation  ;  Limits  of  Temperature 470 

122.  Methods  of  Waste  in  Actual  Engines 471 

123.  Magnitudes  and  Distribution  of  Losses  ;   Back-pressure 476 

124.  The  Unavoidable  Thermodynamic  Waste  in  Actual  Cases 482 

125.  Conditions  of  Maximum  Efficiency  of  Fluids 483 

126.  Heat-wastes  by  Conduction  and  Radiation 483 

1 27.  Methods  of  Reduction  of  such  Losses 487 

128.  Steam-consumption;  Magnitude  of  Cylinder-condensation 488 

129.  Laws  governing  Loss  by  Internal  Condensation   499 

130.  Theory  of  Internal  Condensation  and  Waste ..  517 

131.  Restriction  of  Cylinder-condensation  ;  Superheating;  Steam-jackets; 

Highspeed 534 

132.  Friction  of  Engine  and  Efficiency  of  the  Machine 540 

133.  Investigation  of  Internal  Engine  Friction 558 

134.  Variation  and  Distribution  of  Internal  Friction 565 

135.  Conditions  of  Real  Maximum  Efficiency  of  Machine 570 

136.  Conditions  of  Maximum  Total  Efficiency  of  the  Steam 571 


157.  Actual  Efficiencies  and  Economy  of  p 


CHAPTER  VL 

MO.TIPLI-CTIIXDE*  OK    COTtPOCXD   EXGIXES;    KEDCOXG     WASTES;  JACKETS; 
SOHXHEATRG. 

133.  Geneial  Theory  of  Multiple-cylinder  Engines.  ................  .....  554 

139.  The  Wastes  of  toe  Compound  Engine  ......   .....................   ii 

140.  The  Amelioration  of  Wastes  :  Jacketing;  Superheating.  .............  590 

141.  The  Problems  of  Compounding  .................................  ..  59? 

142.  The  Three  Fundamental  Principles.  .......  ~  .......................  593 

143.  The  First  Step  in  Compounding  .........................  .  ........  59& 

144.  Extent  of  Economical  Expansion...  .......  ...  ....................  597 

145-  Influence  of  SBperfcearing;  Jacketing;  Engine-speed.  ...............  593 

146.  The  Number  of  Cylinders  in  Series.  ..............................  602 

147,  Influence  of  Size  of  Engine  ......................................  604 

140.  Solutions  of  Problems  relating  to  Performance-  .......  .  ............  604 

149.  Examples  of  Computations  of  Efficiency  ...........................  611 

150.  General  Results  of  Experiment.  ...................................  614 

151.  Balance  of  Forces.     Efficiency  of    Mechanism   and  Distribution  of 

T>,      ,  ,  ..,-,---  JL-fc.* 

FiCSSHTCS.  .  ....-.-~  -  .  .  -  -  -  ......................................    D2O 

152.  Steam  jackets  on  Simple  and  Multiple-cylinder  Engines  ............  622 

153.  Action  of  the  Jacket  in  Detafl.  ....................................  627 

154.  Jacket-wastes  K.  Cylinder-wastes  .................................  632 

155.  Computation  of  Efficiency  and  Jacket-waste  ........................  636 

156.  Limitations  of  Jacket-action:  its  Maximum  Efficiency  ...............  643 

157.  Jackets  on  Multiple-cylinder  Engines.  .............................  654 

I5S.  Jacketing  and  Superheating.  ......................................  6§* 

159.  Jackets  on  "  Highspeed  Engines.".  ...................  _".  .......  656 

160.  Temperatures  and  Pressures  in  Jackets  ...........................  658 

161.  Quality  of  Steam  :  Condition  of  Surfaces.  .........................  659 

162.  Jacketing  the  Heads  and  Piston  .................................  66  1 

163.  Proportions  of  Engine  with  Jackets.  .............................  66  1 

164.  Defective  Jacketing  ;  A!r  in  Jackets  ...........     .................  663 

16=.  Experience  with  Jackets;  Experimental  Results  ....................  664 

166.  Conclusions  relative  to  Jacketing:  Engine-efficiency  and  the  Jacket; 

Testimony  ...........................  .  .......................  66i 

167.  Superheated  Steam  as  a  Working  Fluid,  ...........................  671 

i63.  The  Steam-engine  and  Superheated  Steam  .........................  671 

169.  Limit  in  Superheating.  Outlook  ...................................  675 

170.  Experience  and  Testimony.     Conclusions  relative  to  Superheating...  6So 

171.  Compression  and  Clearances:  Back-pressure  .....................  683 

172.  The  Binary-vapor  System  ........................................  697 


xx  CONTENTS. 

CHAPTER  VII. 

THE  EFFICIENCIES   OF   THE    STEAM-ENGINE. 

ART.  PAGE 

173.  Mathematical  Treatment  of  Engine-efficiencies 705 

1 74.  The  Several  Efficiencies  of  the  Engine 705 

175.  Thermodynamic  Efficiency 709 

176.  Thermodynamic  Demand  for  Heat,  Steam,  Fuel 709 

177.  Actual  Efficiency  of  Working  Substance 712 

178.  Estimates  of  Heat,  Steam,  Fuel 713 

179.  Efficiency  of  the  Machine  and  the  Engine 714 

180.  Actual  Thermal  Lines  and  "  Curves  of  Efficiency" 71$ 

181.  Ratios  of  Expansion  at  Maximum  Efficiencies 725 

182.  Size  of  Engines;  Efficiency  of  Capital 741 

183.  Efficiencies  of  the  Ideal  Engine 746 

184.  Rankine's  Diagram  of  Ideal  Efficiency 749 

185.  Theory  of  Efficiencies  for  Real  Engines 752 

186.  Curves  of  Efficiency  for  Real  Engines 756 

187.  Thurston's  Curves  of  Real  Efficiency   757 

1 88.  Solution  of  Practical  Problems. ...    "59 

189.  Construction  of  Efficiency.      Diagram  from  Actual  Cases 762 

190.  Method  of  Use  of  Diagrams  of  Efficiency 765 

191 .  Estimation  of  Costs 766 

192.  Statement  of  Results 768 

193.  Relation  of  Costs  and  Profits 772 

194.  Profits  at  a  fixed  Expansion 774 

195.  Cost  of  Engine  as  affecting  the  Best  Ratio  of  Expansion 775 

196.  Back  Pressure  as  modifying  Economy 776 

197.  Deductions  from  the  Investigation  of  Costs 77° 

198.  Variation  of  Cylinder-condensation 783 

199.  Efficiency  Problems  solved  by  Inspection 784 

200.  Conclusions  relative  to  Maximum  Efficiencies 785 

201.  Absolute  Limits  to  Expansion 786 


MANUAL  OF  THE  STEAM-ENGINE. 


PART   I. 


CHAPTER   I. 
THE  DEVELOPMENT  OF  THE  STEAM-ENGINE. 

1.  The  Purpose   of  any  Heat-engine  is  the  useful  and 
economical  transformation,  in  the  largest  possible  degree,  of 
the  heat-energy  derived  from  combustion,  or  other  source,  and 
temporarily  stored,  in  greater  or  less  quantity,  in  a  fluid  capa- 
ble of  variation  of  pressure  and  volume  with  changes  of  heat 
and  of  temperature  and  pressure.     In  all  familiar  forms  this 
heat  is  derived  from  the  combustion  of  coal,  or  of  some  prod- 
uct of  fuel-distillation,  natural  or  artificial,  and   is  transferred 
from  the  products  of  combustion  to  the  working  fluid,  which 
may  be  gas,  air,  steam,  or  other  vapor ;  or  it  may  be  that  the 
storage  medium  and  the  vehicle  of  transfer,  the  working  fluid, 
is  the  mixture  composing  those  products  of  combustion  them- 
selves. 

2.  The  General  Methods  of  Energy -transformation  are 
the  same  for  any  working  substance.     It  is  caused  to  undergo 
such  changes  of  pressure,  volume,  and  temperature  as  will  effect 
the  conversion  of  a  portion  of   the   stored   heat-energy  into 
mechanical  energy,  usually  by  driving  a  piston,  but  very  rarely 
by  the  reaction  of  a  jet  passing  out  from  under  high  pressure 
and  at  very  high  velocity.     During  these  changes  the  fluid 
drives  the  piston  forward   by  its  expansion  at  comparatively 
high  temperature  and  pressure,  and  is,  later,  compressed  by  the 


2  A  MANUAL    OF   THE   STEAM-ENGINE. 

piston  on  its  return-stroke  at  a  lower  temperature  and  pressure; 
the  net  work  done  being  thus  a  positive  quantity  and  measured 
by  the  difference  in  the  amount  of  work  done,  positively  and 
negatively,  in  the  complete  revolution  of  the  crank  of  the 
engine  and  a  double-stroke  of  the  piston. 

3.  Heat-engines   are    classified  variously:    as  according 
to  the  physical  state  of  the*ir  working  fluids  ;  according  to  the 
specific  fluid  used  ;  or  according  to  the  method  of  their  opera- 
tion of  that  fluid.     Thus  we  have  gas-engines,  vapor-engines, 
binary-vapor  engines ;  or,  we  have  steam-engines,  ammonia  or 
carbon-disulphide  engines  ;  petroleum-vapor  engines;  illuminat- 
ing-gas engines;  or,  engines  employing  working  fluids  of  con- 
stant or  variable  weight.     All  are,  however,  subject  to  the  same 
general  principles  of  heat-transformation  and,  ordinarily,  to  the 
same  methods  of  thermal  or  thermo-dynamic,  or  of  dynamic, 
waste. 

In  all  cases  their  operation  involves  the  thermo-dynamic 
science  of  the  purely  ideal  engine,  combined  with  the  physical 
science  of  heat  as  applied  to  the  phenomena  of  real  engines. 
The  steam-engine  represents  simply  a  single  case  among 
numerous  heat-engines  and  motors ;  and  its  problem  is  merely 
a  single  application  of  principles  involved  in  the  philosophy 
of  all. 

4.  The  Definition  of  a  Steam-engine  maybe  enunciated 
thus: 

The  steam-engine  is  a  machine  designed  and  constructed 
especially  for  the  purpose  of  converting  the  heat-energy 
stored  in  the  vapor  of  water,  in  as  large  proportion  as  may  be 
practicable,  into  dynamical,  or  mechanical,  energy,  and  to 
apply  that  energy  as  directly  and  effectively  as  possible  to  the 
performance  of  useful  work. 

It  may  consist  of  a  single  element,  or  vessel,  as  in  the  oldest 
form  of  steam-engine — to  be  presently  described  ;  or  it  may,  as 
in  modern  forms  of  engine,  consist  of  a  train  of  mechanism  of 
considerable  complexity.  It  may  actuate  a  reciprocating  sys- 
tem, as  in  pumping-engines  of  several  forms ;  or  it  may  turn  a 
shaft ;  it  may  even  impel  a  projectile,  as  in  Perkins'  steam- 


THE  DEVELOPMENT  OF   THE   STEAM-ENGINE.  3 

gun ;  but,  in  all  cases  and  in  all  forms,  it  is  a  thermo-dynamic 
machine,  subject  to  thermo-dynamic  and  thermal  losses  and  to 
wastes  of  dynamical  energy. 

5.  The  Origin  and   Growth  of  the   Steam-engine  are 
historically  notable  for  great   antiquity  and   long  and,  until 
within  a  century,  slow  progress.     Precisely  when  the  power  of 
steam  began  to  attract  the  attention  of  mankind  is  quite  un- 
known ;  but  it  was  certainly  before  history  had  begun  to  record 
any  other  than  political  events  and  before  any  industrial  devel- 
opments, any  inventions,  any  useful  art  had  become  a  matter 
of  notice  among  historians.     The  people  of  some  early  pre- 
historic time  deified  their  great  mechanics  and  inventors,  as 
they  did  their  great  warriors  ;  but  at  the  beginning  of  historic 
times  this  appreciation  of  those  classes  had  largely  ceased. 

The  first  period  of  invention  of  the  steam-engine  was  one  of 
purely  speculative  knowledge,  and  it  was  known,  at  some  time 
before  the  Christian  era,  as  simply  a  toy,  and  the  force  of  steam 
was  only  thought  of  as  possibly  applicable  to  the  purposes  of 
the  priestly  prestidigitators  of  that  time.  This  period  of  specula- 
tion continued  until  the  middle  of  the  seventeenth  century, 
when  the  Marquis  of  Worcester  and  his  contemporaries  and 
predecessors  sought  to  make  useful  application  of  the  latent 
powers  of  steam.  A  second  period  of  application  was  thus 
inaugurated  which*  continued  up  to  the  end  of  the  first  quarter 
of  the  nineteenth  century ;  when,  the  inventions  of  Watt  and 
others  having  revealed  the  value,  the  power,  and  the  wide 
adaptability  of  the  machine,  in  all  its  principal  forms,  a  third 
period  of  refinement  and  of  improvement  in  all  details  and  all 
applications  brought  the  engine  into  substantially  its  existing 
form.* 

6.  Hero's  Engine  is  described  by  Hero  the  Younger  of 
Alexandria  and  dated  about  120  B.C.,  and  here  we  find  the 
first  record  of  the  early  history  of  the  steam-engine. 

In  the  home  of  Euclid,  the  great  geometrician,  and  possibly 
contemporary  with  that  talented  engineer  and  mathematician 

*  History  of  the  Steam-engine  ;  R.  H.  Thoiston.     New  York  : 
ton  «  Co.    International  Series. 


4  A  MANUAL    OF    THE   STEAM-ENGINE. 

Archimedes,  Hero  produced  a  manuscript  which  he  entitled 
"Spiritalia  seu  Pneumatica."  The  work  is  still  extant,  and 
has  been  several  times  republished.  In  it  are  described  a 
number  of  interesting  though  primitive  forms  of  water  and 
heat  engines,  and,  among  the  latter,  that  shown  in  Fig.  I,*  an 
apparatus  moved  by  the  force  of  steam. 

This  earliest  of  steam-engines  consisted  of  a  globe  sus- 
pended between  trunnions,  through  one  of  which  steam  enters 
through  pipes  from  the  boiler  below.  The  hollow  bent  arms 
cause  the  vapor  to  issue  in  such  a  direction  that  the  reaction 
produces  a  rotary  movement  of  the  globe,  just  as  the  rotation 
of  reaction  water-wheels  is  produced  by  outflowing  water. 

It  is  quite  uncertain  whether  this  machine  was  ever  more 
than  a  toy,  although  it  has  been  supposed  by  some  authorities 
that  it  was  actually  used  by  the  Greek  priests  for  the  purpose 
of  producing  motion  of  other  apparatus  in  their  temples. 

It  seems  sufficiently  remark- 
able that,  while  the  power  of 
steam  had  been,  during  all  the 
many  centuries  that  man  has 
existed  upon  the  globe,  so 
universally  displayed  in  so  many 
of  the  phenomena  of  natural 
change,  mankind  lived  almost  up 
to  the  Christian  era  without  mak- 
ing it  useful  in  giving  motion 
even  to  a  toy  ;  but  it  must  excite 
still  greater  surprise  that,  from 
the  time  of  Hero,  we  meet  with 
no  good  evidence  of  its  applica- 
tion to  any  practical  use  for 
many  hundreds  of  years.  Here 
FIG.  i.— HERO'S  ENGINE,  B.C.  200.  and  there,  in  the  pages  of  history 
and  in  special  treatises,  we  find  a  hint  that  the  knowledge  of 
the  force  of  steam  is  not  forgotten  ;  but  biographers  and  his- 

*  Vide  Woodcroft's  "  Translation  of  Hero."     The  cut  is  from  Thurston's  His- 
tory of  the  Steam-engine 


THE  DEVELOPMENT  OF   THE   STEAM-ENGINE.  5 

torians  have  devoted  little  time  to  the  task  of  seeking  and 
recording  information  relating  to  the  progress  of  this  and  other 
important  inventions  and  improvements  in  the  mechanic 
arts. 

7.  Early  Knowledge  of  Steam  and  of  its  power  was  con- 
fined to  the  understanding  that  the  vapor  of  water  was  capable 
of  exerting  some  force  in  its  exit  from  closed  vessels,  and  that 
it  might  be  given  application  to  a  few  simple  and  unimportant 
operations.     Hero  shows  a  variety  of  such  applications,  some 
of  them  very  ingenious  but  all  of  no  importance.     For  example, 
he  sketches  and  describes  methods  of  applying  the  expansive 
force  of  steam  to  the  opening  and  closing  of  temple  doors,  to 
the   working   of   various    automata,   and   to   the    production 
of  sounds.      Nothing   indicates   that   any  ancient   writer  or 
mechanic  had  the  slightest  idea  or  expectation  of  the  future 
use  of  this,  to  them,  concealed  power  in  the  operations  of  the 
arts. 

8.  Steam-power  in  the  Middle  Ages  was  but  little  better 
understood  and  appreciated  than  in  earlier  times.  "  /Eolipiles," 
such  as  Hero's  machine  for  use  as  a  turnspit,  and  the  various 
forms  of  apparatus  in  which  steam  was  produced  and  from 
which  it  was  allowed  to  issue  in  a  jet  for  the  purpose  of  "  blow- 
ing the  fire,"  seem  to  have  been  the  earliest  and  latest  produc- 
tions of  this  period ;  although    predictions    of   a  later  applica- 
tion  to   important   purposes   were   sometimes   made    by   the 
speculative   philosophers   and    inventors    of    those    centuries 
succeeding  the  tenth  and  up  to  about  the  beginning  of  the 
seventeenth.     At  this  latter  date  a  number  of  crude  schemes 
and  rude  forms  of  apparatus,  as  those  of  Porta  (1601),  of  Da 
Caus  (1615),  and  of  Branca  (1629),  were  suggested  by  various 
ingenious  philosophers  and  writers ;  but  none  seems  to  have 
been  actually  constructed  and  used,  even  experimentally,  until 
later. 

9.  The  Marquis  of  Worcester,  and   Papin   the   distin- 
guished   contemporary  physicist    and  philosopher,  were    the 
first  of  these  schemers  who  seem  to  have  actually  constructed 
their  apparatus. 


O  A  MANUAL   OF   THE    STEAM-ENGINE. 

In  1663  Edward  Somerset,  second  Marquis  of  Worcester, 
published  a  curious  collection  of  descriptions  of  his  inventions, 
couched  in-  obscure  and  singular  language,  and  called  a  "  Cen- 
tury of  the  Names  and  Scantlings  of  Inventions  by  me  already 
practised."  One  of  these  inventions  is  an  apparatus  for  raising 
water  by  steam.  The  description  was  not  accompanied  by  a 
drawing,  but  the  sketch  here  given  probably  resembles  his 
contrivance  very  closely.  Steam  is  generated  in  the  boiler  D, 
and  thence  is  led  into  the  vessel  A,  already  nearly  filled  with 
water.  It  drives  the  water  in  a  jet  out  through  a  pipe,  F  or  F ' . 
The  vessel  A  is  then  shut  off  from  the  boiler  and  again  filled 
"  by  suction,"  after  the  steam  has  condensed, 
through  the  pipe  G,  and  the  operation  is  repeated, 
the  vessel  B  being  used  alternately  with  A. 

This  apparatus  was  used  for  the  purpose  of 
elevating  water  for  practical  purposes  at  Vaux- 
hall,  near  London.  It  was  still  earlier  used  at 
the  home  of  Worcester,  Raglan  Castle,  where 
the  openings  cut  in  the  wall  for  its  reception  are 
still  to  be  seen.  The  separate  boiler,  as  here 
used,  constitutes  a  very  important  improvement 
upon  the  preceding  forms  of  apparatus,  although 

ENG.NE,  A.D.  1650.      thg  jdea   was  orjginal  wjth   Porta. 

The  "  water-commanding  engine,"  as  its  inventor  called  it, 
was,  therefore,  the  first  instance  in  the  history  of  the  steam- 
engine  in  which  the  inventor  is  known  to  have  "  reduced  his 
invention  to  practice." 

It  is  evident,  however,  that  the  invention,  important  as  it 
was,  does  not  entitle  the  marquis  to  the  honor  claimed  for  him 
by  many  authorities  of  being  the  inventor  of  the  steam-engine. 
Somerset  was  simply  one  of  those  whose  works  collectively 
make  the  steam-engine. 

The  invention  of  the  Marquis  of  Worcester  was  revived 
twenty  years  later  by  Sir  Samuel  Morland,  but  in  what  form  is 
not  now  known.  In  a  memoir  which  he  wrote  upon  the  sub- 
ject in  1683,  he  exhibited  a  degree  of  familiarity  with  the 
properties  of  steam  that  could  hardly  have  been  expected  of 


THE  DEVELOPMENT  OF  THE  STEAM-ENGINE,  7 

any  one  at  that  early  date.  In  his  manuscript,  now  preserved 
in  the  Haarlem  Collection  of  the  British  Museum,  he  states 
the  size  of  the  cylinders  required  in  his  machine  to  raise  given 
quantities  of  water  per  hour,  and  gives  very  exactly  the  relative 
volumes  of  equal  weights  of  water  and  of  steam  under  atmos- 
pheric pressure.  He  tells  us  that  one  of  his  engines,  with  a 
cylinder  six  feet  in  diameter  and  twelve  feet  long,  was  capable 
of  raising  3240  pounds  of  water  through  a  height  of  six  inches, 
1800  times  an  hour. 

From  this  time  forward  the  minds  of  many  mechanicians 
were  earnestly  at  work  on  this  problem — the  raising  of  water 
by  aid  of  steam.  Hitherto,  although  many  ingenious  toys, 
embodying  the  principles  of  the  steam-engine  separately,  and 
sometimes,  to  a  certain  extent,  collectively,  had  been  proposed 
and  even  occasionally  constructed,  the  world  was  only  just 
ready  to  profit  by  the  labors  of  inventors  in  this  direction. 
But,  at  the  end  of  the  seventeenth  century,  English  miners 
were  beginning  to  find  the  greatest  difficulty  in  clearing  their 
shafts  of  the  vast  quantities  of  water  which  they  were  meeting 
at  the  considerable  depths  to  which  they  had  penetrated,  and 
it  had  become  a  matter  of  vital  importance  to  them  to  find  a 
more  powerful  aid  in  that  work  than  was  then  available.  They 
were,  therefore,  by  their  necessities,  stimulated  to  watch  for, 
and  to  be  prepared  promptly  to  take  advantage  of,  such  an 
invention  when  it  should  be  offered  them.  The  experiments 
of  Papin,  and  the  practical  application  of  known  principles  by 
Savery,  placed  the  needed  apparatus  in  their  hands. 

When  Louis  XIV.  revoked  the  Edict  of  Nantes,  the  persecu- 
tions at  once  commenced  drove  from  the  kingdom  some  of  its 
greatest  men.  Among  these  was  Denys  Papin,  a  native  of 
Blois  and  a  distinguished  philosopher.  He  studied  medicine 
at  Paris,  and,  when  expatriated,  went  to  England,  where  he 
met  the  celebrated  philosopher  Boyle,  who  introduced  him  into 
the  Ro)^  Society,  of  which  Papin  became  a  member  and  to 
whose  "  Transactions  "  he  contributed  several  valuable  papers. 
He  invented,  in  1680,  the  "  Digester,"  in  which  substances, 
unaffected  by  water  boiling  under  atmospheric  pressure,  can  be 


8  A  MANUAL    OF   THE   STEAM-ENGINE. 

subjected  to  the  action  of  water  boiling  under  high  pressure, 
and  thus  thoroughly  "  digested  "  or  cooked.  The  danger  of 
bursting  these  vessels  caused  him,  in  1681,  to  invent  and  apply 
the  lever  safety-valve*  now  an  indispensable  appurtenance  to 
every  steam-boiler. 

In  1690  he  constructed  a  working  model  of  an  engine,  con- 
sisting of  a  steam-cylinder  with  a  piston  which  was  raised  by 
steam  pressure,  and  which  descended  again  when  the  conden- 
sation of  the  steam  produced  a  vacuum  beneath  it.  This  appa- 
ratus the  inventor  proposed  to  use  as  a  motor  for  working 
pumps  and  for  driving  paddle-wheels  ;  but  he  never  built  a 
successful  working  machine  on  this  plan,  so  far  as  we  can 
ascertain.f 

Papin,  in  1707,  proposed  to  avoid  the  loss  due  to  conden- 
sation of  steam  in  the  vessel  to  some  extent  at  least  by  the  use 
of  his  piston,  which  he  interposed  between  the  steam  and  the 
water.  +  This  engine  is  in  principle  a  Marquis  of  Worcester  en- 
gine, in  which  the  piston  is  introduced  to  separate  the  steam 
from  the  water  which  it  impels,  and  thus  to  reduce  the  amount 
of  loss  by  condensation.  This  engine  was  never  constructed 
except  experimentally,  however,  and  is  principally  of  interest 
in  a  history  of  the  steam-engine  from  the  fact  that  it  was  a  use- 
ful suggestion  to  succeeding  inventors. 

10.  Savery's  "Fire-engine"  was  the  first  among  all  the 
earlier  devices  which  came  into  actual  use  in  the  application  of 
the  energy  stored  in  steam  to  the  purposes  of  industry. 

The  constant  and  embarrassing  expense  and  the  engineer- 
ing difficulties  presented  by  the  necessity  of  keeping  the  British 
mines,  and  particularly  the  deep  pits  of  Cornwall,  free  from 
water,  and  the  failure  of  every  attempt  previously  made  to 
provide  effective  and  economical  pumping  machinery,  were 

*  Other  forms  of  safety-valve  had  been  previously  used. 

f  "  Recueil  des  diverses  Pieces  touchant  quelques  nouvelles  Machines  et 
autres  Sujets  philosophiques,"  M.  D.  Papin,  Cassel,  1695. 

J  "  Nouvelle  Maniere  de  lever  d'Eau  par  la  Force  de  Feu,  mise  en  Lumi- 
fere."  Par  M.  D.  Papin,  Docteur  en  Medecme,  Professeur  en  Mathematique  a 
Cassel,  1707. 


THE  DEVELOPMENT  OF   THE  STEAM-£NGINE.  9 

noted  by  Savery,  who,  July  25,  1698,  patented  the  design  of  the 
first  engine  which  ever  was  actually  employed  in  this  work. 

A  working  model  was  submitted  to  the  Royal  Society  of 
London  in  1699,*  and  successful  experiments  were  made  with 
it.  This  engine  is  shown  in  Fig.  3,  as  described  by  Savery  him- 
self in  1702  in  the  "  Miners'  Friend."  L  L  is  the  boiler,  in 
which  steam  is  raised,  and  through  the  pipes  O  Oit  is  alternately 
let  into  the  vessels  P  P. 

Suppose  it  to  pass  into  the  left-hand  vessel  first.  The  valve 
J/  being  closed  and  r  being  opened,  the  water  contained  in  P 
is  driven  out  and  up  the  pipe  5  to  the  desired  height,  where  it 
is  discharged.  The  valve  r  is  then  closed,  and  ?lso  the  valve 
in  the  pipe  O.  The  valve  J/  is  next  opened,  and  condensing 
water  is  turned  upon  the  exterior  of  P  by  the  cock  K,  leading 
water  from  the  cistern  X.  As  the  steam  contained  in  P  is  con- 
densed, forming  a  vacuum,  a  fresh  charge  of  water  is  driven  by 
atmospheric  pressure  up  the  pipe  T.  Meantime,  steam  from 
the  boiler  has  been  let  into  the  right-hand  vessel/*, the  cock  W 
having  been  first  closed  and  R  opened.  The  charge  of  water  is 
driven  out  through  the  lower  pipe  and  the  cock  R,  and  up  the 
pipe  5  as  before,  while  the  other  vessel  is  refilling  preparatory 
to  acting  in  its  turn.  The  two  vessels  thus  are  alternately 
charged  and  discharged  as  long  as  is  necessary.  Savery 's 
method  of  supplying  his  boiler  with  water  was  at  once  simple 
and  ingenious. 

The  small  boiler  D  is  filled  with  water  from  any  convenient 
source,  as  from  the  stand-pipe  5.  A  fire  is  then  built  under  it, 
and  when  the  pressure  of  steam  in  D  becomes  greater  than  in 
the  main  boiler  Z,  a  communication  is  opened  between  their 
lower  ends  and  the  water  passes  under  pressure  from  the 
smaller  to  the  larger  boiler,  which  is  thus  "  fed "  without 
interrupting  the  work.  G  and  A^  are  gauge-cocks  by  which 
the  height  of  water  in  the  boilers  is  determined,  and  these 
attachments  were  first  adopted  by  Savery. 

Here    we  find,  therefore,   the   first    really  practicable  and 

*  "Transactions  of  the  Royal  Society,"  1699. 


10 


A  MANUAL    OF   THE   STEAM-ENGINE. 


FIG.  3. — SAVERY'S  ENGINE,  A.D.  1699. 


commercially  valuable  steam-engine.  Thomas  Savery  is 
entitled  to  the  credit  of  having 
been  the  first  to  introduce  into  gen- 
eral use  a  machine  in  which  the 
power  of  heat,  acting  through  the 
medium  of  steam,  was  rendered  use- 
ful. It  will  be  noticed  that  Savery, 
like  the  Marquis  of  Worcester  and 
like  Porta,  used  a  boiler  separate 
from  the  water-reservoir.  He  added 
to  the  "  water-commanding  engine" 
of  the  Marquis  the  system  of  surface- 
condensation,  by  which  he  was  en- 
abled to  change  his  vessels  when  it 
became  necessary  to  refill  them  ;  and 
the  secondary  boiler,  which  enabled 
him  to  supply  the  working  boiler  with  water  without 
interrupting  its  action.  The  machine  was  capable  of  work- 
ing uninterruptedly  for  a  period  of  time  only  limited  by 
its  own  endurance.  Savery  never  fitted  his  boilers  with  the 
safety-valve,  although  it  was  subsequently  used  on  Savery 
engines  by  Desaguliers ;  and  in  deep  mines  he  was  com- 
pelled to  make  use  of  higher  pressures  than  his  rudely-con- 
structed boilers  could  safely  bear.  The  introduction  of  his 
machines  was  therefore  greatly  retarded  by  the  fear,  among 
miners,  of  the  explosion  of  his  boilers.  In  fact,  such  explosion 
did  occur  on  more  than  one  occasion. 

The  Savery  engine  was  improved,  about  1716  or  1718,  by  Dr. 
Desaguliers,  who  attached  to  it  Papin's  safety-valve,  and  substi- 
tuted a  jet-injection  from  the  stand-pipe  into  the  "  forcing- 
vessels "  for  the  surface-condensation  of  Savery's  original 
arrangement.  The  Savery  engine,  however,  after  all  improve- 
ment in  design  and  construction,  though  a  working  and  a 
useful  machine,  was  still  a  very  wasteful  one.  The  steam  from 
the  boiler,  passing  into  the  cold,  wet  water-reservoir  or  forcing- 
vessel,  was  condensed  in  large  quantity,  and  also  to  a  very 


THE  DEVELOPMENT  OF  THE   STEAM-ENGINE.  II 

serious  extent,  by  coming  into  actual  contact  with  the  water 
itself. 

n.  The  Performance  of  the  Savery  Engine  was  thus 
evidently  unsatisfactory,  as  judged  from  the  modern  stand- 
point ;  yet,  as  the  first  machine  applying  natural  forces  to  a 
great  task,  and  for  the  first  time  accomplishing  it,  it  was  a 
grand  success.  The  operation  of  deep  mines  had  become  im- 
practicable where  water  was  met  with  in  any  considerable 
quantity,  and,  in  some  cases,  hundreds  of  horses  had  been  kept 
employed,  at  enormous  and  even  fatal  expense,  to  keep  the 
lower  levels  in  working.  These  were  displaced  by  steam  and 
the  Saver}"  engine,  and  mines  which  must  otherwise  have  been 
abandoned  were  once  more  made  profitable. 

The  defects  of  this  class  of  engines  were  nevertheless  great. 
Their  enormous  consumption  of  fuel  was  one  serious  difficulty 
everywhere  except  in  the  coal  districts ;  their  heavy  pressures 
needed  at  deep  shafts  and  for  high  lif ts  gave  rise  to  dangers 
which  threatened  constantly  both  life  and  property  when,  as 
was  very  usual,  the  workmanship  of  the  "  forcing-vessel  *"  was 
defective.  In  fact,  the  invention  of  the  Savery  engine  was 
introductory  to  the  steam-boiler  .explosion :  several  of  the 
boilers  exploding  while  at  work  and  doing  some  damage.  This 
new  and  intimidating  experience,  and  the  evident  wastefulness 
of  the  machine,  led  mechanics,  very  soon,  to  study  the  problem 
anew  with  a  view  to  improvement  in  these  respects :  its  extrava- 
gant consumption  of  fuel,  the  inconvenient  necessity  of  placing 
it  near  the  bottom  of  the  mine  to  be  drained,  and  of  putting 
in  several  for  successive  lifts  where  the  depth  was  considerable, 
and,  especially,  the  risk  which  its  use  with  high  pressures  in- 
volved even  in  its  best  form,  had  considerably  retarded  its 
introduction,  and  it  therefore  came  into  use  very  slowly,  not- 
withstanding its  superiority  in  economic  efficiency  over  horse- 
power. 

Many  years  after  Savery "s  death,  in  1774.  Smeaton  made  the 
first  duty-trials  of  engines  of  this  land.  He  found  that  an 
engine  having  a  cylindrical  receiver  16  inches  in  diameter  and 
22  feet  high,  discharging  the  water  raised  14  feet  above  the 


12  A  MANUAL   OF   THE   STEAM-ENGINE. 

surface  of  the  water  in  the  well,  making  12  strokes,  and  raising 
100  cubic  feet  per  minute,  developed  2§  horse-power,  and  con- 
sumed 3  hundredweight  of  coals  in  four  hours.  Its  duty  was, 
therefore,  5,250,000  pounds  raised  one  foot  per  bushel  of  84 
pounds  of  coals,  or  62,500  "foot-pounds"  of  work  per  pound 
of  fuel.  An  engine  of  slightly  greater  size  gave  a  duty  about 
5  per  cent  greater.* 

12.  Newcomen's  Engine. — The  first  important  step  taken 
towards  remedying  the  defects  of  Savery's  machine  was  taken 
by  Thomas  Newcomen  and  John  Cawley,  or  Galley,  two  me- 
chanics of  the  town  of  Dartmouth,  Devonshire,  England,  who 
produced  what  has  been  known  as  the  Atmospheric  or  Newco- 
men Engine.  Newcomen  was  a  blacksmith,  and  Cawley  a 
glazier  and  plumber.  It  has  been  stated  that  a  visit  to  Corn- 
wall, where  they  witnessed  the  working  of  a  Savery  engine, 
first  turned  their  attention  to  the  subject ;  but  a  friend  of 
Savery  has  stated  that  Newcomen  was  as  early  with  his  general 
plans  as  Savery.  After  some  discussion  with  Cawley,  Newco- 
men entered  into  correspondence  with  Dr.  Hooke,  proposing  a 
steam-engine,  to  consist  of  a  steam-cylinder  containing  a  piston 
similar  to  those  of  Huyghens's  and  Papin's  engines,  and  driving  a 
separate  pump,  similar  to  those  generally  in  use  where  water  was 
raised  by  horse  or  wind  power.  Dr.  Hooke  advised  and  argued 
strongly  against  their  plan  ;  but,  fortunately,  the  obstinate  belief 
of  the  unlearned  mechanics  was  not  overpowered  by  the  dis- 
quisitions of  their  distinguished  correspondent,  and  Newcomen 
and  Cawley  attempted  an  engine  on  their  peculiar  plan. 

This  succeeded  so  well  as  to  induce  them  to  continue  their 
labors,  and  in  1705  to  patent  f — in  combination  with  Savery, 
who  held  the  right  of  surface-condensation,  and  who  induced 
them  to  allow  him  an  interest  with  them — an  engine  combin- 
ing a  steam-cylinder  and  piston,  surface-condensation,  and  a 
separate  boiler  and  separate  pumps.  In  the  atmospheric  en- 

*  History  of  the  Steam-engine,  R.  H.  Thurston,  p.  45  ;  Farey  on  the 
Steam-engine,  p.  125. 

f  It  has  been  denied  that  a  patent  was  issued  ;  but  there  is  no  doubt  that 
Savery  claimed  and  received  an  interest  in  the  new  engine. 


THE  DEVELOPMENT  OF   THE  STEAM-ENGINE.  13 

gine  as  first  designed,  the  slow  process  of  condensation  by  the 
application  of  the  condensing  water  to  the  exterior  of  the  cyl- 
inder to  produce  the  vacuum  caused  the  strokes  of  the  engine 
to  take  place  at  very  long  intervals.  An  improvement  was, 
however,  soon  effected  which  immensely  increased  this  rapidity 
of  condensation.  A  jet  of  water  was  thrown  directly  into  the 
cylinder,  thus  effecting  for  the  Newcomen  engine  what  Desa- 
guliers  had  previously  done  for  the 
Savery  engine.  As  thus  improved, 
the  Newcomen  engine  is  shown  in 
Fig.  4. 

Here  d  is  the  boiler.  Steam  pass- 
es from  it  through  the  cock  </,  and  up 
into  the  cylinder  a,  equilibrating  the 
pressure  of  the  atmosphere,  and  allow- 
ing the  heavy  pump-rod  k  to  fall,  and, 
by  its  greater  weight,  acting  through 
the  beam  /  /,  to  raise  the  piston  s  to 

the    position    shown.       The    COCk  d  be-       FIG.  4.— XEWCOMEX'S  EXGIXK, 

ing  shut,  /  is  then  opened,  and  a  jet 

of  water  from  the  reservoir  s  enters  the  cylinder,  producing  a 
vacuum  by  the  condensation  of  the  steam.  The  pressure  of 
the  air  above  the  piston  now  forces  it  down,  again  raising  the 
pump-rods,  and  thus  the  engine  works  on  indefinitely.  The 
pipe  //  is  used  for  the  purpose  of  keeping  the  upper  side  of  the 
piston  covered  with  water,  to  prevent  air-leaks — a  device  of 
Newcomen.  Two  gauge-cocks,  c,  c,  and  a  safety-valve,  N,  are 
represented  in  the  figure,  but  it  will  be  noticed  that  the  latter 
is  quite  different  from  the  now  usual  form.  Here,  the  pressure 
used  was  hardly  greater  than  that  of  the  atmosphere,  and  the 
weight  of  the  valve  itself  was  ordinarily  sufficient  to  keep  it 
down.  The  rod  m  was  intended  to  carry  a  counter-weight 
when  needed.  The  condensing  water,  together  with  the  water 
of  condensation,  flows  off  through  the  open  pipe/. 

Xewcomen's  first  engine  made  six  or  eight  strokes  a  min- 
ute :  the  later  and  improved  engines  made  ten  or  twelve. 

The  steam-engine  had  now  assumed  a  form  that  somewhat 


A  MANUAL   OF   THE   STEAM-ENGINE. 


resembled  the  modern  machine.  An  important  defect  still  ex- 
isted in  the  necessity  of  keeping  an  attendant  by  the  engine 
to  open  and  shut  the  cocks.  A  bright  boy,  however,  Hum- 
phrey Potter,  to  whom  was  assigned  this  duty  on  a  Newcomen 
engine,  in  1/13  contrived  what  he  called  a  scoggan  —  a  catch 
rigged  with  a  cord  from  the  beam  overhead  —  which  performed 

the  work  for  him.  The  boy, 
thus  making  the  operation  of 
the  valve-gear  automatic,  in- 
creased the  speed  of  the  engine 
to  fifteen  or  sixteen  strokes  a 
minute,  and  gave  it  a  regularity 
and  certainty  of  action  that 
could  only  be  obtained  by  such 
an  adjustment  of  its  valves. 

This  ingenious  young  me- 
chanic afterward  became  a  skil- 
ful workman  and  an  excellent 
engineer,  and  went  abroad  on 
the  Continent,  where  he  erected 
several  fine  engines.  Potter's 
rude  valve-gear  was  soon  im- 
proved by  Henry  Beighton,  and 

W3S      alied      tO 


FIG.5.-BE,GHTON'SVALVE-GEAR,A.D.I718. 

an  engine  which  that  talented  engineer  erected  at  Newcastle- 
on-Tyne  in  1718,  in  which  engine  he  substituted  substantial 
materials  for  Potter's  unmechanical  arrangement  6f  cords,  as 
seen  in  Fig.  5. 

In  this  sketch  r  is  a  plug-tree,  plug-rod,  or  plug-frame,  as  it 
is  variously  called,  suspended  from  the  great  beam  with  which 
it  rises  and  falls,  bringing  the  pins  p  and  k,  at  the  proper  mo- 
ment, in  contact  with  the  handles  kk  and  »  n  of  the  valves, 
moving  them  in  the  proper  direction  and  to  the  proper  extent. 
A  lever  safety-valve  is  here  used,  at  the  suggestion,  it  is  said, 
of  Desaguliers.  The  piston  was  packed  with  leather  or  with 
rope,  and  lubricated  with  tallow. 

In  illustration  of  the  application  of  the  Newcomen  engine 


THE  DEVELOPMENT  OF  THE  STEAM-ENGIXE.  1$ 

to  the  drainage  of  mines,  Farey  describes  a  small  machine,  of 
which  the  pump  is  8  inches  in  diameter,  and  the  lift  162  feet. 
The  column  of  water  to  be  raised  weighed  3535  pounds.  The 
steam-piston  was  made  2.  feet  in  diameter,  giving  an  area  of 
452  square  inches.  The  net  working-pressure  was  assumed  at 
lof  pounds  per  square  inch ;  the  temperature  of  the  water  of 
condensation  and  of  uncondensed  vapor  after  the  entrance  of 
the  injection-water  being  usually  about  150°  Fahr.  This  gave 
an  excess  of  pressure  on  the  steam-side  of  1324  pounds,  the 
total  pressure  on  the  piston  being  4859  pounds.  One  half 
of  this  excess  is  counterweighted  by  the  pump-rods,  and  by 
weight  on  that  end  of  the  beam  ;  and  the  weight,  662  pounds, 
acting  on  each  side  alternately  as  a  surplus,  produced  the 
requisite  rapidity  of  movement  of  the  machine.  This  engine 
was  said  to  make  15  strokes  per  minute,  giving  a  speed  of  pis- 
ton of  75  feet  per  minute,,  and  the  power  exerted  usefully  was 
equivalent  to  265,125  pounds  raised  one  foot  high  per  minute. 
As  the  horse-power  is  equivalent  to  33,000  "  foot-pounds  "  per 
minute,  the  engine  was  of  V/AV  =  8-°34 — almost  exactly  8 
horse-power. 

It  is  instructive  to  contrast  this  estimate  with  that  made  for 
a  Savery  engine  doing  the  same  work.  The  latter  would  have 
raised  the  water  about  26  feet  in  its  "  suction-pipe,"  and  would 
then  have  forced  it,  by  the  direct  pressure  of  steam,  the  re- 
maining distance  of  136  feet :  and  the  steam-pressure  required 
would  have  been  nearly  60  pounds  per  square  inch.  With  this 
high  temperature  and  pressure,  the  waste  of  steam  by  conden- 
sation in  the  forcing-vessels  would  have  been  so  great  that  it 
would  have  compelled  the  adoption  of  two  engines  of  consid- 
erable size,  each  lifting  the  water  one  half  the  height,  and  using 
steam  of  about  25  pounds  pressure. 

Further  improvements  were  effected  in  the  Xewcomen 
engine  by  several  engineers,  and  particularly  by  Smeaton,  and 
it  soon  came  into  quite  extensive  use  in  all  of  the  mining  dis- 
tricts of  Great  Britain,  and  it  also  became  generally  known  upon 
the  Continent  of  Europe.  Its  greater  economy  of  fuel  as  com- 
pared with  the  Savery  engine  in  its  best  form,  its  greater  safety 


1 6  A  MANUAL    OF    THE   STEAM-ENGINE. 

— a  consequence  of  the  low  steam- pressure  adopted, — and  its 
greater  working  capacity,  gave  it  such  manifest  superiority  that 
its  adoption  took  place  quite  rapidly,  and  it  continued  in  gen- 
eral use  in  some  districts  where  fuel  was  cheap  up  to  a  very 
recent  date.  Some  of  these  engines  are  even  now  in  existence. 
From  about  1758  to  the  time  of  the  introduction  of  the  Watt 
engine,  this  was  the  machine  in  almost  universal  use  for  raising 
large  quantities  of  water. 

13.  The  Merits  and  Demerits  of  the  Newcomen  engine 
were  those  characterizing  a  novel  and  radically  altered  form  of 
machine,  which  was  the  first  of  a  new  type :  that  which  may  be 
called  the  modern  type  of  steam-engine.  A  complete  revolu- 
tion had  been  thus  effected,  and  the  genius  of  the  great  in- 
ventors had  produced  a  more  complete  and  thorough  change 
of  type  than  had  been  previously  seen,  or  even  than  has  ever 
been  since  effected  by  even  Watt  and  his  contemporaries  and 
successors.  It  may  then  be  said  that,  defining  the  steam-engine 
as  a  train  of  mechanism,  Newcomen  and  Cawley  were  its  in- 
ventors, and  that  their  machine  was  the  first  steam-engine. 
The  invention  of  the  modern  type  of  steam-engine  is  to  be 
credited  to  them,  and  not  to  any  of  those  later  inventors  who 
simply  improved  upon  it  in  matters  of  detail.  In  this  respect 
Newcomen  antedates  Watt. 

Comparing  the  engine  with  those  preceding  it,  we  see  that 
at  first  we  find  a  single  vessel  performing  the  functions  of  all 
the  parts  of  a  modern  pumping-engine ;  it  was  at  once  boiler, 
steam-cylinder,  and  condenser,  as  well  as  both  a  lifting  and  a 
forcing  pump.  The  Marquis  of  Worcester,  and,  still  earlier,  Da 
Porta,  divided  the  engine  into  two  parts ;  using  one  part  as  a 
steam-boiler,  and  the  other  as  a  separate  water-vessel.  Savery 
duplicated  those  parts  of  the  earlier  engine  which  acted  the 
several  parts  of  pump,  steam-cylinder,  and  condenser,  and  added 
the  use  of  the  jet  of  water  to  effect  rapid  condensation.  New- 
comen and  Cawley  next  introduced  the  modern  type  of  engine, 
and  separated  the  pump  from  the  steam-engine  proper.  In 
their  engine,  as  in  Savery's,  we  will  observe  the  use  of  surface- 


THE  DEVELOPMENT  OF   THE   STEAM-ENGINE.  \7 

condensation  first;  and  subsequently  that  of  a  jet  of  water 
thrown  into  the  midst  of  the  steam  to  be  condensed. 

Thus  an  engine  was  produced  which,  by  the  separation  of 
the  boiler  from  the  engine,  made  it  practicable  to  secure  the 
economical  production  of  steam  by  correct  design  and  giving 
ample  areas  of  heating  surface.  By  the  liberty  thus  gained, 
also,  of  proportioning  the  pumps  independently,  it  was  practi- 
cable to  obtain  the  needed  power  with  steam  of  low  pressure ; 
it  became  practicable  to  apply  simply  atmospheric  pressure  to 
the  work,  using  steam  simply  to  remove  the  atmosphere  from 
the  opposite  side  of  the  piston,  thus  at  once  and  entirely  evad- 
ing all  dangers  coming  of  the  employment  of  high  pressures. 
Finally,  by  the  separation  of  the  engine  from  the  other  ele- 
ments of  the  machine,  it  became  possible  to  appreciably  reduce 
the  wastes  by  initial  condensation  of  steam  while  doing  its  work 
of  impulsion.  It  was  by  these  several  ways  that  an  enormous 
advance  was  made,  economically,  in  the  application  of  steam 
to  raising  water. 

The  defects  of  the  engine,  as  judged  from  a  modern  stand- 
point, were  the  great  size  and  weight  of  the  machine,  relatively 
to  its  power;  its  still  enormous  consumption  of  steam  and 
fuel:  and  its  rude  construction.  It  was  still  far  from  perfect  in 
either  design  or  construction,  or  satisfactory  as  to  economical 
performance,  even  as  finally  built  by  Smeaton,  the  great  en- 
gineer of  that  time  who  made  its  very  best  examples.  The 
latter  raised  the  best  duty  of  the  engine  from  about  ten  per 
cent  to  more  nearly  twelve  per  cent  of  that  of  the  better  class 
of  modern  pumping-engines. 

Smeaton  made  a  number  of  test-trials  of  Newcomen  engines 
to  determine  their  "duty" — i.e.,  to  ascertain  the  expenditure 
of  fuel  required  to  raise  a  definite  quantity  of  water  to  a  stated 
height.  He  found  an  engine  10  inches  in  diameter  of  cylinder, 
and  of  3  feet  stroke,  could  do  work  equal  to  raising  2,919,017 
pounds  of  water  one  foot  high,  with  a  bushel  of  coals  weighing 
84  pounds. 

Thus,  by  the  end  of  the  third  quarter  of  the  eighteenth  cen- 
tury, the  steam-engine  had  become  generally  introduced,  and 


1 8  A    MANUAL   OF   THE   STEAM-ENGINE. 

had  been  applied  to  nearly  all  of  the  purposes  for  which  a  sin- 
gle-acting engine  could  be  used.  The  path  which  had  been 
opened  by  Worcester  had  been  fairly  laid  out  by  Savery  and 
his  contemporaries,  and  the  builders  of  the  Newcomen  engine, 
with  such  improvements  as  they  had  been  able  to  effect,  had 
followed  it  as  far  as  they  were  able.  The  real  and  practical 
introduction  of  the  steam-engine  is  as  fairly  attributable  to 
Smeaton  as  to  any  one  of  the  inventors  whose  names  are  more 
generally  known  in  connection  with  it.  As  a  mechanic  he  was 
unrivalled  ;  as  an  engineer  he  was  head  and  shoulders  above  any 
constructor  of  his  time  engaged  in  general  practice.  There 
were  very  few  important  public  works  built  in  Great  Britain  at 
that  time  in  relation  to  which  he  was  not  consulted  ;  and  he  was 
often  visited  by  foreign  engineers,  who  desired  his  advice  with 
regard  to  works  in  progress  on  the  Continent.* 

14.  James  Watt  and  his  engine  now  come  into  view. 
The  success  of  the  Newcomen  engine  naturally  attracted  the 
attention  of  mechanics,  and  of  scientific  men  as  well,  to  the 
possibility  of  making  other  applications  of  steam-power.  The 
greatest  men  of  the  time  gave  much  attention  to  the  subject ; 
but  until  Watt  began  the  work  that  has  made  him  famous, 
nothing  more  was  done  than  to  improve  the  proportions  and 
to  slightly  alter  the  details  of  the  Newcomen  and  Cawley  en- 
gine, even  by  such  skilful  engineers  as  Brindley  and  Smeaton. 

This  great  man  was  born  at  Greenock,  January  19,  1736. 
He  was  a  bright  boy,  but  exceedingly  delicate  in  health,  and 
quite  unable  to  attend  school  regularly,  or  to  apply  himself 
closely  to  either  study  or  play.  At  the  age  of  eighteen  Watt 
was  sent  to  Glasgow,  there  to  reside  with  his  mother's  relatives, 
and  to  learn  the  trade  of  a  mathematical-instrument  maker. 
The  mechanic  with  whom  he  was  placed  was  incapable  of  giv- 
ing much  aid  in  the  project ;  and  Dr.  Dick,  of  the  University 
of  Glasgow,  with  whom  Watt  became  acquainted,  advised  him 
to  go  to  London.  Accordingly,  he  set  out  in  June,  1755,  for 
the  metropolis,  where,  on  his  arrival,  he  arranged  with  Mr.  John 


*  History  of  the  Steam-engine. 


THE  DEVELOPMEXT  OF   THE  STEAM-ENGIXE.  ig 

Morgan,  in  Cornhill,  to  work  for  a  year  at  his  chosen  business, 
receiving  as  compensation  twenty  guineas.  At  the  end  of  the 
year  he  was  compelled  by  serious  ill-health  to  return  home. 
Having  become  restored  to  health,  he  went  again  to  Glasgow, 
in  1756,  with  the  intention  of  pursuing  his  calling  there.  Dr. 
Dick  employed  him  to  repair  some  apparatus  which  had  been 
bequeathed  to  the  college.  He  remained  here  until  1760,  when 
he  took  a  shop  in  the  city,  and  in  1761  moved  again  into  a  shop 
on  the  north  side  of  the  Trongate.  where  he  earned  a  scanty  liv- 
ing, still  IwTjpmg  up  his  connection  with  the  college.  He  spent 
much  of  his  leisure  time  in  making  philosophical  experiments. 
The  introduction  of  the  Xewcomen  engine  in  the  neighbor- 
hood of  Glasgow,  and  the  presence  of  a  model  in  the  college 
collections,  which  model  was  placed  in  his  hands  in  1763  for 
repairs,  led  him  to  study  the  history  of  the  steam-engine,  and 
to  conduct  for  himself  an  experimental  research  into  the  prop- 
erties of  steam,  using  a  set  of  improvised  apparatus. 

15.  The  Newcomen  Model,  as  it  happened,  had  a  boiler, 
which,  although  made  to  a  scale  from  engines  in  actual  use,  was 
quite  incapable  of  furnishing  steam  enough  to  work  the  engine. 
It  was  about  nine  inches  in  diameter,  and  the  steam-cylinder 
was  two  inches  in  diameter,  and  of  six  inches  stroke  of  piston. 
Watt  at  once  noticed  the  defect  referred  to,  and  immediately 
sought,  first  the  cause  and  then  the  remedy. 

He  soon  concluded  that  the  sources  of  loss  of  heat  in  the 
Newcomen  engine-r-which  loss  would  be  greatly  exaggerated 
in  a  small  model — were :  first,  the  dissipation  of  heat  by  the 
cylinder  itself,  which  was  of  brass,  and  was  both  a  good 
conductor  and  a  good  radiator :  secondly,  the  loss  of  heat  con- 
sequent upon  the  necessity  of  cooling  down  the  cylinder  at 
every  stroke  in  producing  the  vacuum ;  and,  finally,  a  loss  of 
power  was  due  to  the  existence  of  vapor  beneath  the  piston, 
the  presence  of  which  vapor  was  a  consequence  of  the  imper- 
fect method  of  condensation  which  characterizes  the  Xewcomen 
engine. 

He  first  made  a  cylinder  of  non-conducting  material — wood 
soaked  in  oil  and  then  baked — and  found  a  decided  advantgae 


20  A    MANUAL   OF   THE   STEAM-ENGINE. 

in  the  economy  of  steam  thus  secured.  He  then  conducted  a 
series  of  experiments  upon  the  temperature  and  pressure  of 
steam  at  such  points  in  the  scale  as  he  could  readily  reach,  and, 
constructing  a  curve  with  his  results,  the  abscissas  representing 
temperatures,  and  the  pressures  being  represented  by  the  ordi- 
nates,  he  ran  the  curve  backward  until  he  had  obtained 
approximate  measures  of  temperatures  less  than  212°,  and  of 
pressures  less  than  atmospheric.  He  thus  discovered  that, 
with  the  amount  of  injection-water  used  in  the  Newcomen  en- 
gine, bringing  the  temperature  of  the  interior,  as  he  found, 
down  to  from  140°  to  175°  Fahr.,  a  very  considerable  back- 
pressure would  be  met  with. 

Continuing  his  research  still  further,  he  measured  the 
amount  of  steam  used  at  each  stroke ;  and,  comparing  it  with 
the  quantity  that  would  just  fill  the  cylinder,  he  found  that  at 
least  three  fourths  was  wasted.  The  quantity  of  cold  water 
necessary  to  produce  condensation  of  a  given  weight  of  steam 
was  next  determined,  and  he  found  that  one  pound  of  steam 
contained  enough  heat  to  raise  about  six  pounds  of  cold  water, 
as  used  for  condensation,  from  the  temperature  of  52°  Fahr.  to 
the  boiling-point ;  and,  going  still  further,  he  found  that  he  was 
compelled  to  use,  at  each  stroke  of  the  Newcomen  engine,  four 
times  as  much  injection-water  as  should  suffice  to  condense  a 
cylinder  full  of  steam.  Thus  was  confirmed  his  previous  con- 
clusion that  three  fourths  of  the  heat  supplied  to  the  engine 
was  wasted. 

His  experiments  having  revealed  to  him  the  now  well-known 
fact  of  the  existence  of  latent  heat,  he  went  to  his  friend  Dr. 
Black,  of  the  university,  with  this  intelligence ;  and  the  latter 
then  informed  him  of  the  Theory  of  Latent  Heat  which  had 
but  a  short  time  earlier  been  discovered  by  Dr.  Black  himself. 

Watt  had  now,  therefore,  determined  by  his  own  researches, 
as  he  himself  enumerates  them,*  the  following  facts : 

(i)  The  capacities  for  heat  of  iron,  copper,  and  of  some 
sorts  of  wood,  as  compared  with  water. 

*  Robinson's  "Mechanical  Philosophy."  edited  by  Brewster. 


THE  DEVELOPMENT  OF   THE  STEAJf-ElffGllTE.  21 

(2)  The  bulk  of  steam  compared  with  that  of  water. 

(3)  The  quantity  of  water  evaporated  in  a  certain  boiler  by 
a.  pound  of  coal. 

«4>i  The  elasticities  of  steam,  at  various  temperatures 
greater  than  that  of  boiling  water,  and  an  approximation  to 
the  law  which  it  follows  at  other  temperatures. 

5  -I  How  much  water,  in  the  form  of  steam,  was  required, 
at  every  stroke,  by  a  small  Newcomen  engine,  with  a  wooden 
cylinder  six  inches  in  diameter  and  twelve  inches  stroke. 

(6)  The  quantity-  of  cold  water  required,  at  every  stroke,  to 
condense  the  steam  in  that  cylinder,  so  as  to  give  it  a  working 
power  of  about  seven  pounds  on  the  square  inch. 

After  these  well-devised  and  truly  scientific  investigations. 
Watt  was  enabled  to  enter  upon  his  work  of  improving  the 
steam-engine  with  an  intelligent  understanding  of  its  "Tinting 
defects,  and  with  a  knowledge  of  their  cause.  It  was  on  a 
Sunday  afternoon,  in  the  spring  of  1765,  that  he  devised  his 
first  and  his  greatest  invention — the  separate  condenser.  His 
object  in  using  it  was,  as  he  says  himself,  to  keep  the  cylinder  as 
hat  as  the  steam  that  entered  it.  He  was  therefore  the  first  to 
apprehend  and  to  state  a  problem  which  the  modern  engineer 
is  still  vainly  endeavoring  completely  to  solve. 

Watt  was,  at  this  time,  twenty-nine  years  of  age.  Having 
taken  this  first  step  and  made  such  a  radical  improvement,  the 
success  of  the  invention  was  no  sooner  determined  than  others 
followed  in  rapid  succession  as  consequences  of  the  exigencies 
arising  from  the  first  radical  change  in  the  old  Newcomen  en- 
gine. But  in  the  working  out  of  the  forms  and  proportions  of 
4JPtHffc  in  the  new  engine,  even  Watt's  powerful  mind,  with  its 
stores  of  happily-combined  scientific  and  practical  information, 
was  occupied  for  years. 

In  attaching  the  separate  condenser,  he  first  tried  surface 
condensation ;  but  this  not  succeeding  well,  he  substituted  th« 
jet.  Some  provision  became  at  once  necessary  for  preventing 
the  filling  of  the  condenser  with  water. 

Watt  at  first  intended  adopting  the  same  expedient  which 
worked  satisfactorily  with  the  less  effective  condensation  of 


22  A    MANUAL    OF   THE  STEAM-ENGINE. 

Newcomen's  engine,  i.e.,  leading  a  pipe  from  the  condenser  to 
a  depth  greater  than  the  height  of  the  column  of  water  which 
could  be  counterbalanced  by  the  pressure  of  the  atmosphere  ; 
but  he  subsequently  employed  the  air-pump,  which  relieves 
the  condenser,  not  only  of  the  water,  but  of  the  air  which 
also  usually  collects  in  considerable  volume,  and  vitiates  the 
vacuum. 

He  next  substituted  oil  and  tallow  for  the  water  previously 
used  in  lubrication  of  the  piston  and  keeping  it  steam-tight,  in 
order  to  avoid  the  cooling  of  the  cylinder  incident  to  the  use 
of  water.  Still  another  cause  of  refrigeration  of  the  cylinder, 
and  consequent  waste  of  power  in  its  operation,  was  seen  to  be 
the  entrance  of  the  atmosphere,  which  came  in  at  the  top  and 
followed  the  piston  down  the  cylinder  at  each  stroke.  This  the 
inventor  concluded  to  prevent  by  covering  the  top  of  the 
cylinder,  and  allowing  the  piston-rod  to  play  through  a  "stuff- 
ing-box," which  device  had  long  been  known  to  mechanics. 
He  accordingly  not  only  covered  the  top,  but  surrounded  the 
whole  cylinder  with  an  external  casing  or  "  steam-jacket,"  and 
allowed  the  steam  from  the  boiler  to  pass  around  the  steam- 
cylinder  and  to  press  upon  the  upper  surface  of  the  piston, 
where  its  pressure  was  readily  variable  and  therefore  more 
manageable  than  that  of  the  atmosphere.  It  also,  besides 
keeping  the  cylinder  hot,  could  do  comparatively  little  harm 
should  it  leak  by  the  piston,  as  it  might  be  condensed  and 
readily  disposed  of. 

16.  The  Single-acting  Engine  of  Watt  was  now  fully  de- 
veloped from  the  "  atmospheric  engine  "  of  Newcomen.  As 
improved  it  is  shown  in  Fig.  6,  which  represents  the  engine 
as  patented  in  April,  1769.  Watt's  first  engine  was  erected 
with  the  pecuniary  aid  of  Dr.  Roebuck,  the  lessor  of  a  coal, 
mine  on  the  estate  of  the  Duke  of  Hamilton,  at  Kinneil,  near 
Borrowstounness.  This  engine,  which  was  put  up  at  the  mine, 
had  a  steam-cylinder  eighteen  inches  in  diameter. 

In  the  figure,  the  steam  passes  from  the  boiler  through 
the  pipe  d  and  the  valve  c  to  the  cylinder  casing,  or  steam- 
jacket,  Y  Y,  and  above  the  piston  b,  which  it  follows  in  its 


THE  DEVELOPMENT  OF  THE  STEAM-ENGINE. 


descent  in  the  cylinder  a,  the  valve  /  being  at  this  time  open 
to  allow  the  exhaust  to  pass 
into  the  condenser  h. 

The  piston  now  being  at  the 
lower  end  of  the  cylinder,  and 
the  pump-rods  at  the  opposite 
end  of  the  beam  y  thus  raised, 
and  the  pumps  filled  with  water, 
the  valves  c  and  /  close,  while 
e  opens,  allowing  the  steam 
which  remains  above  the  piston 
to  flow  beneath  it,  until,  the 
pressure  becoming  equal  above 
and  below  by  the  weight  of  the 
pump,  it  is  rapidly  drawn  to 
the  top  of  the  cylinder,  while 
the  steam  is  displaced  above, 
passing  to  the  underside  of  the 
piston. 

Now  the  valve  e  is  closed, 
and  <:and  /are  again  opened,  FlG- ^.-WATT'S PUM«XG-EN-G..NE,  A.D.  1769. 
and  the  down-stroke  is  repeated  as  before.  The  water  and  air 
entering  the  condenser  are  removed,  at  each  stroke,  by  the 
air-pump  *,  which  communicates  with  the  condenser  by  the 
passage  s.  The  pump  q  supplies  condensing-water,  and  the 
pump  A  takes  away  a  part  of  the  water  of  condensation,  which 
is  thrown  by  the  air-pump  into  the  "  hot- well  "  k,  and  with  it 
supplies  the  boiler.  The  valves  are  moved  by  valve-gear  very 
similar  to  Beighton's,  by  the  pins  m  m  in  the  "  plug-frame  "  or 
"  tappet-rod  "  n  n. 

The  engine  is  mounted  upon  a  substantial  foundation,  B  B. 
F  is  an  opening,  out  of  which,  before  starting  the  engine,  the 
air  is  driven  from  the  cylinder  and  condenser. 

17.  Watt's  Double-acting  Engine  was  the  next  of  his 
great  inventions ;  and  his  scheme  of  the  expansion  of  steam 
was  quite  as  important. 

Watt  conceived  the  idea  of  economizing  some  of  that  power, 


24  A    MANUAL   OF   THE    STEAM-ENGINE. 

the  loss  of  which  was  so  plainly  indicated  by  the  violent  rush 
of  the  exhaust  steam  into  the  condenser,  and  described  the  ad- 
vantages that  would  follow  the  use  of  steam  expansively,  by 
means  of  a  "cut-off,"  in  a  letter  to  Dr.  Small,  of  Birmingham, 
dated  Glasgow,  May,  1769.  He  also  planned  a  "  compound 
engine."  This  invention  of  the  expansion  of  steam,  which,  in 
importance,  was  hardly  exceeded  by  any  other  improvement  of 
the  steam-engine,  was  adopted  at  Soho  in  1776,  but  the  patent 
was  not  obtained  until  1782. 


FIG.  7. — WATT'S  ENGINE,  A.D.  1780. 

During  this  interval,  Watt  invented  the  crank  and  fly-wheel, 
but,  as  the  former  had  been  first  patented  by  Wasborough, 
who  is  supposed  to  have  obtained  a  knowledge  of  it  from 
workmen  employed  by  Watt,  the  latter  patented  several  other 
methods  of  producing  rotary  motions,  and  temporarily  adopted 
that  known  as  the  "  sun-and-planet  wheels,"  subsequently  using 
the  crank.  The  adaptation  of  the  steam-engine  to  the  produc- 
tion of  rotary  motion  was  soon  succeeded  by  the  introduction 
of  the  Double-acting  Engine,  the  Fly-ball  Governor,  the 
Counter,  the  Steam-engine  Indicator,  and  other  minor  but 


THE  DEVELOPMENT  OF  THE  STEAM-EXGIKE.  2§ 

valuable  improvements,  which  where  the  final  steps  by  which 
the  Watt  steam-engine  became  applicable  to  driving  mills,  to 
use  on  railroads,  to  steam-navigation,  and  to  the  countless  pur- 
poses by  which  it  has  become,  as  it  has  already  been  denomi- 
nated, the  great  material  agent  of  civilization. 

Fig.  7  represents  the  Watt  Double-acting  Engine.  It  will 
be  noticed  that  it  differs  from  the  Single-acting  Engine  in  hav- 
ing steam-valves,  B  Bt  and  exhaust-valves,  E  E,  at  each  end  of 
the  cylinder,  thus  enabling  the  steam  to  act  on  each  side  of  the 
piston  alternately,  and  practically  doubling  the  power  of  the 
engine. 

The  end  of  the  beam  opposite  to  the  cylinder  is  usually 
connected  with  a  crank-shaft. 

18.  The  Later  Pumping  engine  of  this  type  is  shown  in 
the  succeeding  figure,  exhibiting  the  principal  form  of  pump- 
ing-engine  as  now  constructed. 


F::-   1  -7--I  C: 


Fig.  8  represents  the  Cornish  pumping-engine,  which,  in 
spite  of  its  great  weight  and  high  cost,  is  still  in  use. 

It  wfll  be  seen  that  it  is  the  engine  of  James  Watt  in  all  its 


26  A   MANUAL    OF   THE   STEAM-ENGINE. 

general  features,  with  the  addition,  in  its  operation,  of  the  ap- 
plication of  Watt's  idea  of  expansion  of  steam  to  something 
approximating  the  extent  customary  at  the  present  time. 

It  is  single-acting,  and  has  a  steam-jacket  and  a  plug-rod 
valve-gear,  J  K.  The  improvements  are  principally  in  the 
form  and  proportions  of  its  parts,  and  in  its  adaptation  to  high 
steam  and  "  short  '  cut-off.' "  A  is  the  steam-cylinder,  B  C 
the  piston  and  rod,  D  the  beam,  and  the  pump-rod.  The 
condenser  is  seen  at  G,  and  the  air-pump  at  H.  The  steam- 
cylinder  is  "  steam-jacketed,"  and  is  surrounded  by  a  casing, 
O,  composed  of  brickwork  or  other  non-conducting  material. 
Steam  is  first  admitted  above  the  piston,  driving  it  rapidly 
downward  and  raising  the  pump-rod.  At  an  early  point  in  the 
stroke  the  admission  of  steam  is  checked  by  the  sudden  closing 
of  the  induction-valve,  and  the  stroke  is  completed  under  the 
action  of  expanding  steam  assisted  by  the  inertia  of  the  heavy 
parts  already  in  motion.  The  necessary  weight  and  inertia  are 
afforded  in  many  cases,  where  the  engine  is  applied  to  the 
pumping  of  deep  mines,  by  the  immensely  long  and  heavy 
pump-rods.  Where  this  weight  is  too  great,  it  is  counter- 
balanced ;  and  where,  as  when  used  for  the  water-supply  of 
cities,  too  small,  weights  are  added.  When  the  stroke  is  com- 
pleted, the  "  equilibrium-valve  "  is  opened,  and  the  steam  passes 
from  above  to  the  space  below  the  piston,  and,  an  equilibrium 
of  pressure  being  thus  produced,  the  pump-rods  descend,  forcing 
the  water  from  the  pumps  and  raising  the  steam-piston. 

The  absence  of  the  crank  or  other  device  which  might  de- 
termine absolutely  the  length  of  stroke  compels  a  very  careful 
adjustment  of  steam  admission  to  the  amount  of  load.  Should 
the  stroke  be  allowed  to  exceed  the  proper  length,  and  should 
danger  thus  arise  of  the  piston  striking  the  cylinder-heads,  the 
movement  is  checked  by  buffer-beams.  The  regulation  is 
effected  by  a  "  cataract,"  a  kind  of  hydraulic  governor,  consist- 
ing of  a  plunger-pump  with  a  reservoir  attached.  The  plunger 
is  raised  by  the  engine,  and  then  automatically  detached.  It 
falls  with  greater  or  less  rapidity,  its  velocity  being  determined 
by  the  size  of  the  eduction  orifice,  which  is  adjustable  by  hand. 


THE  DEVELOPMENT  OF  THE   STEAM-ENGIXE.  2/ 

When  the  plunger  reaches  the  bottom  of  the  pump-barrel,  it 
disengages  a  catch,  a  weight  is  allowed  to  act  upon  the  steam- 
valve,  opening  it,  and  the  engine  is  caused  to  make  a  stroke. 
When  the  outlet  of  the  cataract  is  nearly  closed,  the  engine 
stands  still  a  considerable  time  while  the  plunger  is  descending, 
and  the  strokes  succeed  each  other  at  long  intervals.  When 
the  opening  is  greater,  the  cataract  acts  more  rapidly,  and  the 
engine  works  faster.  This  has  been  regarded  until  recently  as 
the  most  economical  of  pumping-engines,  and  it  is  still  gener- 
ally used  in  Europe  in  freeing  mines  of  water. 

19.  The  Compound  Engine  originated  in  Watt's  time.  Fig. 
9  represents  the  first  "  compound  "  or  "  two-cylinder  "  engine. 
This  class  of  engines,  in  which  the  steam  exhausted  from  one 
cylinder  is  further  expanded  in  the  second,  was  first  introduced 
by  Hornblower,  in  1781,  and  was  patented,  in  combination  with 
the  Watt  condenser,  by  Woolf,  at  a  later  date  (1804),  with  a 
view  to  adopting  high  steam  and  considerable  expansion.  The 
Woolf  engine  was  to  some  extent  adopted,  but  was  not  suc- 
cessful in  competing  with  Watt  engines  where  the  latter  were 
well  built,  and,  like  Honiblower's  engine,  was  soon  given  up. 

The  compound  engine  has  come  up  again  within  a  few 
years,  and  with  what  is  mow  considered  high  steam  and  con- 
siderable expansion,  and  designed  with  more  intelligent  refer- 
ence to  the  requirements  of  economy  of  working  steam  in  this 
manner,  it  is  gradually  displacing  other  forms  of  engine. 

The  engine  patented  by  Hornblower  in  1781  was  first  de- 
scribed by  the  inventor  in  the  "  Encyclopaedia  Britannica."  It 
consists,  as  is  seen  by  reference  to  the  engraving,  of  two  steam- 
cylinders,  A  and  B — A  being  the  low-  and  B  the  high-pressure 
cylinder — the  steam  leaving  the  latter  being  exhausted  into 
the  former,  and,  after  doing  its  work  there,  passing  into  the 
condenser,  as  already  described.  The  piston-rods,  C  and  D,  are 
both  connected  to  the  same  part  of  the  beam  by  chains,  as  in 
the  other  early  engines.  These  rods  pass  through  stuffing- 
boxes  in  the  cylinder-heads,  which  are  fitted  up  like  those  seen 
on  the  Watt  engine.  Steam  is  led  to  the  engine  through  the 
pipe,  G  Y,  and  cocks,  a,  b.  c,  and  d.  are  adjustable,  as  required, 


28 


A    MANUAL   OF    THE   STEAM-ENGINE. 


to  lead  steam  into  and  from  the  cylinders,  and  are  moved  by 
the  plug-rod,  W,  which  actuates  handles  not  shown.  K  is  the 
exhaust-pipe  leading  to  the  condenser.  V  is  the  engine  feed- 
pump, and  X  the  pump-rod  carrying  the  pump-buckets  at  the 
bottom  of  the  shaft. 

The  cocks  c  and  a  being  open  and  b  and  d  shut,  the  steam 
passes  from  the  boiler  into  the  upper  part  of  the  steam-cylinder, 
B\  and  the  communication  between  the  lower  part  of  B  and 
the  top  of  A  is  also  open.  Before  starting,  steam  being  shut 
off  from  the  engine,  the  great  weight  of  the  pump-rod,  X, 


FIG.  9. — HORNBLOWER'S  COMPOUND  ENGINE,  1781. 

causes  that  end  of  the  beam  to  preponderate,  the  pistons  stand- 
ing, as  shown,  at  the  top  of  their  respective  steam-cylinders. 

The  engine  being  freed  from  all  air  by  opening  all  the  valves 
arid  permitting  the  steam  to  drive  it  through  the  engine  and 
out  of  the  condenser  through  the  "snifting-valve,"  O,  the 
valves  b  and  d  are  closed,  and  the  cock  in  the  exhaust-pipe 
opened. 


THE  DEVELOPMENT  OF   THE  STEAX-EXGIXE.  2O, 

The  steam  beneath  the  piston  of  the  large  cylinder  is 
immediately  condensed,  and  the  pressure  on  the  upper  side  of 
that  piston  causes  it  to  descend,  carrying  that  end  of  the  beam 
with  it,  and  raising  the  opposite  end  with  the  pump-rods  and 
their  attachments.  At  the  same  time,  the  steam  from  the 
lower  end  of  the  small  high-pressure  cylinder  being  let  into  the 
upper  end  of  the  larger  cylinder,  the  completion  of  the  stroke 
finds  a  cylinder  full  of  steam  transferred  from  the  one  to  the 
other  with  corresponding  increase  of  volume  and  decrease  of 
pressure.  While  expanding  and  diminishing  in  pressure  as  it 
passes  from  the  smaller  into  the  larger  cylinder,  this  charge  of 
steam  gradually  resists  less  and  less  the  pressure  of  the  steam 
from  the  boiler  on  the  upper  side  of  the  piston  of  the  small 
cylinder,  B,  and  the  net  result  is  the  movement  of  the  engine 
by  pressures  exerted  on  the  upper  sides  of  both  pistons  and 
against  pressures  of  less  intensity  on  the  under  sides  of  both. 
The  pressures  in  the  lower  part  of  the  small  cylinder,  in 
the  upper  part  of  the  large  cylinder,  and  in  the  communicating 
paiiijni  are  evidently  all  equal  at  any  given  time.  When  the 
pistons  have  reached  the  bottoms  of  their  respective  cylinders, 
the  valves  at  the  top  of  the  small  cylinder,  B,  and  at  the 
bottom  of  the  large  cylinder.  A.  are  closed,  and  the  valves  c 
and  d  are  opened.  Steam  from  the  boiler  now  enters  beneath 
the  piston  of  the  small  cylinder:  the  steam  in  the  larger 
cylinder  is  exhaused  into  the  condenser,  and  the  steam  already 
in  the  small  cylinder  passes  over  into  the  large  cylinder,  follow- 
ing up  the  piston  as  it  rises. 

Thus,  at  each  stroke  a  small  cylinder  full  of  steam  is  taken 
from  the  boiler,  and  the  same  weight,  occupying  the  volume  of 
the  larger  cylinder,  is  exhausted  into  the  condenser  from  the 
latter  cylinder. 

Referring  to  the  method  of  operation  of  this  engine,  Prof. 
Robison  demonstrated  that  the  effect  produced  was  the  same 
as  in  Watt's  single-cylinder  engine — a  fact  which  is  com- 
prehended in  the  law  enunciated  many  years  later  by  Rankine, 
that,  **  so  far  as  the  theoretical  action  of  the  steam  on  the  pis- 


3O  A    MANUAL   OF   THE   STEAM-ENGINE. 

ton  is  concerned,  it  is  immaterial  whether  the  expansion  takes 
place  in  one  cylinder,  or  in  two  or  more  cylinders."  It  was 
found,  in  practice,  that  the  Hornblower  engine  was  no  more 
economical  than  the  Watt  engine  ;  and  that  erected  at  the  Tin 
Croft  Mine,  Cornwall,  in  1792,  did  even  less  work  with  the 
same  fuel  than  the  Watt  engines. 

The  plan  unsuccessfully  introduced  by  Hornblower  was 
subsequently  modified  and  adopted  by  others  among  the  con- 
temporaries of  Watt ;  and,  with  higher  steam  and  the  use  of 
the  Watt  condenser,  the  "  compound  "  gradually  became  a 
standard  type  of  steam-engine. 

Arthur  Woolf,  in  1804,  re-introduced  the  Hornblower  or 
Falck  engine,  with  its  two  steam-cylinders,  using  steam  of 
higher  tension.  His  first  engine  was  built  for  a  brewery  in 
London,  and  a  considerable  number  were  subsequently  made. 
Woolf  expanded  his  steam  from  six  to  nine  times,  and  the 
pumping-engines  built  from  his  plans  were  said  to  have  raised 
about  40,000,000  pounds  one  foot  high  per  bushel  of  coals, 
when  the  Watt  engine  was  raising  but  little  more  than  30,000,- 
ooo.  In  one  case  a  duty  of  57,000,000  was  claimed. 

The  accompanying  engraving  exhibits  a  modern  and  success- 
ful type  of  compound  engine,  which  may  be  taken  for  compari- 
son in  style,  general  design,  proportions,  and  performance  with 
the  earlier  forms  of  pumping-engine.  It  was  designed  by  Mr. 
E.  Reynolds  and  is  in  operation  in  the  city  of  Milwaukee,  where 
it  was  constructed. 

Here  the  pumps  are  in  line  with  the  steam-cylinders,  bring- 
ing the  working-strain  direct  to  the  plungers.  The  valve-gear  has 
a  cut-off  on  both  cylinders,  which  allows  the  steam  to  be  worked 
from  boiler-pressure  down  to  8  or  9  pounds.  The  cylinders 
are  steam-jacketed.  The  pump,  condenser,  boiler  feed-pumps, 
and  air-chambers  are  placed  below  the  floor.  The  contract  re- 
quired a  delivery  of  12,000,000  gallons  of  water,  150  feet  high, 
every  24  hours,  and  a  duty  of  97,000,000  foot-pounds  for  every 
IOO  Ibs.  of  coal  consumed. 


32  A    MANUAL   OF   THE   STEAM-ENGINE. 

The  principal  dimensions  of  the  engines  are: 

Diameter  high-pressure  cylinder  ......................  inches,  34 

Diameter  low-pressure  cylinder  .......................        "      66 

Diameter  of  pump  ..................................        "       41.78 

Diameter  of  pump-plunger  ...........................  30 

Length  of  stroke  ....................................        "       60 

The  performance  of  this  engine  may  be  compared  with 
those  reported  for  Savery's,  Newcomen's,  'and  Watt's  machines 
to  obtain  some  idea  of  the  progress  of  modern  times  in  the 
economical  use  of  steam. 

The  following  are  the  results  of  the  trial  : 

Duration  of  trials  ...............................  hours,  48 

Steam-pressure  in  engine-room  ...................  pounds,         74-8l 

Vacuum  by  gauge  .................  ^  ..............  inches,  26.25 

Water-pressure  gauge  ............................  pounds,  62.02 

Total  head,  including  suction-lift  ................         "  67.29 

Revolutions  of  engine  per  minute  ........................  25.51 

Piston  speed  per  minute  .............................  feet,  255.10 

Coal  consumed  ..................................  pounds,         32.395 

Duty  in  foot-pounds,  per  100  pounds  of  coal  consumed..  .104,820,431 

Exceeding  the  duty  and  the  capacity  guaranteed  under  the 
ordinary,  every-day  conditions,  and  the  actual  weight  of  coal 
consumed  being  charged  up  without  deductions  of  any  kind. 

The  progress  of  steam-pumping  engine  efficiency,  from  the 
time  of  Newcomen  and  of  Watt  to  date,  is  seen  in  the  follow- 
ing figures  : 


1769  Newcomen  (by  Smeaton)  .........................      7,000,000 

1772  "          "       ...........................    12,000,000 

1776  Watt  ...........................................  21,600,000 

1778  "    expansive  ..................................  26,600,000 

1830  Cornish   ........................................  86,585,000 

1880  Compound  .......................................  100,000,000 

1885  .......................................  110,000,000 

1890  .......................................  120,000,000 

The  duties  given  are  those  either  guaranteed  or  actually 
resulting  from  trials.  The  fuel  demanded  per  horse-power 
per  hour  thus  has  decreased  from  about  35  pounds  in  Smea- 
tion's  Newcomen  engines,  and  8  in  Watt's  best  work,  to  2 


THE  DEVELOPMENT  OF  THE  STEAM-ENGIXE.  33 

pounds  in  the  Cornish,  and  to  less  than  1.75  in  later  engines  of 
the  compound  type:  the  minimum  given  above  being  1.5. 
Even  this  figure  has  been  reduced  with  later  engines  of  the 
three-  and  four-cylinder  types. 

2O.  The  Stationary  Engine  is,  as  has  been  already  seen, 
an  evolution  from  the  earlier  types  of  pumping-engine,  and  is  a 
product  of  the  fertile  and  fruitful  brain  of  James  Watt.  The 
Watt  double-acting  engine,  turning  a  shaft,  regulated  by  a 
"  fly-wheel  "  and  controlled  by  the  Watt  governor,  represents 
the  type  of  the  modern  stationary  engine  as  well  as  that  of 
Watt's  own  time.  The  changes  which  have  occurred  since 
that  period  have  been  mainly  in  matters  of  detail. 

The  old  "  parallel  motion  "  guiding  the  head  of  the  piston- 
rod  has  now  become  generally  superseded  by  the  guides  and 
sliding  cross-head.  The  valve-gear  has  been  simplified  and  bet- 
ter adapted  to  efficient  action  as  a  "  cut-off  "  gear.  The  gover- 
nor has  been  so  attached  as  to  adjust  the  steam  supply  to  work 
momentarily  performed, by  variation  of  the  point  of  cut-off,  and, 
revolution  by  revolution,  fixing  the  ratio  of  expansion.  The 
general  design  and  construction  of  the  engine  have  been  modi- 
fied in  the  direction  of  simplicity,  cheapness,  and  lightness, 
combined  with  strength.  The  use  of  the  direct-acting  engine, 
rather  than  the  beam-engine,  is  now  general,  and,  for  all  but 
"  high-speed  "  engines  which  make  1 50  to  300  revolutions  or 
more  per  minute,  some  form  of  "detachable  valve-gear"  is 
employed. 

The  first  successful  "  drop  cut-off "  engine  was  that  of  F. 
E.  Sickels,  of  1841,  which  employed  "puppet-valves"  on  the 
steam  side,  which  could  be  detached  and  allowed  to  fall  into 
their  seats  at  any  desired  point  in  the  stroke,  by  a  detaching 
mechanism  operated  either  by  hand  or  by  the  governor.  To 
prevent  injury  by  the  impact  of  the  valve  on  the  seat,  a  "  dash- 
pot  "  was  used,  consisting  of  a  vessel,  containing  either  water 
or  air,  into  which  a  loosely-fitted  piston  was  fitted.  This  piston, 
attached  to  the  valve-stem,  directly  or  indirectly,  rose  and  fell 
with  the  latter,  and  when  the  valve  was  about  to  strike  the 
seat  at  the  end  of  its  descent,  the  fall  was  checked  and  the 


34  A    MANUAL    OF   THE   STEAM-ENGINE. 

valve  "  eased  "  down  to  the  seat  by  the  resistance  of  the  fluid  in 
the  dash-pot,  on  which  the  piston  fell,  and  through  which,  for 
a  very  short  distance,  it  then  forced  its  way. 

Modifications  of  these  devices  were  devised  by  G.  H.  Cor- 
liss in  1849,  and  constitute  the  so-called  Corliss  engine  of  the 
present  time,  which  will  be  described  later.  Many  other  in- 
ventors have  since  constructed  still  other  engines  of  the  same 
general  character. 

The  latest  improvements  of  the  stationary  engine  relate 
to  what  are  distinctively  known  as  the  "  high-speed  "  engine, 
and  have  led  to  the  production  of  engines  especially  adapted 
to  driving  machinery  at  very  high  speeds  of  revolution.  In 
the  most  successful  engines  of  this  type  it  is  usual  to  make  the 
engine  itself  of  the  simplest  possible  design  ;  to  adopt  a  simple 
valve-motion,  and  to  secure  regulation  by  means  of  a  governor 
placed  on  the  main  shaft  and  adjusting  the  point  of  cut-off  by 
shifting  the  eccentric.  A  single  valve  is  often  used.  These 
engines  will  be  fully  described  in  the  next  chapter. 

Where  the  cost  of  securing  the  needed  condensing  water  is 
not  too  great,  and  where  the  steam-pressure  is  moderate,  a 
condenser  may  be  economically  added  to  the  non-condensing 
engine,  thus  obtaining  a  gain  in  power  of  considerable  amount 
and  an  increase  in  economy  of  steam  and  of  fuel,  if  the  engine 
is  well  proportioned  to  its  work  when  thus  altered,  of  often  one 
third — three  pounds  and  two  pounds  of  good  coal  per  horse- 
power and  per  hour  being  common  figures  for  such  engines 
working  non-condensing  and  condensing.  The  gain  in  power 
is  often  one  fourth  or  one  third.  But  with  increasing  pressure 
of  steam  this  gain  becomes  lessened. 

21.  The  Locomotive  was  one  of  the  fruits  of  the  inventive 
genius  of  Watt  and  his  contemporaries. 

When  the  steam-engine  had  so  far  been  perfected  that  the 
possibility  of  its  application  to  other  purposes  than  the  eleva- 
tion of  water  had  become  generally  recognized,  the  problem  of 
its  adaptation  to  the  propulsion  of  carriages  was  attacked  by 
many  engineers  and  inventors. 

As  early  as  1759  Dr.  Robison  called  the  attention  of  Watt 


THE  DEVELOPMENT  OF   THE   STEAM-ENGINE.  35 

to  the  possibility  of  constructing  a  carriage  to  be  driven  by  a 
steam-engine.  Watt,  at  a  very  early  period,  proposed  to  apply 
his  engine  to  locomotion,  and  contemplated  using  either  a  non- 
condensing  engine  or  an  air  surface-condenser.  He  included 
the  locomotive-engine  in  his  patent  of  1784,  and  his  assistant, 
Murdoch,  in  the  same  year  made  a  working-model  locomotive 
which  was  capable  of  running  at  a  rapid  rate. 

The  first  actual  experiment  was  made,  as  is  supposed,  by 
a  French  army  officer,  Nicolas  Joseph  Cugnot,  who  in  1769 
built  a  steam-carriage,  which  was  set  at  work  in  presence  of 
the  French  Minister  of  War,  the  Due  de  ChoiseuL  The  funds 
required  were  furnished  by  the  Comte  de  Saxe.  Encouraged 
by  the  partial  success  of  the  first  locomotive,  Cugnot,  in  1770, 
constructed  a  second,  which  is  still  preserved  in  the  Conserva- 
toire des  Arts  et  Metiers  Paris.  This  more  powerful  carriage 
was  fitted  with  two  non-condensing  single-acting  cylinders  thir- 
teen inches  in  diameter.  Although  the  experiment  seems  to 
have  been  successful,  there  appears  to  have  been  nothing  more 
done  with  it. 

An  American  of  considerable  distinction,  Nathan  Read, 
patented  a  steam-carriage,  1790.* 

In  1804  Oliver  Evans  completed  a  flat-bottomed  boat  to  be 
used  at  the  Philadelphia  docks,  and,  mounting  it  upon  wheels, 
drew  it  by  its  own  steam  engine  to  the  river-bank.  Launching 
the  craft,  he  propelled  it  down  the  river,  using  its  steam-engine 
to  drive  its  paddle-wheels.  Evans's  "oructor  ampltibolis*'  as  he 
named  the  machine,  was  the  first  road-locomotive  that  we  find 
described  after  Cugnot's  time.  Evans  asserted  that  carriages 
propelled  by  steam  would  soon  be  in  common  use :  and  offered 
a  wager  of  three  hundred  dollars  that  he  could  build  a  "steam- 
wagon"  that  should  excel  in  speed  the  swiftest  horse  that 
could  be  matched  against  it. 

Trevithick  and  Vivian  built  a  locomotive-engine  in  1804 
(Fig.  1 1)  for  the  railway  at  Merthyr-Tydvil,  in  South  Wales, 
which  was  quite  successful,  although  sometimes  giving  trouble 

*"  Nathan  Read  and  his  Steam-engine."    Xew  York : 


36  A    MANUAL    OF   THE   STEAM-ENGINE. 

by  slipping  its  wheels.    This  engine  had  one  steam-cylinder  4! 
inches  diameter,  and  carried  forty  pounds  steam. 

Colonel  John  Stevens,  of  Hoboken,  was  undoubtedly  the 
greatest  engineer  and  naval  architect  living  at  the  beginning  of 
the  present  century.  Without  having  .made  any  one  super- 
latively great  improvement  in  the  mechanism  of  the  steam- 
engine,  like  that  which  gave  Watt  his  fame  ;  without  having  the 


J_L 


FIG.  ii.— TREVITHICK'S  LOCOMOTIVE,  1804. 

honor  of  being  the  first  to  propose  navigation  by  steam,  or 
steam-transportation  on  land,  he  exhibited  a  far  better  knowl- 
edge of  the  science  and  of  the  art  of  engineering  than  any  man 
of  his  time,  and  he  entertained  and  urged  more  advanced  opin- 
ions and  more  statesmanlike  views,  in  relation  to  the  economi- 
cal importance  of  the  improvement  of  the  steam-engine,  both 
on  land  and  water,  than  seem  to  have  been  attributable  to  any 
other  leading  engineer  of  that  time. 

"""In"  1812  he  published  a  pamphlet  embodying  "  Documents 
tending  to  prove    the  Superior  Advantages  of  Railways   and 


THE   DEVELOPMENT  OF   THE   STEAM-ENGINE.  37 

Steam-carriages  over  Canal  Navigation."  *  At  this  time  the 
only  working  locomotive  in  the  world  was  that  of  Trevithick 
and  Vivian,  at  Merthyr-Tydvil,  and  the  railroad  itself  had  not 
grown  beyond  the  old  wooden  tram-roads  of  the  collieries.  Yet 
Colonel  Stevens  says  in  this  paper :  "  I  can  see  nothing  to 
hinder  a  steam-carriage  moving  on  its  ways  with  a  velocity  of 
one  hundred  miles  an  hour  " — adding  in  a  footnote :  "  This 
astonishing  velocity  is  considered  here  merely  possible.  It  is 
probable  that  it  may  not,  in  practice,  be  convenient  to  exceed 
twenty  or  thirty  miles  per  hour.  Actual  experiments  can  only 
determine  this  matter,  and  I  should  not  be  surprised  at  seeing 
steam-carriages  propelled  at  the  rate  of  forty  or  fifty  miles  an 
hour." 

He  proposed  rails  of  timber,  protected  when  necessary  by 
iron  plates,  or  to  be  made  wholly  of  iron.  The  car-wheels  were 
to  be  of  cast  iron,  with  inside  flanges  to  keep  them  on  the  track. 
The  steam-engine  was  to  be  driven  by  steam  of  fifty  pounds 
pressure  and  to  be  non-condensing. 

He  gives  500  to  JOOO  pounds  as  the  maximum  weight  to  be 
placed  on  each  wheel,  shows  that  the  trains — or  "  suites  of  car- 
riages," as  he  calls  them — will  make  their  journeys  "  with  as 
much  certainty  and  celerity  in  the  darkest  night  as  in  the  light 
of  day,"  shows  that  the  grades  of  proposed  roads  would  offer 
but  little  resistance,  and  places  the  whole  subject  before  the 
public  with  accuracy  of  statement  and  evident  appreciation  of 
its  true  value. 

In  1814  George  Stephenson,  to  whom  is  generally  accorded 
the  honor  of  having  first  made  the  locomotive-engine  a  success, 
built  his  first  engine  at  Killingworth,  England. 

In  1815  he  applied  the  blast-pipe  in  the  chimney,  by  which 
the  puff  of  the  exhaust  steam  is  made  useful  in  intensifying  the 
draught,  and  applied  it  successfully  to  his  second  locomotive, 
here  seen  in  section  (Fig.  12).  This  is  the  essential  character- 
istic of  the  locomotive-engine.  In  1815,  therefore,  the  modern 
locomotive  steam-engine  came  into  existence,  for  it  is  this 

*  Printed  by  T.  &  ].  Swords,  1160  Pearl  Street,  New  York,  1812. 


21C3D5 


38  A   MANUAL    OF   THE   STEAM-ENGINE. 

invention  of  the  blast-pipe  that  gives  it  its  life,  and  it  is  the 
mechanical  adaptation  of  this  and  of  the  other  organs  of  the 
steam-engine  to  locomotion  that  gives  George  Stephenson  his 
greatest  claim  to  distinction. 

In  1825  the  Stockton  and  Darlington  Railroad  was  opened, 
and  one  of  Stevenson's  locomotives,  in  which  he  employed  his 
"  steam-blast,"  was  successfully  used,  drawing  passenger  as  well 


FIG.  12. — STEPHEN-SON'S  LOCOMOTIVE,  1815. 

as  coal  trains.  Stephenson  had  at  this  time  become  engineer 
of  the  road.  The  time  required  to  travel  the  distance  of  twelve 
miles  was  two  hours. 

One  of  the  most  important  and  interesting  occasions  in  the 
history  of  the  application  of  the  non-condensing  steam-engine 
to  railroads,  as  well  as  in  the  life  of  Stephenson,  was  the  open- 
ing of  the  Liverpool  and  Manchester  Railroad  in  the  year  1829. 
When  this  road  was  built,  it  was  determined,  after  long  and 
earnest  discussion,  to  try  whether  locomotive-engines  might  not 
be  used  to  the  exclusion  of  horses,  and  a  prize  of  £500  was 
offered  for  the  best  that  should  be  presented  at  a  date  which 
was  finally  settled  at  the  6th  of  October,  1829.  Four  engines 
competed,  and  the  "  Rocket,"  built  by  Stephenson,  received 
the  prize. 

This  engine  (Fig.  13)  weighed  four  and  one  fourth  tons, 
with  its  supply  of  water.  Its  boiler  was  of  the  fire-tubular 
type,  a  form  that  had  grown  into  shape  in  the  hands  of  several 


THE  DEVELOPMENT  Of  THE  STEAM-EXGIXE.          39 


inventors,*  and  was  three  feet  in  tKamrtrr^  six  feet  long,  with 
twenty-fire  three-inch  tubes*  extending  from  end  to  end  of  the 
boiler.  The  steam-blast  was  carefully  adjusted  by  experiment, 
to  give  the  best  effect.  Stiry"  pressure  was  carried  at  fifty 
pounds  per  square  inch. 

The  average  speed  of  the  Rocket 
on  its  trial  was  fifteen  miles  per  hour, 
amf  •$•*  imyfrnnm  was  nearly  double 
that,  twenty-nine  miles  an  hour;  and 
afterward,  running  alone,  it  reached  a 
speed  of  thirty-five  miles. 

In  America  the  locomotive  was  set 
at  regular  work  on  railroads,  for  the 
first  time,  on  the  8th  of  August,  1829. 
This  first  locomotive  was  buOt  by  Fos- 
ter, Rastrick  &Co-,  at  Stourbridge,  Eng- 

land, and  was  purchased  by  Mr.  Horatio  Alien  for  the  Delia- 
ware  and  Hudson  Canal  Company's  road  from  Carbondale  to 
Honesdale,  Pennsylvania. 

It  was  at  about  this  time  (1831)  that  Mr.  Horatio  Allen 
introduced  the  first  eight-wheeled  locomotives  ever  built,  and 
gave  them  a  form  which  was  the  prototype  of  a  recentiy-baih 
locomotive  which  has  been  brought  out  in  Great  Britain.  In 
this  year,  also,  an  engine,  the  De  Witt  Clinton,  was  buflt  for 
John  B.  Jervis  of  the  Mohawk  and  Hudson  Railroad.  At  about 
the  time  of  the  opening  of  the  early  railroads,  the  introduction 
of  steam-carriages  on  the  common  highway  had  become  a 
favorite  idea  with  engineers.f 

In  December,  1833,  about  twenty  steam-carriages  and 
traction  road-engines  were  running  or  weie  in  course  of  con- 
struction in  and  near  London. 

In  our  own  country  the  roughness  off  roads  discouraged 
inventors,  and  in  Great  Britain,  even,  the  successful  introduc- 


i  &  COL,  Kew  Yotfc.  1879. 


4O  A    MANUAL   OF   THE   STEAM-ENGINE. 

tion  of  road-locomotives,  which  seemed  at  one  time  almost  an 
accomplished  fact,  finally  met  with  so  many  obstacles  that 
even  Hancock  and  Gurney,  the  most  ingenious,  persistent,  and 
successful  of  constructors,  gave  up  in  despair.  Hostile  legisla- 
tion procured  by  opposing  interests,  and  possibly  also  the 
rapid  progress  of  steam-locomotion  on  railroads,  caused  this 
result. 

The  steam-blast  of  Hackworth,  the  tubular  boiler  of  Seguin, 
and  the  link-motion  of  Stephenson  constitute  the  essential 
features  of  the  modern  locomotive-engine.  Locomotives  have 
gradually  and  steadily  increased  in  size  and  power  from  the  date 
of  their  introduction.  The  Rocket,  which  first  proved  con- 
clusively, in  1829,  the  value  of  steam-locomotion,  weighed  4^ 
tons.  In  1835  Robert  Stephenson,  who  had  constructed  it 
with  his  father,  writing  to  Robert  L.  Stevens,  said  that  he 
was  making  his  engines  heavier  and  heavier,  and  that  the  engine 
of  which  he  enclosed  a  sketch  weighed  nine  tons,  and  could 
draw  "  100  tons  at  the  rate  of  sixteen  miles  an  hour,  on  a  level." 
Locomotives  are  now  built  weighing  seventy  tons,  and  even 
pne  hundred,  and  powerful  enough  to  draw  more  than  2000 
tons  at  a  speed  of  twenty  miles  an  hour.  The  modern  loco- 
motive consists  of  a  boiler,  mounted  upon  a  strong  light  frame 
of  forged  iron,  by  which  it  is  connected  with  the  wheels.  The 
largest  engine  yet  constructed  in  the  United  States  is  said  to 
have  a  weight  of  about  200,000  pounds,  which  is  carried  on 
twelve  driving-wheels.  A  locomotive  has  two  steam-cylinders, 
either  side  by  side  within  the  frame,  and  immediately  beneath 
the  forward  end  of  the  boiler,  or  on  each  side  and  exterior  to 
the  frame.  The  engines  are  non-condensing  and  of  the  simplest 
possible  construction.  The  whole  machine  is  carried  upon 
strong  but  flexible  steel  springs.  The  steam-pressure  is  usually 
more  than  a  hundred  pounds.  The  pulling-power  is  generally 
about  one  fifth  the  weight  under  most  favorable  conditions, 
but  becomes  as  low  as  one  tenth  on  wet  rails.  The  fuel  em- 
ployed is  wood  in  new  countries,  coke  in  bituminous-coal 
districts,  and  anthracite  coal  in  the  eastern  part  of  the  United 
States.  The  general  arrangement  and  the  proportions  of  loco- 


THE  DEVELOPMENT  OF   THE  STEAM-ENGINE.  4! 

motives  differ  somewhat  in  different  localities,  as  will  be  seen 
later. 

The  common  three-ported  slide-valve  was  invented  by  Mur- 
doch, while  with  Watt,  about  1799.  This  valve,  driven  by  a 
system  of  single  loose  eccentrics  and  stops,  for  either  forward 
or  backward  gear,  was  adopted  by  Stephenson  and  others,  and 
probably  by  some  of  the  first  builders  of  the  marine  engine,  as 
well  as  on  the  locomotive,  as  early  as  or  earlier  than  1820.  At 
about  this  latter  date  the  heart-shaped  cam  and  its  frame  came 
into  temporary  use,  to  be  superseded  in  1840  or  18142  by  the 
so-called  Stephenson  link.  The  two  eccentrics,  for  forward  and 
backward  motion,  with  their  hooks  and  the  wedge-motion,  were 
also  in  use  during  this  period,  the  hooks  being  the  favorite 
arrangement,  towards  its  close,  on  locomotives.  The  link 


continues  in  use  as,  on  the  whole,  the  most  satisfactory  gear, 
although,  since  1855-60,  many  modifications  and  the  later  class 
of  "  radial "  gears  have  been  brought  into  competition  with  it. 
After  their  introduction,  the  growth  of  railroads  and  the  use 
of  locomotives  extended  in  the  United  States  and  in  Europe  with 
great  rapidity.  The  first  railroad  in  the  United  States  was 
built  near  Quincy,  Massachusetts,  in  1826.  In  1850  there  were 
about  700  miles  in  operation ;  in  1860  there  were  over  30,000, 
and  in  1890  about  160,000  miles  of  completed  road  in  the  United 
States ;  and  the  rate  of  increase  has  risen  in  1873  to  above  7000 
miles  per  year,  as  a  maximum,  and  the  consumption  of  rails  for 
renewal  alone  amounts  to  probably  a  million  tons  yer  year. 


42  A    MANUAL    OF    THE   STEAM-ENGINE. 

The  now  standard  engine  for  any  given  class  of  traffic  has 
assumed  such  exact  proportions  and  such  generally  accepted 
form  that  the  engines  of  any  two  well-known  builders,  though 
readily  distinguishable  by  the  expert  engineer,  appear  to  the 
inexperienced  observer  to  be  duplicates.  Thus  the  two  engines 
here  shown,  the  one  by  the  Baldwin  Works,  the  other  by  the 
Brooks  Company,  have  every  essential  feature  common ;  and 
all  are  more  or  less  obviously  related  and  modernized  forms  of 
the  older  types  of  engine. 


FIG.  15.— BROOKS  ENGINE. 

The  tubular  boiler  has  been  given  better  proportions  and 
has  greatly  gained  in  size ;  the  steam-blast  and  smoke-pipe  are 
as  used  in  Stephenson's  day ;  the  whole  system  of  "  running 
gear  "  is  that  of  Stephenson  ;  the  bell,  sand-box,  and  whistle 
are  characteristic  of  American  practice,  but  are  substantially 
the  same  with  all  American  builders.  The  frame  and  the  gen- 
eral external  arrangements  differ  from  those  of  the  British 
engine,  presently  to  be  shown  ;  but  in  even  this  comparison,  the 
main  characteristics  of  the  locomotive-engine  remain  equally 
distinguishable  and  equally  striking  in  both  forms. 

The  Gooch  and  Allan  forms  of  link  were  brought  out  about 
1855,  both  giving  nearly  equal  lead  at  both  ends,  and  simple 
kinematic  chains.  Engelmann,  in  1859,  substituted  pins  and 
links  for  the  sliding-block,  while  Stewart  and  Fink  had  already 
adopted  (1857)  a  single  eccentric.*  The  Von  Waldegg-Wal- 
schaerts  gear  came  out  in  1861. 

*  Trans.  Engrs.  of  Scotland;  Nov.,  1800. 


THE  DEVELOPMENT  OF   THE   STEAM-ENGINE.  43 

Hackworth's,  the  first  radial  gear,  came  out  in  1859,  an<^ 
many  years  later  (1878—88)  those  of  Brown,  Marshall,  Joy,  and 
Strong. 

The  "  drop,"  the  "  trip,"  or  the  "  detachable  "  gears  came 
in  in  1840  with  the  Hogg,  the  Sickels  (1841),  the  Corliss  (1849), 
the  Greene  (1855),  and  numerous  others,  both  in  Europe  and 
the  United  States. 

The  Steam  Fire-engine  is  still  another  form  of  transportable 
engine,  and  is  peculiarly  an  American  production. 

As  early  as  1830,  Braithwaite  and  Ericsson,  of  London,  Eng- 
land, built  an  engine  with  steam  and  pump  cylinders  of  7  and 
6^  inches  diameter,  respectively,  with  16  inches  stroke  of  piston. 
This  machine  weighed  2\  tons,  and  is  said  to  have  thrown  150 
gallons  of  water  per  minute  to  a  height  of  between  80  and  100 
feet.  It  was  ready  for  work  in  about  20  minutes  after  lighting 
the  fire.  The  first  attempt  made  in  the  United  States  to  con- 
struct a  steam  fire-engine  was  probably  that  of  Hodge :  who 
built  one  in  New  York  in  1841.  It  was  a  strong  and  very 
effective  machine,  but  was  too  heavy  for  rapid  transportation. 
The  late  J.  K.  Fisher,  who  throughout  his  life  persistently 
urged  the  use  of  steam-carriages  and  traction-engines,  design- 
ing and  building  several,  also  planned  a  steam  fire-engine. 
Two  were  built  from  his  designs  by  the  Novelty  Works,  New 
York,  about  1860,  for  Messrs.  Lee  &  Larned.  They  were 
"  self-propellers,"  and  one  of  them,  built  for  the  city  of  Phila- 
delphia, was  sent  to  that  city  over  the  highway,  driven  by  its 
own  engines.  The  other  was  built  for  and  used  by  the  New 
York  Fire  Department,  and  did  good  service  for  several  years. 
These  engines  were  heavy  but  powerful,  and  moved  at  good 
speed  under  steam.  The  Messrs.  Latta,  of  Cincinnati,  soon 
after  succeeded  in  constructing  comparatively  light  and  very 
effective  engines,  and  the  fire  department  of  that  city  was  the 
first  to  adopt  steam  fire-engines  definitely  as  their  principal  re- 
liance. 

The  steam  fire-engine  has  now  entirely  displaced  the  old 
hand-engine.  It  does  its  work  at  a  fraction  of  the  cost  of  the 
latter.  It  can  force  its  water  to  a  height  of  225  feet,  and  to  a 


44 


A   MANUAL   OF   THE  STEAM-ENGINE. 

jJllii 


THE  DEVEIJQPMEXT  OF  THE  STEAM-  EXC1XE.  45 

distance  of  more  than  500  feet  horizontally,  while  the  hand- 
engine  can  seldom  throw  it  one  thud  these  distances  :  and  the 
"steamer"  may  be  relied  upon  to  work  at  full  power  many 
hours  if  necessary,  while  the  men  at  the  hand-engine  soon  be- 
come fatigued,  and  require  frequent  relief. 

In  the  modern  standard  steam  fire-engine,  Fig.  16.  recipro- 
cating engines  and  pumps  are  adopted.  There  are  pairs  of 
engines  and  companion-pumps,,  working  on  cranks,  set  at 
right  angles,  and  turning  a  balance-wheel  set  hg-JiwM  them. 

Such  machines  illustrate  the  most  remarkable  concentration 
of  power  in  small  compass,  with  lightness  and  strength  of  parts. 
As  constructed  by  the  best  builders,  they  are  composed  of 
cfcoJC"*  materials,  are  exceedingly  carefully  and  well  propor- 
tioned, and  are  beautifully  finished.  Their  boilers  contain 
little  water,  and  are  crowded  with  J^Jf'ipg  surface  ;  they  there- 
fore make  steam  with  great  rapidity  ;  their  pumps  have  large 
pacn^gF«t  and  valves  of  small  lift,  and  deliver  large  volumes  of 
water  easily;  and  they  are  arranged  on  a  carriage  permitting 
rapid  and  easy  haulage.  The  heaviest  of  these  engines  rarefy 
weigh  much  over  three  tons,  and  they  are  made  as  light  as  two 


22-  The  Earif  Marine  Engine  was  an  early  outgrowth 
of  the  work  on  the  steam-engine  in  the  latter  part  of  the 
eighteenth  and  early  portion  of  the  nineteenth  century. 

In  1690  Papin  proposed  to  use  his  piston-engine  to  drive 
paddle-wheels  to  propel  vessels  ;  and  in  1707  he  applied  the 
steam-engine  which  he  had  proposed  as  a  pumping-enginc  to 
driving  a  model  boat  on  the  Fulda,  at  CasseL  His  pumping- 
engine  forced  up  water  to  turn  a  water-wheel,  which,  in  torn, 
was  made  to  drive  the  paddles.  An  account  of  his  experiment 
is  to  be  found  in  manuscript  in  the  correspondence  between 
Leibnitz  and  Papin,  preserved  in  the  Royal  Library  at  Ham- 
over. 

December  21,  1736,  Jonathan  HuHs  took  out  an  English 
patent  for  the  use  of  a  steam-engine  for  ship-propulsion,  pro- 
posing to  employ  his  steamboat  in  towing.  He  proposed  using 
the  Newcomen  engine,  fitted  with  a  counterpoise  weight,  and  a 


46  A    MANUAL    OF   THE   STEAM-ENGINE. 

system  of  ropes  and  grooved  wheels,  which,  by  a  peculiar 
ratchet-like  action,  gave  a  a  continuous  rotary  motion.  There 
is  no  positive  evidence  that  Hulls  ever  put  his  scheme  to  the 
test  of  experiment,  although  tradition  does  say  that  he  made  a 
model,  which  he  tried  with  such  ill  success  as  to  prevent  his 
further  prosecution  of  the  experiment. 

In  1774  the  Comte  d'Auxiron,  a  French  nobleman  and  a 
gentleman  of  some  scientific  attainments,  constructed  a  steam- 
boat, and  tried  it  on  the  Seine,  with  the  aid  of  M.  Perier.  This 
experiment  proving  unsuccessful,  M.  Perier  built  another  boat, 
which  he  tried  independently  in  1775,  but  was  again  unsuccess- 
ful, owing  principally  to  the  small  power  of  his  engine.  In 
1778,  and  again  1781  or  1782,  the  French  Marquis  de  Jouffroy, 
who,  in  his  later  experiments,  used  quite  a  large  vessel,  suc- 
ceeded in  obtaining  such  good  results  as  to  encourage  him  to 
persevere,  but,  political  disturbances  driving  him  from  his  coun- 
try, his  labors  terminated  abruptly. 

About  1785,  John  Fitch  and  James  Rumsey,  two  ingenious 
American  mechanics,  were  engaged  in  experiments  having  in 
view  the  application  of  steam  to  navigation.  Rumsey's  experi- 
ments began  in  1774,  and  in  1786  he  succeeded  in  driving  a 
boat  at  the  rate  of  four  miles  an  hour  against  the  current  of 
the  Potomac,  at  Shepardstown,  Maryland.  Rumsey  employed 
his  engine  to  drive  a  great  pump,  which  forced  a  stream  of 
water  aft,  thus  propelling  the  boat  forward.  This  same  method 
has  been  tried  by  the  British  Admiralty  in  the  Water-witch,  a 
gunboat  of  moderate  size,  using  a  centrifugal  p-ump  to  set  in 
motion  the  propelling  stream,  and  with  some  other  modifica- 
tions which  are  decided  improvements  upon  Rumsey's  rude  ar- 
rangements, but  which  have  not  done  much  more  than  did  his 
toward  the  introduction  of  "  hydraulic  propulsion,"  as  it  is  now 
called.  John  Fitch  was  an  ingenious  Connecticut  mechanic. 
After  roaming  about  until  forty  years  of  age,  he  finally  settled 
on  the  banks  of  the  Delaware,  where  he  built  his  first  steam- 
boat. In  1788  he  obtained  a  patent  for  the  application  of 
steam  to  navigation.  His  boat  was  sixty  feet  long  and  twenty 
feet  wide.  The  propelling  apparatus  was  a  system  of  paddles, 


THE  DEVELOPMENT  OF  THE   STEAM-ENGINE.  47 

which  were  suspended  by  the  upper  ends  of  their  shafts,  and 
moved  by  a  series  of  cranks,  one  to  each,  taking  hold  at  the 
middle,  and  giving  them  almost  exactly  the  motion  which  is 
imparted  to  his  paddle  by  the  Indian  in  his  canoe.  Fitch's 
boat,  when  tried  at  Philadelphia,  was  found  capable  of  making 
eight  miles  an  hour.  It  was  laid  up  in  1/92. 

In  1788  Patrick  Miller,  James  Taylor,  and  William  Symming- 
ton  attached  a  steam-engine  to  a  boat  with  paddle-wheels, 
which  had  been  built  by  the  first-named,  and  tried  it  for  the 
first  time  on  Dalswinton  Lake,  in  Dumfriesshire,  Scotland. 
This  boat  having  attained  a  speed  of  five  miles  an  hour, 
another  was  constructed  and  was  tried  in  1789.  This  vessel 
was  driven  by  an  engine  of  twelve  horse-power,  and  made 
seven  miles  an  hour.  This  result,  encouraging  as  it  was,  led 
to  no  further  immediate  action,  the  funds  of  the  experimenters 
having  failed. 

In  1801,  however,  Symmington  was  employed  by  Lord 
Dundas  to  construct  a  steamboat,  with  a  design  of  substituting 
steam  for  horse-power  on  canals.  The  Charlotte  Dundas,  as 
this  boat  was  named,  was  so  evidently  a  success  that  the  Duke 
of  Bridgewater  ordered  eiglit  similar  vessels  for  his  canal ;  but 
his  death,  soon  afterward,  prevented  the  order  being  filled. 

At  this  time,  several  American  mechanics  were  also  still 
working  at  this  attractive  problem.  In  i8o2-*3,  Robert  Fulton, 
with  Mr.  Joel  Barlow,  in  whose  family  he  resided,  and  Chan- 
cellor Livingston,  who  had  also  then  taken  up  a  temporary 
residence  in  Paris,  commenced  a  small  steamboat  eighty  six 
feet  long  and  of  eight  feet  beam.  The  hull  was  altogether 
too  slight  to  bear  the  weight  of  the  machinery,  and,  when 
almost  completed,  the  little  craft  literally  broke  in  two,  and 
sank  at  her  moorings. 

The  wreck  was  promptly  recovered  and  rebuilt,  and  in 
August,  1803,  the  trial-trip  was  made  in  presence  of  a  large 
party  of  invited  guests.  The  experiment  was  sufficiently 
successful  to  induce  Fulton  and  Livingston  to  order  an  engine 
of  Messrs.  Boulton  and  Watt,  directing  it  to  be  sent  to  America, 
where  Livingston  soon  returned.  In  1806  Fulton  followed, 


48 


A    MANUAL    OF    THE    STEAM-ENGINE. 


reaching  New  York  in  December,  and  at  once  going  to  work 
on  the  vessel  for  which  the  English  firm  sent  the  engine,  with- 
out being  informed  of  its  intended  use.  In  the  spring  of  1807 
the  Clermont  (Fig.  17),  as  the  new  boat  was  christened,  was 
launched  from  the  ship-yard  of  Charles  Brown,  on  the  East 
River,  New  York.  In  August  the  machinery  was  on  board, 


FIG.  17. — THE  CLERMONT,  1807. 

and  in  successful  operation.  The  hull  of  this  boat  was  one 
hundred  and  thirty-three  feet  long,  eighteen  feet  beam,  and 
seven  feet  in  depth.  The  boat  soon  afterwards  made  a  trip  to 
Albany,  making  the  distance  of  one  hundred  and  fifty  miles  in 
thirty-two  hours  running  time,  and  returning  in  thirty  hours. 
The  sails  were  not  used  on  either  occasion.  This  was  the  first 
voyage  of  considerable  length  ever  made  by  a  steam-vessel, 
and  the  Clermont  was  soon  after  regularly  employed  as  a 
passenger-boat  between  the  two  cities. 

Fulton,  though  not  to  be  classed  with  James  Watt  as  an 
inventor,  is  entitled  to  the  great  honor  of  having  been  the  first 
to  make  steam-navigation  an  every-day  commercial  success, 
and  of  having  thus  made  the  first  application  of  the  steam- 
engine  to  ship-propulsion  which  was  not  followed  by  the  retire- 
ment of  the  experimenter  from  the  field  of  his  labors  before 
success  was  permanently  insured. 

The  engine  of  the  Clermont  (Fig.  18)  was  of  rather  peculiar 


THE  DEVELOPMENT  OF   THE   STEAM-EXGIXE.  49 

form,  the  engine  being  coupled  to  the  crank-shaft  by  a  bell-crank, 
and  the  paddle-wheel  shaft  being  separated  from  the  crank- 
shaft, but  connected  with  the  latter  by  gearing.  The  cylinders 
were  twenty-four  inches  in  diameter  and  of  four  feet  stroke. 
The  paddle-wheels  had  buckets  four  feet  long,  with  a  dip  of 
two  feet. 


FIG.  sS.— Kxaxe  OF  THE  CLEKMOXT.  1807. 

Subsequently,  Fulton  built  several  steamers  and  ferry-boats, 
to  ply  about  the  waters  of  the  States  of  New  York  and 
Connecticut.  The  Clermont  was  a  boat  of  but  160  tons 
burden :  the  Car  of  Neptune,  built  in  1807,  was  295  tons ;  the 
Paragon,  in  1811,  measured  331:  the  Richmond,  1813,  370 
tons:  and  the  Fulton  the  First,  built  in  1814— '15,  measured 
2475  tons.  The  latter  vessel,  whose  size  was  simply  enormous 
for  that  time,  was  what  was  then  considered  an  exceedingly 
formidable  steam-battery,  and  was  built  for  the  United  States 
Navy.  Before  the  completion  of  this  vessel,  Fulton  died  of 
disease  resulting  from  exposure.  February  24,  1815,  and  his 
death  was  mourned  as  a  national  calamity. 

The  prize  gained  by  Fulton  was,  however,  most  closely  con- 
tested by  Colonel  John  Stevens,  of  Hoboken,  who  has  been 
already  mentioned  in  connection  with  the  early  history  of  rail- 
roads, and  who  had  been,  since  1791,  engaged  in  similar  ex- 
periments. In  1789  he  had  petitioned  the  Legislature  of  the 
State  of  New  York  for  an  act  similar  to  that  granted  Living- 
ston, and  stated  that  his  plans  were  complete  and  on  paper. 

In  1804,  while  Fulton  was  in  Europe,  Stevens  had  com- 
pleted a  steamboat  sixty-eight  feet  long  and  fourteen  feet 
beam,  which  combined  novelties  and  merits  of  design  in  a 


A    MANUAL   OF   THE   STEAM-ENGINE. 


FIG.  19.— S 


manner  that  was  the  best  possible  evidence  of  remarkable  in- 
ventive talent,  as  well  as  of  the  most  perfect  appreciation  of 
the  nature  of  the  problem  which  he  had  proposed  to  himself 
to  solve. 

The  steamboat  boiler  of  1804  (Fig.  19)  was  built  to  bear  a 
working  pressure  of  over  fifty  pounds  to  the  square  inch,  at  a 
time  when  the  usual  pressures  were 
from  four  to  seven  pounds.  It  con- 
sists of  two  sets  of  tubes,  closed  at 
one  end  by  solid  plugs,  and  at  their 
opposite  extremities  screwed  into  a 
stayed  water  and  steam  reservoir, 
which  was  strengthened  by  hoops. 
jjie  Wjj0ic  Of  tjje  iower  portion  was 

inclosed  in  a  jacket  of  iron  lined  with  non-conducting  material. 
The  fire  was  built  at  one  end,  in  a  furnace  inclosed  in  this 
jacket.  The  furnace-gases  passed  among  the  tubes,  down 
under  the  body  of  the  boiler,  up  among  the  opposite  set  of 
tubes,  and  thence  to  the 
smoke-pipe. 

The  engine  (Fig  20) 
was  a  direct-acting,  high- 
pressure  condensing  en- 
gine of  ten  inches  diam- 
eter of  cylinder,  two  feet 
stroke  of  piston,  and  drove 
a  screw  of  four  blades,  and 
of  a  form  which,  even  to- 
day, appears  quite  good. 

The  first  of  Stevens's  boats  performed  so  well  that  he  im- 
mediately built  another  one,  using  the  same  engine  as  before, 
but  employing  a  larger  boiler,  and  propelling  the  vessel  by 
twin-screws  (Fig.  21),  the  latter  being  another  instance  of  his 
use  of  a  device  brought  forward  long  afterward  as  new,  and 
since  frequently  adopted.  This  boat  was  sufficiently  success- 
ful to  indicate  the  probability  of  making  steam-navigation  a 
commercial  success,  and  Stevens,  assisted  by  his  sons,  built  a 


FIG.  20. — MACHINERY  OF  TWIN-SCREW  STEAMER 
OF  1804. 


THE  DEVELOPMENT  OF  THE  STEAM-EXCItfE.  $1 

boat  which  he  named  the  Phoenix,  and  made  the  first  trial  in 
1807.  just  too  late  to  anticipate  Fulton.  This  boat  was  driven 
by  paddle-wheels.  The  Phoenix,  shut  out  of  the  waters  of  the 
State  of  New  York  by  the  monopoly  held  by  Fulton  and  Liv- 
ingston, was  placed  for  a  time  on  a  route  between  Hoboken 
and  New  Brunswick :  and  then,  anticipating  a  better  pecuniary 


Fie.  zi.— SinrasV  Tvix-Kxns.  1*05- 

return,  it  was  concluded  to  send  her  to  Philadelphia  to  ply  on 
the  Delaware. 

At  that  time  no  canal  offered  the  opportunity  to  make  an 
inland  passage,  and  in  June,  1808,  Robert  L.  Stevens,  a  son  of 
John,  started  with  Captain  Bunker  to  make  the  passage  by  sea. 
Although  meeting  a  gale  of  wind,  he  arrived  at  Philadelphia 
safely,  having  been  the  first  to  trust  himself  on  the  open  sea  in 
a  vessel  relying  entirely  upon  steam-power.  From  this  time 
forward  the  Messrs.  Stevens,  father  and  sons,  continued  to  con- 
struct steam-vessels. 

The  steam-engine  in  most  general  use  for  sea-going  ships 
when  the  introduction  of  the  screw  compelled  its  withdrawal,, 
with  the  paddle-wheel  which  it  drove,  was  that  shown  in  Fig. 
22.  which  represents  the  side-lever  engine  of  the  steamer  Pacific, 
as  designed  by  Charles  \V.  Copeland. 

In  the  sketch,  A  is  the  steam-cylinder:  HCthe  side-rods,  or 
links,  connecting  the  cross-head  in  the  piston-rod  with  the  end- 
centre,  D,  of  the  side-lever  D  E  Ft  which  vibrates  about  the 
main  centre  E,  like  the  overhead  beams.  A  cross-tail  at  G  is 
connected  with  the  side-lever  and  with  the  connecting-rod  GH\ 


5  2  A --MA-NO At    Of   THE   STEAM-ENGINE. 

which  latter  communicates  motion  to  the  crank //,  turning  the 
main  shaft/.  The  air-pump  and  condenser  are  seen  at  O  M. 
This  engine  was  one  of  the  earliest  and  best  examples  of  the 
type,  and  perhaps  the  first  ever  fitted  with  a  framing  of 
wrought-iron. 


,849. 


After  the  experiments  of  Stevens,  we  find  no  evidence  of 
the  use  of  the  screw,  although  schemes  were  proposed  and 
various  forms  were  even  patented,  until  about  1836. 

In  1836  Francis  P.  Smith,  an  English  farmer  who  had  be- 
come interested  in  the  subject,  experimented  with  a  screw 
made  of  wood  and  fitted  in  a  boat  built  with  funds  furnished 
by  a  Mr.  Wright,  a  London  banker.  He  exhibited  it  on  the 
Thames  and  on  the  Paddington  Canal  for  several  months.  In 
February,  1837,  by  an  accident,  a  part  of  the  screw-blade  was 
broken  off,  and  the  improved  performance  of  the  boat  called 
attention  to  the  advisability  of  determining  its  best  propor- 
tions. In  1837  Smith  exhibited  his  courage  and  his  faith  in  the 


THE  DEVELOPMENT  OF   THE  ^TEAM-ENGINE.  53 

reliability  of  his  little  steamer  by  making  a  coasting-voyage  in 
quite  heavy  weather,  and  the  performance  of  his  vessel  was 
such  as  to  fully  justify  the  confidence  felt  in  it  by  its  designer. 
The  British  Admiralty  soon  had  its  attention  called  to  the  per- 
formance of  this  vessel,  and  to  the  very  excellent  results  at- 
tained  by  the  Archimedes,  a  vessel  of  237  tons  burden,  which  was 
built  by  Smith  and  his  coadjutors  in  1838  and  tried  in  1839,  at- 
taining a  speed  of  eight  knots  an  hour.  By  the  performance  of 
the  Archimedes,  the  advantages  of  screw-propulsion,  especially 
for  naval  purposes,  were  rendered  so  evident  that  the  British 
Government  built  its  first  screw-vessel,  the  Rattler,  and  Brunei 
adopted  the  screw  in  the  iron  steamer  Great  Britain,  which 
had  been  designed  originally  as  a  paddle-steamer. 

Simultaneously  with  Smith,  Captain  John  Ericsson  was  en- 
gaged in  the  same  project.  He  patented,  July,  1836,  a  propel- 
ler which  was  found  at  the  first  trial  to  be  of  such  good  form 
and  proportions  as  to  give  excellent  results.  His  first  vessel 
was  the  Francis  B.  Ogden,  named  after  the  United  States 
Consul  at  Liverpool,  who  had  lent  the  inventor  valuable  aid  in 
his  work.  The  boat  was  forty-five  feet  long,  eight  feet  beam, 
and  drew  three  feet  of  water.  It  attained  a  speed  of  ten  miles 
an  hour,  and  towed  an  American  packet-ship,  the  Toronto, 
four  and  a  half  miles  an  hour  on  the  Thames.  This  was  a 
splendid  success. 

Ericsson  built  several  screw-boats,  and  finally,  meeting  Cap- 
tain Robert  F.  Stockton,  of  the  United  States  Navy,  that  gen- 
tleman was  so  fully  convinced  of  the  merits  of  Ericsson's  plans 
that  he  ordered  an  iron  vessel  of  seventy  feet  length  and  ten 
feet  beam,  with  engines  of  fifty  horse-power.  The  trial  of  the 
Stockton,  in  1839,  was  eminently  satisfactory.  The  vessel 
was  sent  to  America  under  sail,  and  the  designer  was  soon  in- 
duced to  follow  her  to  this  country,  where  his  later  achieve- 
ments are  well  known.  The  engines  of  the  Stockton  were 
direct-acting,  the  first  examples  of  engines  coupled  directly  to 
the  crank-shaft,  without  intermediate  gearing,  that  we  meet  with 
after  that  of  John  Stevens.  Soon  after  Ericsson  arrived  in  the 
United  States  he  obtained  an  opportunity  to  design  a  screw- 


54  A   MANUAL    OF   THE    STEAM-ENGINE. 

steamer  for  the  United  States  Navy,  the  Princeton,  and,  at 
about  the  same  time,  the  English  and  French  governments 
had  screw-steamers  built  from  his  plans,  or  from  those  of 
his  agent  in  England,  the  Count  de  Posen.  In  these  ships — 
the  Amphion  and  the  Pomona — the  first  horizontal,  direct- 
acting  engines  ever  built  were  used.  They  were  fitted  with 
double-acting  air-pumps,  having  canvas  valves  and  other  novel 
features. 

In  these  ships — the  Amphion  and  the  Pomona — the  first 
horizontal,  direct-acting  engines  ever  built  were  used.  They 
were  fitted  with  double-acting  air-pumps,  having  canvas  valves 
and  other  novel  features. 

From  1840  the  screw  gained  favor  rapidly,  and  finally  began 
to  displace  the  paddle  for  deep-water  navigation.  Progress  in 
this  direction  was  at  first  somewhat  slow.  In  1840,  and  dur- 
ing the  following  ten  years,  many  experiments  were  instituted 
between  the  performances  of  screw  and  paddle  steamers  with- 
out definitely  settling  engineering  practice.  The  reason  was, 
probably,  that  the  introduction  of  the  rapidly-revolving  screw, 
in  place  of  the  slow-moving  paddle-wheel,  necessitated  a  com- 
plete revolution  in  the  design  of  their  steam-engines.  And  the 
unavoidable  change  from  the  heavy,  long-stroked,  low-speed 
engines,  previously  in  use,  to  the  light  engines,  with  small  cyl- 
inders and  high  piston-speed,  called  for  by  the  new  system  of 
propulsion,  was  one  that  necessarily  occurred  slowly,  and  was 
accompanied  by  its  share  of  those  engineering  blunders  and 
accidents  that  invariably  take  place  during  such  periods  of 
transition. 

The  earliest  days  of  screw  propulsion  witnessed  the  use  of 
steam  of  ten  or  fifteen  pounds'  pressure,  in  a  geared  engine 
using  jet-condensation,  and  giving  a  horse-power  at  an  expense 
of  perhaps  seven  or  eight  pounds  of  coal  per  hour.  A  little 
later  came  direct-acting  engines  with  jet-condensation,  and 
steam  at  twenty  pounds  pressure,  costing  about  five  or  six 
pounds  per  horse-power  per  hour.  The  steam-pressure  rose  a 
little  higher  with  the  use  of  greater  expansion,  and  the  economy 
of  fuel  was  further  increased.  The  introduction  of  the  surface- 


THE  DEVELOPMENT  OF   THE   STEAM-ENGINE.  55 

condenser,  which  began  to  be  generally  adopted  some  ten  or 
fifteen  years  ago,  brought  down  the  cost  of  power  to  between 
three  and  four  pounds  in  the  better  class  of  engines. 

At  about  the  same  time,  this  change  to  surface-condensation 
helping  greatly  to  overcome  the  troubles  arising  from  boiler- 
incrustation,  which  had  checked  the  rise  in  steam-pressure 
above  about  twenty-five  pounds,  and  it  being  at  the  same  time 
learned  by  engineers  that  the  deposit  of  the  scale  and  sulphate 
of  lime  in  the  marine  boiler  was  determined  by  temperature 
rather  than  by  the  degree  of  concentration,  and  that  all  the 
lime  entering  the  boiler  was  deposited  at  the  pressure  just 
mentioned,  a  sudden  advance  took  place.  Careful  design,  good 
workmanship,  and  skilful  management  made  the  surface-con- 
denser an  efficient  apparatus,  and,  the  dangers  of  incrustation 
being  thus  lessened,  the  movement  toward  higher  pressures 
recommenced  and  progressed  so  rapidly  that,  now,  over  one 
hundred  pounds  per  square  inch  is  very  usual,  and  three  hun- 
dred and  fifty  pounds  has  been  attained  in  marine  engines  built 
by  the  Messrs.  Perkins,  who  are  said  to  have  reached  the 
remarkable  economy  of  a  horse-power  for  each  pound  of  com- 
bustible in  the  fuel  consumed  in  the  boiler. 

These  high  pressures,  and  the  greater  expansion  of  the 
steam,  in  turn,  produced  another  revolution  in  engine-construc- 
tion. It  at  last  became  generally  known  that  one  of  the  most 
serious  losses  of  heat,  and  consequently  of  power,  in  the  steam- 
engine,  when  expansion  is  carried  to  a  considerable  extent, 
occurs  in  consequence  of  condensation  and  the  deposition  of 
moisture  upon  the  interior  of  the  cylinder,  which  moisture, 
when  the  exhaust  takes  place,  carries,  by  its  re-evaporation, 
large  quantities  of  heat  into  the  condenser,  without  deriving  any 
power  from  it.  This  loss  is  also,  in  some  degree,  prevented  by 
dividing  the  expansive  working  of  the  steam  among  two  or 
more  cylinders,  as  in  the  compound  system.  Here  the  heat 
wasted  in  either  cylinder  is  less,  in  consequence  of  the  lessened 
range  of  temperature  ;  and  that  lost  by  one  cylinder  is  carried 
into  the  second,  and  there,  to  some  extent,  utilized. 

The  amount  of  saving  effected  by  this  means  is  considera- 


56  A    MANUAL   OF   THE   STEAM-ENGINE.  • 

ble — so  great,  in  fact,  as  to  have  produced  a  complete  revolution 
in  engineering  practice  in  the  construction  of  marine  engines 
by  the  best-known  builders.  They,  under  the  lead  of  John 
Elder,  adopted  the  Woolf  engine,  which  had,  in  earlier  times, 
with  lower  steam,  less  expansion,  and  less  intelligent  engineer- 
ing, proved  apparently  a  failure. 

To-day  all  sea-going  steamers  are  fitted  with  multi-cylinder 
engines  having  surface-condensers,  and  with  tubular  boilers, 
which  are  fitted,  frequently,  with  superheaters. 

The  latest  and  largest  of  the  paddle  steamers  of  the  Cunard 
line,  the  Scotia,  built  in  1862,  was  379  feet  long,  and  of  3871 
tons  burden  ;  crossing  the  Atlantic  in  less  than  nine  days.  The 
engines  were  side-lever,  and  100  inches  diameter  of  cylinder,  12 
feet  stroke,  making  18  revolutions  per  minute,  and  producing 
4500  horse-power. 

The  marine  two-crank  compound  screw-engine  was  intro- 
duced still  later  into  the  United  States.  The  George  W. 
Clyde  was  built  by  the  Messrs.  Cramp  in  1871  ;  who,  in  1885, 
also  built  a  triple-expansion  engine  from  the  designs  of  Mr. 
See,  for  the  Peerless  steam-yacht,  as  an  experiment  to  de- 
termine the  value  of  the  system.  Its  success  led  to  their  per- 
manent adoption  of  that  type.  The  U.  S.  S.  Vesuvius,  in 
1889,  had  such  engines,  and  developed  4440  I.  H.  P.,  with 
a  weight  of  machinery  of  but  252  tons ;  and  gave  a  speed 
of  21.65  knots,  with  about  900  tons  displacement.  The  engines 
of  the  U.  S.  S.  Newark,  of  the  same  kind,  and  horizontal  and 
direct-acting,  developed  11.64  horse-power  per  ton  weight,  a 
total  of  8860  I.  H.  P. 

The  later  development  on  the  ocean  included  the  steamers 
Teutonic  and  Majestic,  built  in  1889-90.  The  former  crossed 
the  Atlantic,  from  Queenstown  to  New  York,  in  5  days,  19 
hours,  5  minutes,  the  quickest  trip  recorded  at  its  date. 
These  vessels  are  of  10,000  tons  burden,  17,000  horse-power, 
and  582  feet  long,  57^  feet  beam,  and  39^-  feet  depth.  They 
have  twin-screws,  with  independent  triple-expansion  engines. 
They  carry  1600  people,  of  whom  1300  are  passengers  and 
168  in  the  engineer's  crew. 


THE  DEVELOPMENT  OF   THE   STEAM-ENGINE. 


57 


The  steam-cylinders  are  of  43,  68,  and  I  ID  inches  diameter, 
and  5  feet  stroke,  making,  at  speed,  82  revolutions  per  minute. 
The  surface-condensers  each  contain  20  miles  of  brass  tubes, 
\  inch  diameter.  The  propellers  are  19  feet  diameter  and  28^ 
feet  pitch ;  twin-screws,  with  four  blades.  Twelve  boilers, 
containing  84  furnaces,  with  steam  at  180  pounds,  supply  the 
engines.  The  feed-water  amounts  to  120  tons,  the  condensing 
water  to  4000  tons,  per  hour,  and  the  coal  burned  to  320  tons 
per  day.  The  thrust  on  the  two  propellers  is  about  75  tons, 
total*  (See  Fig.  24.) 

The  advances  made  in  steam-navigation  since  the  days  of 
Stevens  and  Fulton  may  perhaps  be  best  realized  on  com- 
paring a  modern  steam-yacht  of  similar  dimensions  with  the 
little  screw  boat  of  1804.  That  here  shown,  as  built  by  the 
Douglas  Co.,  at  Waukegan,  Illinois,  has  very  nearly  the  same 
measurement — 26  feet  length,  6  feet  beam — but  it  weighs  only 


FIG,  23. — SMALL  STKAH-YACHT. 

one  ton,  carries  an  engine  of  3  effective  horse-power,  and  has  a 
speed  of  about  six  miles  an  hour,  a  higher  speed  than  that  of 
Fulton's  Clermont,  a  boat  of  five  times  its  length. 

23.  The  Later  Phases  of  construction  are  given  in  more 
detail  in  §  24.  By  the  year  1880,  the  standard  form  of  marine 
engine,  for  large  powers  and  for  long  voyages,  had  become 
the  "compound,"  or  double-cylinder  type,  expanding  steam 
from  a  pressure  of  75  to  90  pounds  (5  to  6  atmospheres),  by 
gauge,  through  two  cylinders,  "  in  series,"  into  a  condenser, 

*  London  Engineer,  Dec,  19,  1890, 


$8  A  MANUAL    OF    THE    STEAM-ENGINE. 

the  expansion  terminating  at  7  to  10  pounds  per  square  inch 
(£  to  f  atmosphere)  above  vacuum.  The  largest  engines  were 
constructed  with  a  pair  of  low-pressure  cylinders,  to  reduce  the 
difficulties  experienced  in  the  attempt  to  make  so  large  a  single 
low-pressure  cylinder ;  and  these  were  called  "  three-cylinder 
compound  engines." 

In  1890,  "  triple-expansion  engines"  had  become  common, 
employing  three  cylinders  li  in  series,"  and  using  steam  of  loto 
12  atmospheres  pressure  (150  to  180  pounds  per  square  inch  by 
gauge),  and  the  largest  of  these  were  given  twin  low-pressure 
cylinders. 

Speeds  of  piston  of  600  to  nearly  1000  feet,  and  70  to  90 
revolutions  per  minute,  were  usual,  with  engines  of  5  feet  stroke 
and  more,  producing  10,000  to  20.000  I.  H.  P.  in  the  propul- 
sion of  the  largest  and  fastest  steamships.  Meantime,  the 
weight  of  machinery  fell  from  about  1000  to  400  or  450  pounds 
per  horse-power. 

Ratios  of  expansion  were  restricted,  usually,  to  3  or  5  in 
simple,  7  to  8  in  compound,  and  12  to  15  in  triple-expansion 
engines,  and  the  cost  in  fuel  consumed  dropped  from  2^  or  3 
pounds  per  I.  H.  P.  per  hour  to  2^  and  2  and  to  i£  or  even 
less,  under  favorable  conditions. 

The  steady  rise  in  steam-pressures  during  the  century  is  best 
illustrated  by  naval  steam-engineering.  In  the  time  of  Watt  and 
up  to  about  1840,  the  usual  pressure  in  the  low-pressure  side- 
wheel  engines  of  that  period  was  from  4  to  7  pounds  (£•  to  ^ 
atmosphere)  by  gauge,  and  the  rude  flue-boilers  then  in  use 
were  of  the  simplest  and  weakest  forms.  By  the  middle  of  the 
century  the  fire-tubular  boiler  had  come  into  quite  common  use, 
and  pressures  had  risen  to  double  those  above  stated.  Between 
1850  and  1860,  the  customary  pressures  in  new  engines  and 
boilers  had  become  20  to  25  pounds  (i|  to  if  atmospheres)  and, 
the  introduction  of  the  surface-condenser  removing  the  princi- 
pal difficulty,  the  later  rise  in  pressure  was  rapid  and  has  never 
ceased. 

At  the  pressure  then  reached,  the  deposition  of  the  calcium 
sulphate  contained  in  sea-water  was  complete  and  the  conse- 


TOE  DEVELOPMENT  OF  THE  STEAJi-EXGlXE.  59 

quent  loss  of  economy  was  very  serious.  The  use  of  the  sur- 
face-condenser, by  reducing  this  loss,,  produced  a  gain  of  15  or 
20  per  cent. 

.  The  type  of  boiler  was  next  made  the  cylindrical,  Scotch, 
form,  with  large  flues  serving  as  furnaces  and  the  gases  re- 
turned through  tubes,  both  flues  and  tabes  enclosed  in  one 
cylindrical  shell,  and,  the  compound  engine  introduced,  the 
pressures  rising  rapidly  to  60  or  75  pounds  (4  or  5  atmospheres), 
by  gauge,  these  changes  respiting  in  a  further  economy  of  30 
or  even  40  per  cent  in  engines  designed  during  the  decade 
1860-70.  The  next  ten  years  carried  pressures  for  compound 
engines  up  to  90  and  120  pounds  (6  and  8  atmospheres)  and 
the  triple-expansion  engine,  coming  into  use,  1875-801,  die 
jMca&uic  has  risen  one  fourth  or  one  third  more,  this  type  giv- 
ing a  gain  of  15  or  20  per  cent  over  the  earlier  compound 


_ 

The  following  have  been  considered  fair  average  figures,  as 
representing  what  was  good  and  standard  practice  at  the  dates 
given,  and  as  illustrating  the  piugmat  •  fr^fr'1  in  wnnmin*  engi- 
neering in  the  period  1870-90: 

Cooflpcrl  H.F. 


.:,-::  :-:-  I    .-:    ~- 

1*30  50  X.I  375  =  :•: 

:  ^  480  jSo 

Tii|ili  ----------  iSgo  :-•-  i-3  *•  •'  450 

In  exceptional  cases,  as  in  torpedo-boats,  the  progiebe.  in 
Hgin^raingfriachfncr>,  but  not  in  efficiency,  has  been  still  greater. 


piston  speeds  having  risen  to  above  1000  feet  per  minute.  The 
weights  of  the  two-  and  of  the  three-cyunder  compound  engine, 
as  now  customarily  buflt.  are  not  very  different.  Forexample, 
the  following,  as  given  by  Mr.  Hall  in  1887,  gives  the  weights 
of  two  selected 

TWD  Cyfl.       Tbrce  Cy - 


-' 


1150  lifo 

:    :  457 


60  ;. . ,'   A   MANUAL   OF  .  THE  STEAM-ENGINE. 

The  difference  is  here  rather  less  than  ten  per  cent,  in  favor 
of  the  later  type. 

The  gradual  reduction  of  weights  of  steam  machinery  dur- 
ing the  period  succeeding  the  middle  of  the  nineteenth  century- 
is  best  illustrated  by  reference  to  the  changes  effected  in  naval 
work.  The  minimum  weight  in  1850  was  about  200  pounds 
each,  engines  and  boilers,  per  I.  H.  P.,  400  pounds  total ;  while 
these  figures  were  reduced  by  1860  to  about  175  and  350;  in 
1870  to  150  and  300;  in  1880  to  125  or  140,  and  275  or  280; 
in  1885  to  80  or  90  for  engines,  and  100  for  boiler,  less  than 
200  total;  and  in  1 890  to  40 or  50,  70  or  75,  and  100  to  125  total, 
and  even  less  in  exceptional  cases,  as  in  fast  yachts  and  torpedo- 
boats.  The  lightest  examples  are  as  low  as  60  or  80  pounds, 
total,  per  horse-power.  The  adoption  of  simple  types,  of  high 
engine-speed,  and  of  forced  draught  is  the  secret  of  the  rapid 
gain  at  the  later  dates. 

According  to  Sennett,  the  reduction  in  weight  of  the  ma- 
chinery of  naval  vessels  has  steadily  progressed  since  the  early 
part  of  the  nineteenth  century,  and  since  the  advent  of  steam 
navigation.  In  1832,  with  side-lever  paddle-wheel  engines,  flue- 
boilers  carrying  but  4  Ibs.  of  steam,  and  jet-condensers,  there 
was  but  1.45  I.  H.  P.  obtained  per  ton  of  weight.  Tubular 
boilers  and  9  Ibs.  pressure  increased  the  power  to  3.14  I.  H.  P. 
per  ton  in  1845  •  oscillating  engines  and  14  Ibs.  of  steam  to  4.72 
I.  H.  P.  per  ton  in  1850;  screw  engines  and  20  Ibs.  of  steam 
to  5.52  I.  H.  P.  in  1857  :  anci  the  surface-condenser  and  30  Ibs. 
of  steam  to  7.5  I.  H.  P.  per  ton  in  1870.  The  compound 
engine  with  6b  Ibs.  of  steam  only  gave  6.4  I.  H.  P.  per  ton  of 
machinery  in  1876,  but  greatly  reduced  the  total  weight  carried 
on  account  of  reduced  coal  consumption.  Triple  compound 
engines  produce  a  saving  in  fuel,  rather  than  of  weight,  to  be 
carried.  The  increase  of  weight  due  to  compound  and  triple 
compound  engines  is  chiefly  caused  by  the  heavier  boilers  re- 
quired for  the  higher  pressures,  though  the  engines  are  also 
generally  somewhat  heavier.  The  introduction  of  forced  blast 
has  enabled  the  weight  of  the  boiler  to  be  reduced,  and  this, 
with  high  speed,  reduces  the  weight  of  the  engine  so  that  tor- 


THE.  DEVELOPMENT  OF-  THE  STEAJt-EXGJXE. 


6l 


pedoJboat  machinery  in  1880  gave  3jj66  I.  H.  P.  per  ton  of 
weight,  and  in  a  last  steamer  butft  in  1882,  12.36  L  H.  P.  was 
obtained  per  ton  of  weight. 

The  later  progress  and  current  practice  in  the  application 
of  steam-power  in  smaH  boats  is  well  shown  by  the  facts  in  the 
department  of  naval  construction ;  and  especially  in  the  recent 


introduction  of  surface-condensation  and  compounding  and  of 
a  forced  draught.  About  1863-5,  the  naval  steam-launch  was 
about  40  feet  long,  was  fitted  with  a  high-pressure  engine  of  25 
H.  P.T  and  had  a  speed  of  6  knots.  In  1870  the  speed  and 
power  had  risen  to  8J  knots  and  50  H.  P.:  in  1880  to  nearly 
ten  knots  with  nearly  the  same  power,  in  consequence  of  im- 


62 


A    MANUAL   OF   THE   STEAM-ENGINE. 


proved  lines  and  higher  efficiency  of  machinery  and  reduced 
weights.  At  this  date,  a  boat  sixty  feet  long,  with  engines  of 
150  H.  P.,  and  weighing  6£  tons,  attained  a  speed  of  15  knots 
(17^  miles,  nearly).  Recent  trials  of  simple  and  compound 
engines,  in  competition,  as  reported  to  the  British  Admiralty, 
gave  7^  and  4  pounds  of  fuel  as  respectively  required.  Their 
weights  were  nearly  the  same :  180  and  150  pounds,  nearly,  per 
I.  H.  P.* 

By  the  introduction  of  forced  combustion  in  the  boiler-room, 
of  steam  steering,  and  of  anchor-  and   cargo-hoisting  machin- 


FIG.  25  —THE  NEW  YORK. 

ery,  and  various  other  changes,  the  number  of  tons  trans- 
ported per  person  employed  on  shipboard  has  been  increased 
from  2£  to  3^  between  1860  and  1890,  or  about  doubled  in 
the  present  century.  The  speeds  of  passenger-steamers  now 
often  exceed  20  knots  (about  23  miles)  an  hour  for  an  average, 
crossing  the  Atlantic.  The  mean  of  sixteen  voyages  of  the 
City  of  New  York,  the  City  of  Paris,t  and  the  Teutonic 
was  about  six  days  and  a  quarter,  between  New  York  Bay  and 
Queenstown  harbor  (1890). 

In  contrast  with   the  Clermont,  we  may  note  the  principal 


*  Machinery  of  Small  Boats;  A.  Spyer ;  Trans.  Brit.  Inst.  N.  Archts., 
XXVIIth  Session. 

f  From  paper  by  Mr.  C.  E.  Emery  in  the  Scientific  American  Supplement, 
1890. 


THE   DEVELOPMENT  OF   THE   STEAM-ENGINE.  63 

features   of  the  steamer  New  York,  built  eighty  years  later, 
for  the  same  route,  by  the  Harlan  &  Hollingsvvorth  Company, 
and  "  engined  "  by  the  W.  &  A.  Fletcher  Company.    (Fig.  25.) 
The  dimensions  of  hull  are  as  follows : 

Length  on  the  water-line 301  feet. 

Length  over  all 311  " 

Breadth  of  beam,  moulded 40  " 

Breadth  of  beam,  over  guards 74  " 

Depth,  moulded 12  "3  ins. 

Draught  of  water 6  " 

Tonnage  (net,  1091.89) i$52-S2 

The  wheels  are  aft  of  the  centre  of  length,  instead  of  for- 
ward— a  great  improvement  in  the  appearance  of  the  boat. 

The  engine  is  a  beam-engine,  with  a  cylinder  75  inches  dia- 
meter and  12  feet  stroke  of  piston,  provided  with  Stevens'  cut- 
off. The  use  of  a  surface-condenser,  instead  of  a  jet-con- 
denser, in  this  river  steamer,  is  a  change  made  to  overcome 
the  evil  of  using  mixed  salt  and  fresh  water  in  the  boilers,  as 
the  tides  extend  to  Albany  and  the  water  changes  from  salt  to 
fresh  en  route. 

Another  change  is  the  return  to  the  use  of  Stevens'  feather- 
ing wheels.  These  are  30  feet  2  inches  diameter  outside  of 
buckets.  There  are  twelve  curved  steel  buckets  to  each  wheel. 
Each  bucket  is  3  feet  9  inches  wide  and  12  feet  6  inches  long. 
The  wheels  are  overhung,  and  they  have  a  bearing  on  the  hull 
only.  The  feathering  is  effected  in  the  usual  manner  by  driv- 
ing and  radius  bars,  operated  by  a  centre  placed  eccentric  to 
the  shaft  and  held  by  the  "  A-frame  "  on  the  guard.  These 
wheels  were  introduced  in  the  New  York  for  the  purpose  of  gain- 
ing speed,  and  the  trial-trip  shows  that  the  builders'  expecta- 
tions were  completely  fulfilled.  Absence  of  jar  is  another  gain 
obtained  by  the  use  of  these  wheels,  and  the  comparatively 
thin  buckets  enter  the  water  so  clean  and  smooth  that  one 
notices,  not  the  shake  so  common  on  boats  with  the  ordinary 
wheels,  but  an  almost  entire  absence  of  it. 

Steam  is  supplied  to  the  engine  by  three  return-flue  boilers, 


64  A    MANUAL   OF   THE   STEAM-ENGINE. 

each  g\  feet  diameter  of  shell,  1 1  feet  width  of  front,  and  33 
feet  long,  constructed  for  a  working  pressure  of  50  pounds  per 
square  inch.  Each  boiler  has  a  grate-surface  of  76  square  feet 
or  228  square  feet  in  all,  and  with  the  forced  draught  produce 
3850  horse-power. 

The  exterior  is  of  pine,  painted  white  relieved  with  tints 
and  gold.  The  interior  is  finished  in  cabinet  work,  and  is  all 
hard  wood,  ash  being  used  forward  of  the  shaft  on  the  main 
deck,  and  mahogany  aft  and  in  the  dining-cabin.  Ash  is  also 
used  in  the  "grand  saloons"  on  the  promenade  deck.  The 
saloon-sides  are  almost  entirely  of  glass,  and  the  windows  so 
low  that  persons  seated  inside  have  an  opportunity  to  view  the 
scenery. 

The  Puritan,  Fig.  26,  illustrates  the  adaptation  of  this  type 
of  steamer,  so  nearly  perfected  by  Robert  L.  Stevens,  to  that 
kind  of  navigation,  intermediate  between  river,  or  still-water, 
and  oceanic,  which  permits  the  retention  of  some  features  of 
the  former,  while  modifying  the  shape  of  hull  and  type  of 
engine  to  meet  the  demands  of  "  outside  "  navigation. 

The  plans  of  this  steamer  are  by  Mr.  Pierce,  the  details  of 
hull-construction  by  Mr.  Faron,  and  the  machinery  by  the 
W.  &  A.  Fletcher  Co.  The  principal  dimensions  are  as  fol- 
lows :  Length  over  all,  420  feet ;  length  on  the  water-line,  404 
feet;  width  of  hull,  52  feet;  extreme  breadth  over  guards,  91 
feet ;  depth  of  hull  amidships,  21  feet  6  inches  ;  height  of  dome 
from  base-line,  63  feet ;  whole  depth,  from  base-line  to  top  of 
house  over  the  engine,  70  feet.  Her  total  displacement,  ready 
for  a  trip,  is  4150  tons,  and  her  gross  tonnage  4650  tons. 

The  ship  is  fire-proof  and  unsinkable,  having  a  double  hull, 
divided  into  59  water-tight  compartments,  52  between  the 
hulls  and  7  made  by  athwartship  bulkheads.  In  the  fastenings 
of  hull  and  compartments  there  were  used  700,000  rivets,  and 
upwards  of  thirty  miles  of  steel  angle-bar.  Her  decks  are  of 
steel,  wood-covered.  Her  masts  are  of  steel,  and  hollow,  to 
serve  as  ventilators,  and  are  22  inches  in  diameter.  Her  pad- 
dle-wheels are  encased  in  steel. 

The  hull  is  of  "  mild  steel,"  twenty  per  cent  stronger  than 


66  A   MANUAL   OF   THE  STEAM-ENGINE. 

iron.  The  wheels  are  of  steel,  and  are  35  feet  in  diameter  out- 
side the  buckets.  The  buckets  are  14  feet  long  and  5  feet 
wide,  each  bucket  of  steel  £  inch  thick,  and  weighing  2800 
pounds  without  rocking  arms  and  brackets  attached.  The  total 
weight  of  each  wheel  is  loo  tons.  The  wheels  are  "  feathering," 
and  turn  at  the  rate  of  24  revolutions  a  minute. 

The  boat  has  a  compound,  vertical,  beam,  surface-condensing 
engine  of  7500  horse-power.  The  high-pressure  cylinder  is  75 
inches  in  diameter,  and  9  feet  stroke  of  piston.  The  low-pres- 
sure cylinder  is  110  inches  in  diameter,  and  14  feet  stroke  of 
piston.  The  surface-condenser  has  15,000  square  feet  of  cool- 
ing surface  and  weighs  53  tons.  Of  condenser-tubes  of  brass 
there  are  14^  miles.  Her  working-beam  is  34  feet  in  length 
from  centre  to  centre,  17  feet  wide,  and  weighs  42  tons.  The 
section  of  beam-strap  measures  9i  X  ni  inches.  The  main 
centre  of  the  beam  is  19  inches  in  diameter  in  its  bearings.  The 
shafts  are  27  inches  in  diameter  in  main  bearings,  and  30  inches 
in  gunwale  bearing.  They  weigh  40  tons  each.  The  cranks 
weigh  9  tons  each.  The  crank-pin  is  19  inches  in  diameter 
and  22  inches  long. 

The  boilers  contain  850  square  feet  of  grate-surface  and 
26,000  square  feet  of  heating  surface.  The  products  of  com- 
bustion pass  through  two  super-heaters,  8  feet  10  inches  inside 
diameter,  and  12  feet  4  inches  outside  diameter,  by  12  feet 
high;  thence  into  two  smoke  stacks,  the  top  of  each  being  101 
feet  i  inch  from  the  keel. 

The  dining-saloon  is  108  feet  4  inches  in  length,  by  30  feet 
in  width,  and  12  feet  in  height.  There  are  12  miles  of  electric- 
lighting  wire,  and,  including  annunciators,  fire-alarm,  etc., 
there  are  twenty  miles  of  wire  and  twelve  thousand  feet  of 
steam-pipe.  There  are  capacious  gangways  and  staircases, 
lofty  cornices,  and  ceilings  supported  by  tasteful  pilasters,  the 
tapering  columns  of  which,  in  relief,  flank  exquisitely-tinted 
panelling  throughout  the  length  of  her  saloons.  Every  con- 
venience known  to  civilization,  and  which  can  contribute  to  the 
ease  and  comfort- of  the  traveller  on  land  or  when  afloat,  is  in- 
cluded in  the  internal  arrangements  of  this  floating  caravansary. 


THE  DEVELOPMENT  OF   THE   STEAM-ENGINE.  67 

The  electric-light  currents  are  generated  by  four  dynamos, 
each  designed  with  a  capacity  of  400  lights,  or  a  total  of  1600 
lights,  but  capable  of  maintaining  1850  lights  if  required. 

These  great  steamers  have  all  the  essential  features  of  the 
earlier  river-boats  of  Stevens :  the  same  long,  flat,  shallow  hull, 
the  widely-extended  guards  and  main  deck ;  the  "  hog-frames" 
stiffening  the  whole  structure ;  the  same  type  of  "  beam-engine," 
as  a  rule :  and  the  high  deck-houses ;  but  the  progress  of  the 
century  is  seen  in  their  enormous  size,  great  power  and  speed, 
and  their  innumerable  conveniences  and  luxuries. 

The  fleets  of  vessels  employed  on  the  great  lakes  between 
the  United  States  and  Canada  have  become  mainly  steam- 
fleets  ;  the  principal  part  of  the  lake  transportation  of  ores,  tim- 
ber, and  grain  being  now  carried  on  in  craft  like  that  seen  in 


the  accompanying  illustration,  a  type  of  vessel  peculiarly 
American.  The  figure  represents  the  Tuscarora,  built  at 
Cleveland,  by  the  Globe  Iron  Works,  for  the  Lehigh  Valley 
fleet,  at  a  cost  of  about  $250,000.  Vessels  of  this  class  are 
built  of  steel  and  fitted  with  multiple-cylinder  engines,  and  are 
both  fast  and  economical. 

The  Tuscarora  is  312  feet  over  all,  40  feet  beam,  and  25^ 
feet  deep.     The  weight  of  hull  exceeds  1600  tons.     She  has 


OS  A   MANUAL    OF   THE   STEAM-ENGINE. 

two  flush  steel  decks,  the  top  covered  with  3-inch  pine,  and  an 
additional' tier  of  deck-beams  below,  or  a  third  deck.  The 
water-bottom  runs  clear  aft,  and  there  are  three  longitudinal 
keelsons  on  either  side  of  the  main  keelson.  The  triple-expan- 
sion engines  have  24-,  38-,  and  6t-inch  cylinders  of  42  inches 
stroke.  There  are  three  boilers,  12  X  \2\  feet,  carrying  160 
pounds  of  steam. 

'"  The  growth  of  tonnage  on  these  lakes  now  exceeds  100,000 
tons  per  annum  ;  or  about  the  same  as  the  total  of  the  At- 
lantic and  Pacific  coasts.  The  steamers  employed  are  usually 
very  similar  in  general  construction  to  that  here  illustrated, 
the  high  deck-houses  and  cabins  of  the  river  steamer  being 
necessarily  omitted  as  a  matter  of  safety,  and  the  comparatively 
smooth  and  low  house  of  the  ocean  steamer  substituted.  The 
deeper  water  also  permits  the  use  of  the  screw  on  the  largest 
vessels. 

24.  Recent  Applications  of  the  multiple-cylinder  engine  have 
become  usual  in  every  department  of  steam-engineering.  The 
efforts  of  Hornblower  and  of  Wolff  and  their  contemporaries 
failed,  partly  because  of  the  active  business  competition  of 
Boulton  and  Watt,  who  possessed  at  the  time  enormous  advan- 
tages and  immense  power,  but  mainly  because  the  steam-pres- 
sures and  speeds  of  piston  then  adopted  were  too  low,  and  the 
practicable  range  of  expansion  was  too  small,  to  permit  the 
advantages  of  the  more  complex  type  of  engine  to  become  obvious 
and  important.  But  when  the  steam-pressure  carried  on  other 
engines  began  to  rise  toward  three  and  four  atmospheres,  the 
ratios  of  expansion  to  exceed  three  or  five,  the  serious  wastes 
arising  from  initial  cylinder-condensation  began  to  be  seen,  and 
were  found  to  place  an  early  limit  to  economically  increased 
expansion.  This  limit,  as  well  as  the  economical  operation  of 
the  engine  at  the  earlier  limit,  was  promptly  modified  when  the 
new  construction  was  adopted  ;  and  it  was  found  that  not  only 
was  the  efficiency  of  the  engine  at  ratios  of  expansion  then 
considered  maxima  greatly  increased,  but  that  it  was  possible 
to  economically  extend  expansion  very  much  farther  than  was 
practicable  in  a  single  cylinder.  As  steam-pressures  continued 


THE  DEVELOPMENT  OF  THE  STEAM-EXGIXE.  69 

to  rise,  and  as  expansion  was  correspondingly  increased,  the 
gain  by  compounding  became  more  observable  and  important, 
and  the  new  engine  found  more  general  application;  nntil 
now  it  is  employed  almost  exclusively  in  marine  engineering, 
and  very  extensively  in  other  departments.  The  increase  of 
steam-pressure  above  one  hundred  pounds  per  square  inch, 
above  six  or  seven  atmospheres,  has  led  to  the  introduction  of 
the  triple-compound,  or  "triple-expansion."  engine,  and  pres- 
sures exceeding  ten  atmospheres  are  already  making  the 
"  quadruple-expansion  "  engine  a  desirable  type  where  great 
economy  of  fuel  is  essential.  In  all  cases,  in  marine  engines,  it 
is  found  advisable,  in  good  types  of  engine,  to  expand  steam 
down  to  from  ten  to  eight  pounds  per  square  inch  above  per- 
fect vacuum,  to  about  a  half  atmosphere  pressure,  to  secure 
best  results.  The  better  the  design  the  lower  this  limit. 

The  advantages  of  the  multicylinder  engines  have  become 
so  evident  that,  since  about  1870;  they  have  been  adopted  as 
standard  by  the  .navies  of  the  world,  in  spite  of  the  obvious 
objections  to  high  steam  and  their  inflexibility  of  power  adjust- 
ment in  modern  warfare. 

Multiple-cylinder  marine  engines  are  used  to  the  almost 
entire  exclusion  of  the  older  forms  of  simple  engine.  Although 
invented  by  Horn  blower  in  1781,  and,  in  the  more  common 
types,  by  Wolff  in  1804,  it  was  only  when,  a  half-century 
later  still,  Messrs.  Randolph  and  Elder  in  the  screw- 
steamer  Brandon  (1854)  and  the  paddle-steamers  Valpa- 
raiso and  Xica  and  others,  still  later,  of  the  Pacific  Steam 
Navigation  Co..  made  this  type  practically  a  success,  that  it 
attracted  the  general  attention  of  engineers.  From  that  time 
it  has  steadily  and  rapidly  displaced  the  simple  engine.  The 
gain  of  the  two-cylinder  compound  engine,  when  compared 
with  the  standard  simple  marine  engine,  was  found  to  be  from 
20  to  40  per  cent,  averaging  in  those  early  days  probably  33 
per  cent.  This  was  enough  to  secure  their  general  introduc- 
tion with  great  rapidity,  once  the  fact  was  established. 

The  most  common  form  given  the  two-cylinder  compound 
engine,  of  the.  best  construction,  is  that  shown  in  a  succeeding 


70  A   MANUAL    OF   THE   STEAM-ENGINE. 

illustration  (Chap.  II,  Fig.  112),  and  is  that  almost  universally 
adopted  for  vessels  of  the  merchant  marine.  Many  designs,  dif- 
fering greatly  among  themselves  and  from  the  above,  have  been 
introduced  into  the  ships  of  the  fighting  classes  in  the  navy, 
having  mainly  in  view  the  reduction  of  their  vertical  dimen- 
sions and  getting  them  well  below  the  water-line  and  out  of 
reach  of  shot.  It  is  also  sometimes  attempted  in  naval 
engines  to  so  make  their  steam-connections  that  either  or  both 
cylinders  may  be  supplied  with  steam  directly  from  the  boilers, 
should  any  exigency  or  an  emergency  make  it  desirable.  The 
principles  of  designing,  of  proportioning,  and  of  construction 
are  precisely  the  same,  however,  whatever  the  method  of 
grouping  the  engine-cylinders  or  their  details  and  accessories. 

In  the  cases,  becoming  common  in  the  United  States,  but 
comparatively  rare  in  Europe,  in  which  the  engine  is  proposed 
to  be  made  a  beam-engine  and  is  to  drive  paddle-wheels,  the 
usual  method  of  compounding  is  to  place  the  two  cylinders  at 
the  same  end  of  the  beam  and  as  closely  together  as  possible.  In 
the  Buckeye  State,  designed  by  Mr.  Erastus  Smith  about  the 
middle  of  the  century,  the  low-pressure  piston  was  an  annulus 
working  between  the  exterior  surface  of  the  high-pressure  and 
the  internal  surface  of  the  low-pressure  cylinder ;  both  pistons 
being  connected  to  a  common  cross-head  and,  by  the  same 
pair  of  links,  to  the  extremity  of  the  beam.  The  compound 
engines  of  the  City  of  Fall  River  were  found  to  give  higher 
efficiency,  by  one  fourth  or  one  third,  than  the  simple  engines 
customarily  employed  on  Long  Island  Sound  in  the  same 
work.* 

Perhaps  as  near  an  approach  to  ideal  efficiency  as  has  yet 
been  recorded,  all  things  considered,  is  that  of  M.  Normand's 
torpedo-boat  in  the  French  navy,  No.  128;  the  engines  of 
which  are  reported  to  have  demanded  but  0.462  kilogs  of  fuel 
per  horse-power  and  per  hour  (1.16  Ibs.  per  British  H.  P.). 

These   engines   were    "receiver-compounds,"    with    steam 


*  Report  on  the  City  of  Fall  River,  by  Messrs.  Sague  and  Adger  ;  with  intrt 
duction  by  R.  H.  Thurston;  Jour.  Frank.  Inst.,  July,  1884. 


THE  DEVELOPMENT  OF   THE   STEAJi-ElfGIXE.  /I 

entering  at  4.3  atmospheres  (70  Ibs.),  with  clearances  of  10.6 
and  614  per  cent.*  The  power  attained  was  940  I.  H.  P.,  the 
displacement  of  the  hull  being  about  35  tons ;  and  speed  not  far 
from  10  knots,  the  maximum,,  when  driven,  being  21  knots. 
The  principal  source  of  this  exceptional  economy  is  presumed 
to  be  a  remarkably  effective  system  of  feed-water  heating  by 
intermediate  steam  to  212*  F.;  full  compression  in  the  small 
cylinder ;  and  a  slight  degree  of  superheating  by  "  wire-drawing  "* 
the  steam.  The  boiler-steam  had  a  pressure  nearly  three  times 
as  great  as  that  in  the  steam-chest.  M.  Normand  has  since, 
nevertheless,  substituted  the  triple-expansion  engine  for  the 
compound.* 

The  Triple-expansion  Engine  has  succeeded  the  ordinary  two- 
cylinder  compound  machine  in  regular  work  of  the  merchant 
£kvy  for  long  routes,  and  is  also  occasionally  adopted  for  station- 
ary engines  where  the  cost  of  fuel  is  such  as  will  justify  the  some- 
what increased  cost  of  construction.  By  its  use,  it  is  found 
practicable  to  raise  the  steam-pressure  to  above  ten  atmospheres 
(150  Ibs.  and  upward!  and  to  increase  the  ratio  of  expansion  to 
15  or  more,  with  good  results.  The  great  cost  of  fuel  and  the 
value  of  tonnage-space  on  shipboard  have  hastened  this  advance 
in  marine-engine  design.  Mr.  O.  E.  Seaton,  comparing  sister- 
ships  fitted  with  the  two  types  of  engine,  found  this  change  to 
produce  a  saving  of  about  20  per  cent  over  the  two-cylinder 
compound  engine,  a  difference  substantially  that  predicted  by 
computations  assuming  the  usual  differences  of  pressure  and 
ratios  of  expansion  and  a  reduction  by  one-third  of  the  cylinder- 
wastes. 

**  Triple-expansion**  engines  were  introduced  as  early  as  1874 
by  Mr.  A.  C.  Kirk  in  designing  the  machinery-  of  the  S.S.  Pro- 
pontis  of  Liverpool,  the  steam  being  supplied  at  160  pounds 
pressure  by  water-tube  boilers  of  the  Rowan  type :  Mr.  Kirk  ob- 
serving that  a  ratio  of  expansion  exceeding  2\  was  not  practically 
more  advantageous  than  this  value :  as  higher  ratios  so  exag- 
gerate internal  wastes  as  not  to  be  economical  in  a  single 

*  OCoal  Repon:  Mem.  de  h  Soc.  des  log.  Ciriis:  Dec.  *go:  P"  *M- 
t  Ibid. 


72       A   MANUAL   OF   THE   STEAM-ENGINE. 

cylinder.  The  result  was  a  considerable  gain  in  economy  of 
steam  and  fuel. 

This  type  of  engine  in  the  long  voyage  between  London 
and  Australia  (1880)  has  given  similar  economy,  saving  500 
tons  in  the  voyage  and  permitting  the  carrying  of  500  tons 
additional  freight. 

Quadruple  expansion  in  engines  carrying  175  to  200  pounds 
steam  has  been  introduced  (1885),  and  promises  still  further 
advantage  should  it  prove  practicable  to  construct  satisfactory 
boilers. 

Quadruple-expansion,  four-cylinder,  compound  engines  are 
adopted  occasionally  when  steam-pressures  are  higher  than 
advisable  for  triple  expansion,  and  permit  the  economical  em- 
ployment, often,  of  twice  the  pressure,  or  more,  customary  in 
ordinary  compound  engines  and  a  third,  or  more,  higher  than 
with  triple  expansion  ;  and  the  best  ratios  of  expansion  are  cor- 
respondingly increased  ;  20  and  25  being  not  unusual  values. 
In  the  arrangement  of  this  engine,  the  cylinders  are  variously 
grouped  by  the  different  designers ;  all  of  whom,  however, 
endeavor  to  secure  a  combination  of  lightness,  compactness, 
small  clearance-spaces,  and  good  steam-distribution,  with  uni- 
form rotatory  action  on  the  crank-shaft.  A  common  design 
mounts  two  cylinders  on  the  upper  ends  of  the  other  two,  thus, 
in  effect,  producing  a  pair  of  "  tandem  "  engines,  with  the  two 
cranks  at  right  angles  and  with  properly  proportioned  receiv- 
ers ;  in  other  designs,  three  cranks  are  employed  in  order  to 
secure  more  uniform  turning  moments,  and  in  such  examples 
one  crank  is  acted  upon  by  two  cylinders  ;  while  the  others  are 
connected  to  a  single  piston  each.  A  less  compact  and  more 
weighty  and  costly  design  applies  each  of  the  four  pistons  to 
each  of  four  cranks,  giving  admirably  good  rotative  effect, 
but  sacrificing  something  of  the  advantages  of  the  other  types. 
For  boiler-pressures  exceeding  15  atmospheres  (above  about 
225  pounds  per  square  inch)  the  quadruple-expansion  engine 
is  unquestionably  an  economical  form,  and  for  marine  pur- 
poses, or  where  fuel  is  very  costly,  it  is  likely  to  supersede 
even  the  triple-expansion  engine. 


THE-0EVELOPMENT  OF  THE  '-STEAM-ENGINE.  73 

25.  The  Process  of  Development  of  the  steam-engine  is, 
fn  resume,  as  follows :  * 

A  century  ago,  James  Watt  had  just  begun  to  introduce  the 
first  engines  belonging  to  a,  then,  new  type.f  A  century  be- 
fore (1698),  the  ingenuity  and  practical  skill  of  Captain  Savery 
had  conferred  an  enormous  benefit  upon  the  mining  industries, 
and  through  them  upon  the  world,  by  applying  the  "•  fire-en- 
gine "  of  the  Marquis  of  Worcester  to  raising  water  from  the 
then  rapidly  deepening  mines.  Savery  used  steam  of  8  to  10 
atmospheres  (120  to  150  pounds)  total  pressure,  in  some  cases: 
and  he  is  entitled  to  fame  as  the  first  to  introduce  that  now 
familiar  concomitant  of  civilization,  the  steam-boiler  explosion. 
The  usual  pressure  was  3  atmospheres.  These  engines  de- 
manded about  30  pounds  of  coal,  per  horse-power  per  hour,  as 
a  minimum.  The  apparatus  of  Savery  was  not  what  would  to- 
day be  called  a  steam-engine,  at  all.  It  was  not  a  train  of 
mechanism,  involving  moving  parts,  cylinder,  piston,  crank,  and 
fly-wheel.  H uyghens  ( 1 680)  and  Papin  ( 1 690)  proposed  true  en- 
gines with  steam-pistons  traversing  their  cylinders,  and  forming, 
on  the  whole,  much  such  a  train  of  mechanism  as  is  now  so  well 
known  ;£  but  the  Newcomen  engine  was  the  first  of  this  type 
to  come  into  practical  use.  A  writer  of  that  time  states  §  that 
"  Mr.  Newcomen 's  invention  of  the  fire-engine  enabled  us  to 
sink  our  mines  to  twice  the  depth  we  could  formerly  do,  by  any 
other  machinery: "  but  "  every  fire-engine  of  magnitude  con- 
sumes £3000  worth  of  coal  per  annum."  The  coal-consump- 
tion was,  at  best,  about  20  pounds  per  hour  and  per  horse- 
power. It  was  this  engine  that  Watt  found  in  operation,  when 
he  entered  upon  the  stage. 

Watt  was  not  simply  a  mechanic  ;  he  was  a  real  philosopher, 
and  a  truly  scientific  investigator.  He  found  that  the  sources 
of  loss  in  engines  were  the  conductivity  and  radiating  power 

*  Stationary  Steam-engines  ;  R.  H.  Thurston  ;  N.  Y.,  J.  Wiley  &  Sons, 
f  History  of  the  Growth  of  the  Steam-engine.    International  Series.    N.  Y., 
D.  Appieton  &  Co. 

t  Mem.  Acad.  ScL;   Paris,  1680.     Ada  EnuKtontm;  Leipsic,  1690. 
>j  Mintralegia  CormttbUnfis;  Price  ;  1778.     Appendix. 


74  A  MANUAL    OF    THE   STEAM-ENGINE. 

of  the  steam-cylinder,  the  alternate  heating  and  cooling  of  the 
metal  at  each  stroke,  the  imperfect  vacuum,  and  the  wastes  from 
boiler  and  steam-pipes.  To  correct  these  defects,  he  clothed 
his  boilers  and  steam-pipes  with  non-conductors,  sometimes  even 
making  boiler-shells  of  wood.  Smeaton  had  already  covered 
the  pistons  and  cylinder-heads  with  wood.  Watt  made  a  more 
practicable  improvement,  however,  when  he  devised  the  steam- 
jacket.  He  attached  a  separate  condenser,  closed  the  cylinder 
at  the  top,  made  the  engine  double-acting,  and  finally  adapted 
the  engine  to  drive  machinery,  fitting  it  with  shaft  and  fly- 
wheel, throttle-valve  and  governor,  and  thus  making  the  steam- 
engine  such  as  we  see  it  to-day,  in  all  essential  particulars. 
His  engine  was  substantially  complete  by  the  year  1784.* 

Later  changes  have  been  a  succession  of  refinements,  and 
of  developments  in  application.  Stephenson,  and  his  contem- 
poraries, applied  steam  on  railroads  ;  Stevens,  Fitch,  and 
Evans,  and,  finally,  Fulton,  in  the  United  States,  and  Bell  and 
others,  in  Europe,  introduced  steam  navigation  ;  Sickels  in- 
vented the  "  detachable  "  cut-off  valve-gear  ;  Corliss  introduced 
the  peculiar  type  of  engine  that  has  given  him  fame,  and  so 
attached  its  governor  as  to  determine  the  point  of  cut-off  au- 
tomatically, and  thus  to  regulate  the  engine.  Robert  L.  and 
Francis  B.  Stevens  designed  the  American  river  steamboat, 
and  its  beam-engine,  with  so  simple  and  effective  a  valve-gear 
that  it  remains,  to-day,  still  standard.  The  compound  engine, 
even,  was  brought  out  by  contemporaries  of  Watt,  and  thus 
every  prominent  feature  and  essential  detail  of  the  modern 
steam-engine  was  introduced  at,  or  before,  the  middle  of  the 
nineteenth  century. 

Yet  practice  has  been  steadily  changing  since  his  time  ;  and 
the  form  and  proportions  of  the  steam-engine,  and  the  methods 
of  steam  distribution,  have  been  undergoing  constant  changes. 
In  the  days  of  Watt,  steam  was  worked  at  about  7  pounds 
pressure,  per  square  inch,  in  stationary  engines  ;  they  were  al- 
ways fitted  with  condenser  and  air-pump,  were  slow  in  move- 

*  History  of  the  Growth  of  the  Steam-engine,  p.  119.      Farey  on  the  Steam- 
engine. 


THE  DEVELOPMENT  OF  THE  STEAM-EXCIXE.  75 

ment,  and  were,  consequently,  of  small  power  in  proportion  to 
their  size ;  they  wasted  heat  and  fuel  to  such  an  extent  as  to  de- 
mand 6  or  8  pounds  of  coal  per  horse-power  and  per  hour.  It 
is  true  that  Wolff,  in  1804,  expanded  6  or  8  times,  using  high- 
er steam,  and  obtained  the  horse-power  with  4  pounds  of  fuel 
per  hour,  and  that  John  Stevens  and  Oliver  Evans,  in  the 
United  States,  and  Trevithick,  in  Great  Britain,  had  already 
used  still  higher  steam  in  non-condensing  engines :  but  these 
examples  simply  illustrated  the  fact  that  isolated  examples 
which  lead  standard  practice  by  a  half-century,  or  more,  are  to 
be  observed  during  the  growth  of  every  art. 

Although  the  principles  of  steam-engine  economy  were,  in 
the  main,  well  understood  by  Watt  and  his  competitors,  and 
have  become  well  settled  in  later  years,  we  are  still  far  from  a 
completely  satisfactory  solution  of  the  problem,  which,  as 
stated  by  the  Author  elsewhere,  may  be  enunciated  thus :  To 
construct  a  machine  which  shall,  in  the  most  perfect  manner 
possible,  convert  the  energy  of  heat  into  mechanical  power: 
the  heat  being  derived  from  the  combustion  of  fuel,  and  steam 
being  the  receiver  and  conveyer  of  that  heat. 

Watt's  first  condenser  has  been  seen  to  have  been  a  surface- 
condenser.  He  immediately  afterward  adopted  a  jet-con- 
denser, however,  to  obtain  "  a  surface  sufficiently  extensive  to 
condense  the  steam  of  a  large  engine,"  and  to  avoid  the  diffi- 
culties that  might  arise  should  the  condensing  water  "  crust 
over  the  thin  plates  "*  of  the  surface-condenser. 

The  surface-condenser  was  used  by  Mr.  S.  Hall,  in  1838.  on 
the  steamship  Wilberforce.  This  condenser  had  2374  copper 
tubes,  8  feet  long  and  one-half  inch  in  diameter,  placed  verti- 
cally in  a  box.  cooling  surface  about  2486  square  feet,  and  8.72 
square  feet  of  condensing  surface  per  horse-power.  The  tubes 
became  coated  with  mud,  and  were  removed ;  the  surface- 
being  changed  to  a  jet-condenser.  In  1859  the  P.  &  O. 
Steamship  Co.  adopted  surface-condensation  on  the  Moulton. 
The  condenser  had  1 178  tubes.  5  feet  10  inches  long,  f  inch  in 
diameter,  0.05  inch  thick,  or  a  surface  of  4200  square  feet.  2.42 
square  feet  of  condensing  surface  per  I.  H.  P.  The  tubes  were 


76 


A  MANUAL   OF   THE   STEAM-ENGINE. 


packed  with  linen  tape  and  screwed  glands.  The  circulating 
water  was  controlled  by  a  centrifugal  pump,  probably  the  first 
independent  circulating-pump  ever  used.  The  tubes  were  ver- 
tical and  the  refrigerating  water  ascended  them  on  the  outside. 

Since  that  date  their  use  has  become  general ;  the  pioneers 
in  the  United  States  having  been  Lighthall  and  Sewall. 

The  general  introduction  of  electric-lighting  systems,  which 
ordinarily  employ  "  dynamos  "  driven  at  very  high  velocities  of 
rotation,  brought  about  a  remarkable  and  radical  change  of 
practice  in  steam-engine  design  and  construction.  The  de- 
mand became  imperative  for  a  motor  system  which  should 
provide  power  with  decreased  weight  and  volume  of  engine 
and  machinery,  and  this  concentration  of  power  required  to  be 
accompanied  by  a  corresponding  increase  in  speed  of  engine- 
piston  and  of  rotation,  and  a  much  better  regulation.  Expe- 
rience has  generally  led  to  the  adoption,  where  practicable, 
of  independent  engines  to  each  dynamo,  and  only  the  high 
speed  of  the  modern  engine  is,  ordinarily,  considered  suitable 
to  this  work. 

Steam-pressures  have  risen,  since  the  improvement  of  the 
steam-engine  by  Watt  was  begun,  somewhat  as  follows,  at  sea 
and  in  condensing  engines  : 


Year. 

A.D. 
l8OO 

St 
lb 

o  tc 

earn  Pressure; 
s.                   atr 

5      o   t 

7           i   ' 
10           £ 
20           § 
20         I 
25          I 
30         l£ 
60         2 

90       4 
120      5 

200         8 

• 

nos. 
0 

I- 

I- 
2 

4 
6 
8 
20 

1810 

c    " 

1820 

c    " 

1830 

IO    " 

1840 

1C" 

1850 

1C" 

1860 

20  " 

1870 

1880 

60  " 

1885 

i  800  .  . 

.  .  100   " 

In  many  cases,  considerable  variations  from  these  figures 
have  been  observed ;  but  they  may  be  taken  as  representative 


THE  DEVELOPMENT  OF   THE   STEAM-ENGIXE.  77 

of  what  was  generally  thought  good  practice  at  the  several 
dates. 

The  history  of  progress  in  marine  engineering  in  the  latter 
half  of  the  nineteenth  century  is  exceedingly  instructive.  As  the 
power  of  the  engine  is,  if  properly  proportioned,  in  the  ratio  of 
its  speed  of  piston  or,  with  any  one  engine,  to  its  revolutions  in 
the  unit  of  time,  these  speeds  have  risen  from  500  or  600  feet 
to  1000,  and  from  40  or  50  to  80  and  100  revolutions,  with 
even  large  engines.  Simple  engines  at  25  pounds  pressure 
have  been  superseded  by  compound  engines  at  60  to  80  and 
these  by  triple  and  quadruple  expansion  from  150  and  200 
pounds ;  while  gaining  30  per  cent  or  more  in  the  first  step 
and  20  or  more  in  the  second,  all  costs  considered.  Forced 
draught  at  6  inches  water  pressure  has  been  used,  and  the 
speed  of  similar  ships  raised  from  10  or  12  knots  to  15  and 
then  to  1 8  and  20,  each  square  foot  of  heating  surface  giving, 
in  some  cases,  20  horse-power. 

In  1 890  the  combined  power  of  all  the  prime  movers  in  the 
world  using  steam  as  the  working  fluid  was  not  far  from  100,- 
OOO,OOO  horse-power,  of  which  the  United  States  had  about 
15,000,000,  Great  Britain  the  same,  France  and  Germany,  col- 
lectively, a  similar  amount,  and  the  balance  was  distributed 
among  other  nations.  Taking  the  horse-power  as  the  equiv- 
alent of  the  \vork  of  five  men,  as  an  average,  including  over- 
time, the  work  of  steam  is  the  equivalent  to  that  of  a  popula- 
tion of  working  men  amounting  to  500,000,000,  to  a  total 
population  of  2,500,000,000,  or  to  about  quadrupling  the  work 
of  the  globe. 

26.  The  Philosophical  Study  of  this  development  will  be 
seen  to  give  rise  to  the  following : 

We  may  rapidly  note  the  prominent  points  of  improvement, 
and  the  most  striking  changes  of  form;  and  may  thus  obtain 
some  idea  of  the  general  direction  in  which  \ve  are  to  look  for 
further  advance. 

Beginning  with  the  earlier  machines,  we  there  found  a  single 
vessel  performing  the  functions  of  all  the  parts  of  a  modern 
pumping-engine ;  it  was  at  once  boiler,  steam-cylinder,  and 


78  A  MANUAL    OF   THE   STEAM-ENGINE. 

condenser,  as  well  as  both  a  lifting  and  a  forcing  pump.  The 
Marquis  of  Worcester,  and,  still  earlier,  Da  Porta,  divided  the 
engine  into  two  parts ;  using  one  part  as  a  steam-boiler,  and 
the  other  as  a  separate  water-vessel.  Savery  duplicated  those 
parts  of  the  earlier  engine  which  acted  the  several  parts  of 
pump,  steam-cylinder,  and  condenser,  and  added  the  use  of  the 
jet  of  water  to  effect  rapid  condensation.  Newcomen  and 
Cawley  next  introduced  the  modern  type  of  engine,  and  sepa- 
rated the  pump  from  the  steam-engine  proper  :  in  their  engine, 
as  in  Savery's,  we  notice  the  use  of  surface-condensation  first ; 
and,  subsequently,  that  of  a  jet  of  water  thrown  into  the  midst 
of  the  steam  to  be  condensed.  Watt  finally  affected  the 
crowning  improvement  of  the  single-cylinder  engine,  and  com- 
pleted this  movement  of  differentiation  by  separating  the  con- 
denser from  the  steam-cylinder,  thus  perfecting  the  general 
structure  of  the  engine.  Here  this  movement  ceased,  the 
several  important  processes  of  the  steam-engine  now  being 
conducted  each  in  a  separate  vessel.  The  boiler  furnished  the 
steam;  the  cylinder  derived  from  it  mechanical  power;  the 
vapor  was  finally  condensed  in  a  separate  vessel ;  while  the 
power,  which  had  been  obtained  from  it  in  the  steam-cylinder, 
was  transmitted  through  still  other  parts  to  the  pumps,  or 
wherever  work  was  to  be  done. 

Watt  and  his  contemporaries  also  commenced  that  move- 
ment toward  higher  pressures  of  steam,  used  with  greater  ex- 
pansion, which  has  been  the  most  striking  feature  noticed  in 
the  progress  of  the  steam-engine  since  his  time.  Newcomen 
used  steam  of  barely  more  than  atmospheric  pressure,  and  raised 
105,00x3  pounds  of  water  one  foot  high,  with  a  pound  of  coal 
consumed.  Smeaton  raised  the  steam-pressure  to  eight  pounds, 
and  increased  the  duty  to  120,000.  Watt  started  with  a  duty 
of  double  that  of  Newcomen,  and  raised  it  320,000  foot-pounds 
per  pound  of  coal,  with  steam  at  ten  pounds.  To-day,  Cornish 
engines  of  the  same  general  plan  as  those  of  Watt,  but  worked 
with  forty  to  sixty  pounds  of  steam,  and  expanding  three  to 
six  times,  do  a  duty  that  will  probably  average,  with  good  or- 
dinary engines,  above  600,000  foot-pounds  per  pound  of  coal. 


THE  DEVELOPMENT  OF   THE   STEAM-EXGINE.  79 

The  increase  of  steam-pressure  and  expansion  which  has 
been  seen  since  Watt's  time  has  been  accompanied  by  a  very 
great  improvement  in  workmanship,  a  consequence  of  rapid 
increase  in  the  perfection  and  the  wide  range  of  adaptation  of 
machine-tools,  of  higher  skill  and  intelligence  in  designing 
engines  and  boilers,  increased  piston-speed,  greater  care  in 
obtaining  dry  steam,  and  in  keeping  it  dry  until  thrown  out  of 
the  cylinder — either  by  superheating,  or  by  steam-jacketing, 
or  by  both  means  combined ;  and  it  has  been  further  accom- 
panied by  greater  attention  to  the  important  matter  of  provid- 
ing carefully  against  losses  by  conduction  and  radiation,  and 
by  internal  wasteful  transfer  of  heat.  The  use,  finally,  of  the 
"compound,"  or  the  multicylinder,  engine  for  the  purpose  of 
reducing  friction,  as  well  as  of  saving  some  of  that  heat  which 
is  usually  lost  in  consequence  of  internal  condensation  and 
re-evaporation  due  to  great  expansion,  has  still  further  aided  in 
this  progress  and  giving  a  duty  of  1,000,000  or  more. 

An  important  consequence  of  the  still  unchecked  rise  of 
piston-speed  in  the  modern  steam-engine  is  the  approach  to  a 
limit  beyond  which  the  now  standard  form  of  "  drop  cut-off/' 
or  "detachable"  valve-gear,  cannot  be  used.  For  the  piston 
would,  at  that  limit  of  speed,  reach  the  end  of  its  stroke  before 
the  dropped  valve  could  reach  its  seat,  and  the  point  of  cut-off 
and  degree  of  expansion  could  no  longer  be  determined 
accurately  and  invariably  by  the  governor.  This  limit  has 
probably  already  been  attained  in  some  engines ;  and  the 
engineer  is  driven  back  to  the  use  of  the  older  types  of  "  posi- 
tive-motion "  valve-gearing,  and  is  compelled  to  devise  special 
forms  of  governor  which  shall  have  sensitiveness,  and  yet  power 
sufficient  to  control  these  less  tractable  kinds  of  mechanism. 
and  to  invent  reliable  and  durable  forms  of  balanced  valves, 
and  to  practise  every  available  expedient  for  making  the 
movement  of  the  valve,  and  its  adjustment  by  the  regulator, 
perfectly  easy.  Positive  motion  and  ease  of  adjustment  by  the 
governor  are,  therefore,  evidently  the  requisites  of  a  successful 
valve-gear  for  the  high-speed  engine  which  will  succeed  the 
standard  engine  of  to-day  for  many  purposes. 


8O  A  MANUAL    OF   THE   STEAM-ENGINE. 

We  may  now  summarize  the  results  of  our  examination  of 
the  development  of  the  steam-engine  thus : 

(1)  The  process  of  improvement  has  been  one,  primarily, 
of  "  differentiation  ;"  the  number  of  parts  has  been  continually 
increased,  while  the  work  of  each  part  has  been  simplified,  a 
separate  organ  being  appropriated  to  each  process  in  the  cycle 
of  operations. 

(2)  A  kind  of  secondary  process  of  "  differentiation"  has, 
to  some  extent,  followed  the  completion  of  the  primary  one,  in 
which  secondary  process  one  operation  is  conducted  partly  in 
one  and  partly  in  another  part  of  the  machine.     This  is  illus- 
trated by  the  cylinders  in  series  of  the  multicylinder  engine. 

(3)  The  direction  of  improvement  has  been  marked  by  a 
continual  increase  of  steam-pressure,  greater  expansion,  special 
provision  for  obtaining  dry  steam,  higher  piston-speed,  careful 
protection  against  loss  of  heat  by  conduction  or  radiation  in- 
ternally, as  well  as  externally,  and,  in  marine  engines,  by  surface- 
condensation. 

The  direction  of  further  improvement,  as  indicated  by 
science  as  well  as  by  our  review  of  the  actual  steps  already  taken, 
would  seem  to  be  :  En  resume,  working  between  the  widest 
attainable  limits  of  temperature,  and  the  saving  of  heat  previ- 
ously wasted  in  the  apparatus  or  rejected  from  it.  Steam  must 
enter  the  machine  at  the  highest  possible  temperature,  must  be 
protected  from  waste  or  loss  of  heat,  and  must  retain,  at  the 
moment  before  exhaust,  the  least  possible  proportion  of 
originally  available  heat.  He  whose  inventive  genius,  or 
mechanical  skill,  contributes  to  effect  either  of  these  objects — 
to  secure  either  the  use  of  higher  steam  with  safety,  or  the 
more  effective  conversion  of  heat  into  mechanical  power  with- 
out waste,  or  the  reduction,  by  transformation  into  work,  of 
the  temperature  of  the  rejected  working-fluid — confers  an 
inestimable  boon  upon  mankind. 

In  detail,  in  the  engine  proper  the  tendency  is,  and  may  be 
expected  to  continue,  in  the  near  future  at  least,  toward  higher 
steam,  greater  expansion  in  more  than  one  cylinder,  steam- 
jacketing,  superheating,  a  careful  use  of  non-conducting  pro- 


THE  DEVELOPMENT  OF   THE  STEAM-ENGINE.  8 1 

tectors  against  waste,  and  higher  piston-speed  with  rapid 
rotation,  and  to  the  adoption  of  special  proportions  and  of 
forms  of  valve-gear  adapted  to  such  high-speed  engines.  In 
the  boiler,  more  complete  combustion,  without  excess  of  air 
passing  through  the  furnace,  is  sought,  and  a  more  thorough 
absorption  of  heat  from  the  furnace-gases.  The  latter  may  be 
ultimately  found  most  satisfactorily  attainable  by  the  use  of 
a  mechanically-produced  draught,  in  place  of  the  far  more 
wasteful  method  of  obtaining  it  by  the  expenditure  of  heat  in 
the  chimney.  In  construction,  we  may  anticipate  the  use  of 
better  materials,  as  already  seen  in  the  substitution  of  "  mild 
steels"  for  the  cruder  material,  iron,  and  more  careful  workman- 
ship, especially  in  the  boiler,  and  still  further  improvement  in 
forms  and  proportions  of  details. 

In  management  there  is  an  immense  field  for  improvement, 
which  improvement  we  may  feel  assured  will  rapidly  take  place, 
as  it  is  now  becoming  well  understood  that  care,  skill,  and 
intelligence  are  absolutely  essential  to  economical  management, 
as  well  as  to  safety,  and  that  they  repay  liberally  all  the  ex- 
penditure of  time  and  money  that  is  requisite  to  secure  them. 


CHAPTER   II. 
STRUCTURE   OF   THE   STEAM-ENGINE. 

27.  The  Structure  and  Uses  of  the  Steam-engine  have 
been  well  defined  and  mutually  adapted,  each  to  the  other, 
since  the  middle  of  the  nineteenth  century,  and  in  such  manner 
as  to  have  led  to  the  production  of  certain  fairly  definite  forms 
of  engine  ;  which  are  each  employed  very  generally,  sometimes 
exclusively,  for  equally  specific  purposes. 

Thus  :  the  modern  mill-engine,  simple  or  compound,  is  com- 
monly a  direct-acting,  horizontal  engine — at  least  for  moderate 
and  large  powers — with  effective  provision  for  adjusting  the 
point  of  cut-off  by  the  action  of  the  governor ;  the  engine  em- 
ployed especially  to  drive  fast  machinery  is  commonly  a 
machine  having  a  "  positive-motion  "  valve-gear  and  as  simple 
of  construction,  as  compact,  and  as  well  balanced  as  the  art  of 
the  builder  can  make  it ;  while  the  locomotive  and  the  marine 
engines  are  each  of  a  type  which  has  been  the  product  of  years 
of  change  and  of  evolution  which  have  resulted  in  their  very 
perfect  adaptation  to  their  peculiar  work.  It  has  thus  hap- 
pened that  engines  are  divided  into  classes ;  each  class  having 
its  characteristic  form  and  structure,  and  its  own  special  nomen- 
clature. 

28.  The  Classification  into  Types  has  been  usually  fol- 
lowed in  substantially  the  manner   indicated  in    the   scheme 
given  in  the  next  article.     It  is  not  invariably  the  fact,  how- 
ever, that  the  classification  with  reference  to  use  is  adhered  to 
in  the  actual  use  of  engines ;  and  it  is  often  the  fact  that  one 
type  is  applied  to  the  purposes  ordinarily  considered  specially 
appropriate  to  another  class.     For  example  :  we  find  the  port- 
able engine,  and  sometimes  a  retired  locomotive,  doing  duty  as 

82 


STRUCTURE  OF  THE  STEAM-EXCISE.  83 

a  stationary,  mill,  engine ;  as  may  also  be  the  case  sometimes 
with  an  engine  constructed  on  what  are  recognized  generally  as 
the  characteristic  plans  of  the  marine  engine. 

Nevertheless,  as  a  rule,  each  kind  of  work  is  best  performed 
by  a  form  of  engine  which  has  been  found,  by  the  experience  of 
years,  to  be  the  best  for  that  place.  The  engineer  is  therefore 
inclined  to  be  somewhat  cautious  in  accepting  any  suggestion 
looking  to  interchange  of  duties  in  this  manner. 

According  to  Weisbach's  system,  the  various  piston-engines 
may  be  grouped  under  the  following  classes  :* 

I.  According  to  the  number  of  cylinders : 

(1)  Single  cylinder. 

(2)  Multiple-cylinder  engines. 

IL  With  reference  to  the  construction  of  cylinders : 
{!)  Fixed  cylinder. 
(2)  Movable  cylinder. 
In  the  first  case,  the  engines  are — 
(a)  Vertical. 
(J)  Horizontal 
(r)  Inclined. 

In  the  second  case,  they  are — 
(a)  Oscillating. 
(*)  Rotary. 

III.  With  reference  to  the  action  of  the  steam : 

(1)  Single  acting. 

(2)  Double-acting. 

IV.  With  reference  to  the  transmission  of  the  steam-power : 

(1)  Direc^acting. 

(2)  Indirect-acting. 

And  in  the  latter  case  either — 

{a)  With  balance  lever,  or  beam. 
(£)  Without  lever  or  working  beam. 

29.  ^t^a«-^«i JIM**  •.  Classed  %rf9f»K"g  to  their  purpose 
and  use,  as  in  the  following  scheme,  may  be  taken  as  practically 
including  all  existing  standard  and  approved  types. 

*  Weistaacli  s  Mechanics,  roL  n.  put  2.  §45*.  P-  «8S- 


84  A  MANUAL    OF   THE   STEAM-ENGINE. 

STANDARD   TYPES   OF    ENGINES. 

GENERAL  CLASS. 

Stationary,  or  Mill,  Engines  : 

Moderate  Speed  or 

High  Speed. 
Agricultural  Engines. 
Pumping  engines. 

Crank  and  fly-wheel. 

Direct-acting. 
Portable  Engines  and 
Semi-portable  Engines. 
Steam  Fire-engines. 
Road  Locomotives. 
Railway      " 
Marine  Engines. 

Paddle-engines. 

Screw-engines. 
Special  Types. 

Engines  may  also  be  classed  according  to  structure:  as 
simple  or  compound;  as  direct  acting,  beam,  vertical,  inverted, 
horizontal,  or  inclined  :  or  as  condensing  or  non-condensing ; 
high-pressure  or  low-pressure  ;  or  as  reciprocating,  vibrating, 
as  steam-turbines,  or  as  rotary  engines ;  or  as  directly  con- 
nected or  geared ;  as  jet-condensing  or  surface-condensing. 
They  are  very  frequently  designated  by  the  name  of  the  in- 
ventor, designer,  or  constructor :  as  the  Watt,  the  Corliss,  or 
the  Porter  engine. 

In  the  first  classification — that  by  reference  to  proposed 
use — the  title  is  sufficiently  indicative  of  its  own  reason  and 
meaning  ;  and  this  is  commonly  the  case  with  the  nomenclature 
based  on  structural  characteristics.  A  simple  engine  does  its 
work  in  a  single  cylinder;  while  a  "compound  or  multicylin- 
der  engine  has  two  or  more  cylinders,"  so  connected  "  in  series" 
that  the  steam  exhausted  from  one  shall  be  successively  worked, 
under  decreasing  pressures,  in  the  others. 


STRUCTURE   OF    THE   STEAM-ENGINE.  85 

Direct-acting  engines  are  directly  connected  from  head  of 
piston-rod  and  the  cross-head  to  the  crank ;  beam-engines  have 
a  ''  working-beam  "  interposed  :  and  the  geared  engine  drives 
its  load — as  the  screw-shaft  in  marine  engines — by  means  of 
pinions  on  the  crank-shaft  and  gears  on  the  screw-shaft ;  thus 
enabling  the  latter  -to  be  driven  at  higher  speed  than  the 
former,  or,  in  very  rare  instances,  the  reverse.  Vertical,  in- 
verted, horizontal,  or  inclined  engines  are  so  named  to  indicate 
the  direction  of  their  k4  centre-lines  "  and  their  position.  Con- 
densing and  non-condensing  engines  are  distinguished  by  the 
fact  that  the  ^AUUf  possesses  a  condenser.  The  condenser, 
however,  is  not  always  made  to  produce  a  vacuum,  when  high 
steam-pressures  are  adopted  :  it  is  occasionally  worked  at  at- 
mospheric pressure,  and  is  then  simply  either  a  heater  or  an 
expedient  for  securing  pure  feed-water  for  the  boilers. 

Reciprocating  engines  are  those — the  usual  type — in  which 
the  piston  moves  backward  and  forward  in  a  true  cylinder; 
vibrating  engines  constitute  a  rare  type  in  which  the  piston 
swings  in  an  arc  inside  a  cylinder  of  appropriate  form ;  while 
rotary  engines  are  those  in  which  the  piston  continuously 
revolves  on  an  axis,  usually  parallel  to  its  own  plane. 

The  classification  adopted  by  the  Author  as  that  which  will 
be  followed  in  the  arrangement  of  this  work  is  the  first,  as  pre- 
sented in  the  table  above ;  but  separate  articles  or  chapters 
will  be  devoted  to  such  modifications  as  are  comprehended  in 
the  other  methods  of  classing  engines  falling  under  those 
heads. 

30.  The  Principles  and  Aim  in  Designing  any  engine, 
as  guiding  the  selection  of  type  and  details,  are  such  as  will 
insure  the  most  exact  adaptation  of  the  machine  to  the  specified 
work.  The  ultimate  purpose  is  always  to  secure  the  best  pos- 
sible combination  of  minimum  first  cost  with  minimum  run- 
ning expenses.  That  is  the  best  engine  which,  at  the  end  of  a 
life  terminated  either  by  its  own  wear  and  tear  and  natural 
decay,  or  by  the  substitution  of  a  later  and  better  form,  gives 
the  best  total  effect,  as  measured  on  the  books  of  the  treasurer, 
and  as  including  interest  on  first  cost,  regular  operating  ex- 


86  A   MANUAL    OF   THE   STEAM-ENGINE. 

penses,  compensation  of  attendant  labor,  rents,  insurance,  oil, 
fuel,  and  incidentals,  making  the  sum  of  all  such  charges  a 
minimum. 

Hence  the  stationary  engine  may  be  chosen  without  much 
regard  to  weight  or  space  occupied ;  locomotive  and  marine 
engines  must  be  light,  compact,  and  powerful ;  and  the  latter 
must  be  chosen  and  constructed,  especially  for  long  voyages, 
with  primary  regard  to  high  economy  in  use  of  fuel.  In  all 
cases,  other  things  equal,  a  direct  application  of  the  engine  to 
its  intended  work  is  desirable ;  and  it  thus  happens  that  we  may 
prefer  an  engine  of  moderate  speed  for  mill-work  and  a  "  high- 
speed engine"  for  driving  dynamo-electric  machines.  In  dis- 
tricts remote  from  coal-fields  every  known  method  is  applied 
to  insure  maximum  economic  efficiency ;  while  among  coal- 
mines steam-jacketing,  superheating,  or  "compounding"  are 
expedients  which  have  no  interest  for  either  the  engineer  or  his 
client.  It  is  such  considerations  as  these  which  sometimes  lead 
to  the  use  of  one  standard  form  of  engine  where  another  type 
would  ordinarily  be  employed — as  a  portable  engine  to  drive  a 
factory,  where  to  be  used  temporarily,  or  as  when  cramped  for 
space  ;  as  in  the  application  of  locomotive  boilers  in  the  torpedo 
fleet. 

31.  The  Principles  of  Construction  of  the  selected  type 
of  engine  are  determined  by  precisely  the  same  considerations. 
The  engine  must  be  so  built  that  the  costs  of  maintenance 
shall  be  made  a  minimum  for  the  life  of  the  machine.  It  must 
be  as  light  as  possible,  yet  the  strength  of  every  part  must  be 
sufficient  to  make  it  safe  against  all  ordinary  contingencies ; 
bearings  must  not  only  be  designed  in  proper  number,  location, 
and  dimensions,  but  they  must  be  made  of  good  material  for 
their  purpose  ;  good  material  and  good  workmanship  will  invari- 
ably, "  in  the  long-run,"  afford  full  compensation  for  their  cost. 
It  is  the  consideration  of  these  principles  and  the  deductions 
from  a  now  long  period  of  extensive  and  continuous  experi- 
ence which  have  led  to  the  production  and  use,  for  their  pre- 
scribed purposes,  of  the  several  standard  types  of  engine  to  be 
presently  described. 


STRUCTURE  OF  THE   STEAM-EXG1XE.  87 

32.  The  Exigencies  of  Operation  determine  many  mat- 
ters of   detail  in  every  type   of  engine;   and   the  designing 
engineer,  or  the  purchaser  or  user,  of  an  engine  can  never  be 
secure  of  a  satisfactory  result  unless  the  conditions  of  operation 
and  possible  accidents  and  exigencies  are  considered.     Thus : 
lubrication  must  be  absolutely  continuous  and  certain  on  en- 
gines working  at  high  speed  of  rotation ;  provision  must  be 
made,  especially  with  marine  engines,  and  elsewhere  where 
"  priming  "  or  "  foaming  "  may  endanger  the  engine,  for  the 
safe  expulsion  of  water  from  the   steam-cylinder ;  reversing- 
gears  must  be  fitted  to  rolling-mill  engines ;  an  adjustable  dis- 
tribution of  steam  is  essential  in  the  case  of  the  locomotive. 

33.  The  Stationary  Engine  has  a  variety  of  forms,  differ- 
ing with  the  special  nature  or  with  the  location  of  the  ma- 
chinery to  be  driven.     It  is  usually  a  simple  engine ;  but  is 
getting  to  be  more  and  more  frequently  **  compound,"  or  even 
**  triple-expansion ;"   it  is  usually  driven   at   moderate   speed, 
and  has  a  "  detachable  valve-gear"  or  "  drop  cut-off ;"  but  it  is 
often  of  the  high-speed  type,  with  a  positive-motion  valve-gear 
and  a  shaft-governor.     Among  the  most  common  forms  are : 

(1)  The  Mill-engine ; 

(2)  The  Pumping-engine,  and  others  of  the  moderate  low- 
speed  class; 

(3)  The  High-speed  Engine,  of  various  kinds,  but  mainly 
used  for  mills  or  electric-lighting  establishments ;  and  a  few 
peculiar  forms  that  need  not  be  here  considered. 

Each  of  these  types  or  forms  is  built  both  simple  and  com- 
pound ;  the  latter  will  be  specially  considered  in  a  distinct 
chapter. 

The  best  known  and  most  generally  used  class  of  stationary 
engines  at  the  present  time,  as  has  been  stated,  is  that 
which  has  the  so-called  "  drop  cut-off,"  or  "  detachable  valve- 
gear."  The  oldest  well-known  form  of  valve-motion  of  this 
description  is  the  Sickels  cut-off,  previously  mentioned,  pat- 
ented by  Frederick  E.  Sickels  about  the  year  1841.  It  was 
introduced  by  the  inventor  in  a  form  which  especially  adapted 
it  to  the  beam-engine  used  on  the  Eastern  waters  of  the 


88  A   MANUAL   OF   THE  STEAM-ENGINE. 

United  States,  and  was  adapted  to  stationary  engines  by  Messrs. 
Thurston,  Greene  &  Co.,  of  Providence,  R.  I.,  who  employed 
it  for  some  years  before  any  other  form  of  "  drop  cut-off  "  came 
into  general  use. 

The  Sickels  cut-off  consisted  of  a  set  of  steam-valves,  made 
independent  of  the  exhaust-valves,  and  each  raised  by  a  catch, 
which  could  be  thrown  out,  at  the  proper  moment,  by  a  wedge 
with  which  it  came  in  contact  as  it  rose  with  the  opening  valve. 
This  wedge,  or  other  equivalent  device,  was  so  adjusted  that 
the  valve  should  be  detached  and  fall  to  its  seat  when  the  pis- 
ton reached  that  point  in  its  movement,  after  taking  steam,  at 
which  expansion  was  to  commence.  From  this  point,  no  steam 
entering  the  cylinder,  the  piston  was  impelled  by  the  expand- 
ing vapor.  The  valve  was  usually  the  double-poppet.  Sickels 
subsequently  invented  what  was  called  the  "  beam-motion,"  to 
detach  the  valve  at  any  point  in  the  stroke.  As  at  first  ar- 
ranged, the  valve  could  only  be  detached  during  the  earlier 
half-stroke,  since  at  mid-stroke  the  direction  of  motion  of  the 
eccentric-rod  was  reversed  and  the  valve  began  to  descend. 
By  introducing  a  "  wiper  "  having  a  motion  transverse  to  that 
of  the  valve  and  its  catch,  and  by  giving  this  wiper  a  motion 
coincident  with  that  of  the  piston  by  connecting  it  with  the 
beam  or  other  part  of  the  engine  moving  with  the  piston,  he 
obtained  a  kinematic  combination  which  permitted  the  valve 
to  be  detached  at  any  point  in  the  stroke,  adding  a  very  simple 
contrivance  which  enabled  the  attendant  to  set  the  wiper  so 
that  it  should  strike  the  catch  at  any  time  during  the  forward 
movement  of  the  "beam-motion." 

On  stationary  engines,  the  point  of  cut-off  was  afterward 
determined  by  the  governor,  which  was  made  to  operate  the 
detaching  mechanism,  the  combination  forming  what  is  some- 
times called  an  "  automatic  "  cut-off.  The  attachment  of  the 
governor  so  as  to  determine  the  degree  of  expansion  had  been 
proposed  before  Sickels's  time.  One  of  the  earliest  of  these 
contrivances  was  that  of  Zachariah  Allen,  in  1834,  using  a  cut- 
off valve  independent  of  the  steam-valve.  The  first  to  so 
attach  the  governor  to  a  drop  cut-off  valve-motion  was  George 


STRUCTURE   OF   THE  STEAM-ENGINE.  89 

H.  Corliss,  who  made  it  a  feature  of  the  Corliss  valve-gear, 
already  referred  to,  in  1849.  1°  tne  vear  l855»  N.  T.  Greene 
introduced  a  form  of  expansion-gear,  in  which  he  combined 
the  range  of  the  Sickels  beam-motion  device  with  the  expan- 
sion-adjustment gained  by  the  attachment  of  the  governor, 
and  with  the  advantage  of  flat  slide-valves  at  all  ports — both 
steam  and  exhaust. 

Many  other  ingenious  forms  of  expansion  valve-gear  have 
been  invented,  and  several  have  been  introduced,  which,  prop- 
erly designed  and  proportioned  to  well-planned  engines,  and 
with  good  construction  and  management,  should  give  economi- 
cal results  little  if  at  all  inferior  to  those  just  named.  Among 
the  most  ingenious  of  these  devices  is  that  of  Babcock  &  Wil- 
cox,  in  which  a  very  small  auxiliary  steam-cylinder  and  piston 
is  employed  to  throw  the  cut-off  valve  over  its  port  at  the  in- 
stant at  which  the  steam  is  to  be  cut  off.  A  very  beautiful 
form  of  isochronous  governor  was  used  on  this  engine,  to  regu- 
late the  speed  of  the  engine  by  determining  the  point  of  cut-off, 

In  some  forms  of  Wright's  engine  the  expansion  is  adjusted 
by  the  movement,  by  the  regulator,  of  cams  which  operate  the 
steam-valves  so  that  they  shall  hold  the  valve  open  a  longer 
or  shorter  time,  as  required. 

The  Older  Forms  of  stationary  engines  were  usually  simple 
in  design,  of  plain  construction,  durable,  economical  in  first 
cost  and  in  maintenance ;  but,  as  compared  with  more  recent 
engines,  wasteful  of  steam  and  fuel.  But  little  space  need 
be  here  given  to  their  description.  They  were  either  beam- 
engines  or  direct-acting,  and  their  valves  and  gear,  from  the 
first  quarter  of  the  century,  consisted  often  of  a  single  three- 
ported  slide-valve  like  that  of  the  modern  locomotive,  driven 
by  a  single  eccentric  and  effecting  the  desired  expansion  and 
compression  of  steam  by  the  lap  and  lead  of  the  valve,  in  a 
manner  to  be  described  in  a  succeeding  chapter.  The  beam- 
engine  gradually  fell  into  disfavor,  on  account  of  its  size  and 
cost,  and  was  displaced  very  generally,  by  the  middle  of  the 
century,  by  the  horizontal  direct-acting  engine ;  and  the  in- 
creased steam-pressures  and  improved  economy  of  the  non 


90  A    MANUAL    OF    THE    STEAM-ENGINE. 

condensing  engine  also  resulted  in  the  increasing  employment 
of  that  form  of  machine,  to  the  exclusion  of  the  condensing 
engine,  which  is,  however,  still  much  used,  especially  for  large 
powers. 

Where  economy  was  particularly  sought,  the  engine  was 
often  fitted  with  a  separate  cut-off  valve,  often  mounted  on 
the  back  of  the  main  valve ;  sometimes,  however,  as  a  distinct 
organ  in  its  own  valve-chest.  In  the  most  common  system — 
that  of  Mayer — this  cut-off  valve  consisted  of  two  blocks  slid- 
ing on  the  back  of  the  main  valve,  actuated  by  an  independent 
eccentric,  and  capable  of  being  separated  or  brought  together, 
as  desired,  by  a  right  and  left  screw,  in  such  manner  as  to  vary 
the  point  of  cut-off  to  any  required  extent.  The  eccentric  is 
set  with  or  180°  from  the  crank,  accordingly  as  the  cut-off  is 
effected  by  the  inside  or  the  outside  edges  of  the  cut-off  blocks. 

Where  much  power  is  required,  the  stationary  engine  is 
now  usually  a  horizontal  direct-acting  engine,  having  a  more 
or  less  effective  cut-off  valve-gear,  according  to  the  size  of  en- 
gine and  the  cost  of  fuel.  A  good  example  of  the  simpler 
form  of  this  kind  of  engine  is  the  small  horizontal  slide-valve 
engine,  with  the  Meyer  system  of  valve-gear.  This  form  is  a 
very  effective  machine,  and  does  excellent  work  when  properly 
proportioned  to  yield  the  required  amount  of  power.  It  is 
well  adapted  to  a  ratio  of  expansion  of  from  four  to  five.  Its 
disadvantages  are  the  difficulty  which  it  presents  in  the  at- 
tachment of  the  regulator,  to  determine  the  point  of  cut-off, 
by  the  heavy  work  which  it  throws  upon  the  governor  when 
attached,  and  the  rather  inflexible  character  of  the  device  as 
an  expansion  valve-gear.  The  best  examples  of  this  class  of 
engine  have  heavy  bed-plates,  well-designed  cylinders  and  de- 
tails, smooth-working  valve-gear,  the  expansion-valve  adjusted 
by  a  right-and  left-hand  screw,  and  regulation  secured  by  the 
attachment  of  the  governor  to  the  throttle-valve. 

The  engine  shown  in  the  accompanying  illustration  (Fig. 
28)  is  an  example  of  an  excellent  stationary  engine,  and  is 
simple,  strong,  and  efficient.  The  frame,  front  cylinder-head, 
cross-head  guides,  and  crank-shaft  "  plumber-block,"  are  cast 


STRUCTURE  OF  THE  STEA3/-EXGINE.  QI 

in  one  piece.  The  cylinder  is  secured  against  the  end  of  the 
bed-plate,  as  was  first  done  by  Corliss.  The  crank-pin  is  set 
in  a  counterbalanced  disk.  The  valve-gear  is  simple,  and  the 
governor  effective  and  provided  with  a  safety-device  to  pre- 


vent  injury  by  the  breaking  of  the  governor-belt.  In  this  ex- 
ample all  parts  are  made  to  exact  size  by  gauges  standardized 
to  Whitworth's  sizes. 

With  many  engines  (as  is  seen  in  Fig.  29)  two  supports  are 
placed — the  one  under  the  main  bearing,  and  the  other  under 
the  cylinder — to  take  the  weight  of  the  engine :  and  through 
them  it  is  secured  to  the  foundation.  A  valve  is  sometimes  used 
consisting  of  two  pistons  connected  by  a  rod  and  worked  by 
an  ordinary  eccentric.  By  a  simple  arrangement  these  pistons 
have  always  the  same  pressure  inside  as  out,  which  prevents 
any  leakage  ;  and  they  are  said  always  to  work  equally  as  well 
and  free  from  friction  under  high  as  under  low  pressure. 

Engines  of  the  class  just  described  are  especially  well  fitted, 
by  their  simplicity,  compactness,  and  solidity,  to  work  at  the 
high  piston-speeds  which  are  gradually  becoming  generally 
adopted  in  the  effort  to  attain  increased  economy  of  fuel  by 


92  A    MANUAL    OF   THE   STEAM-ENGINE. 

the  reduction  of  the  immense  losses  of  heat  which  occur  in 
the  expansion  of  steam  in  the  metallic  cylinders  through 
which  we  are  now  compelled  to  work  it. 


FIG.   29. — HORIZONTAL  STATIONARY  ENGINE. 

The  technical  expressions  "  right-hand  "  and  "  left-hand  " 
engines  are  thus  defined  as  applied  to  engines  of  this  class : 

Stand  by  the  end  of  the  cylinder,  face  the  shaft  and  observe 
the  position  and  direction  of  the  main  driving-pulley,  and  class 
the  engine  as  follows  : 

Right-hand  engines  have  the  main  driving-pulley  on  the 
right  of  the  observer.  Left-hand  engines  have  the  main  driv- 
ing-wheel on  the  left  of  the  observer. 

Forward-running  engines  move  the  top  of  the  main  driving- 
pulley  away  from  the  observer. 

Backward-running  engines  move  the  top  of  the  main  driv- 
ing-pulley towards  the  observer. 

In  deciding  on  the  direction  in  which  an  engine  is  to  run, 
it  is  well  to  remember  that  forward-running  engines  are  prefer- 
able, on  account  of  the  thrust  of  the  connecting-rod  being 
received  on  the  lower  guides,  which  are  always  stiffer  and  better 
lubricated  than  the  upper. 

One  of  the  neatest  and  best  modern  designs  of  stationary 
engine  for  small  powers  is  seen  in  Fig.  30,  which  represents  a 
"  vertical  direct-acting  engine,"  with  base-plate — a  form  which 
is  a  favorite  with  many  engineers. 

The  engine  shown  in  the  engraving  consists  of  two  principal 
parts,  the  cylinder  and  the  frame,  which  is  a  tapering  column 


STRUCTURE  OF   THE   STEAM-EXGIXE. 


93 


having  openings  in  the  sides,  to  allow  free  access  to  all  the 
working  parts  within.  The  slides  and  pillow-blocks  are  cast 
with  the  column,  so  that  they  cannot  become  loose  or  out  of 


line;  the  rubbing  surfaces  are  large  and  easily  lubricated. 
Owing  to  the  vertical  position,  there  is  no  tendency  to  side  wear 
of  cylinder  or  piston.  The  packing-rings  are  self-adjusting :  the 
crank  is  counterbalanced  ;  the  crank-pin,  cross-head  pin,  piston- 


94 


A    MANUAL    OF    THE    STEAM-ENGINE. 


rod,  valve-stem,  etc.,  are  made  of  steel ;  all  the  bearing-surfaces 
are  made  large,  and  accurately  fitted  ;  and  the  best  quality  of 
Babbitt-metal  only  should  be  used  for  the  journal-bearings. 

The  smaller  sizes  of  these  engines,  from  2  to  10  horse- 
power, usually  have  both  pillow-blocks  cast  in  th.e  frame,  giving 
a  bearing  each  side  of  the  double  cranks.  They  are  built  by 
some  constructors  in  quantities,  and  parts  duplicated  by  special 
machinery,  which  secures  great  accuracy  and  uniformity  of 
workmanship,  and  allows  of  any  part  being  quickly  and  cheaply 
replaced,  when  worn  or  broken  by  accident.  The  next  figure 
is  a  vertical  section  through  the  same  engine. 


FIG.  3..— VERTICAL  STATIONARY  ENGINE.     (Scale  TV) 


Engines  fitted  with  the  ordinary  rigid  bearings  require  to 
be  erected  on  a  firm  foundation,  and  to  be  kept  in  perfect  line. 
If,  by  the  settling  of  the  foundation,  or  from  any  other  cause, 
they  get  out  of  line,  heating,  cutting,  and  thumping  result.  To 
obviate  this,  modern  engines  are  often  fitted  with  self-adjusting 


STRUCTURE   OF   THE   STEAM-ENGINE.  95 

bearings  throughout ;  this  gives  the  engine  great  flexibility  and 
freedom  from  friction.  The  preceding  figure  shows  clearly 
how  this  is  accomplished.  The  pillow-block  has  a  spherical 
shell  turned  and  fitted  into  the  spherically-bored  pillow-block, 
thus  allowing  a  slight  angular  motion  in  any  direction.  The 
connecting-rod  is  forged  in  a  single  piece,  without  straps,  gibs, 
or  key,  and  is  mortised  through  at  each  end  for  the  reception 
of  the  brass  boxes,  which  are  curved  on  their  backs,  and  fit  the 
cheek-pieces,  between  which  they  can  turn  to  adjust  themselves 
to  the  pins,  in  the  plane  of  the  axis  of  the  rod.  The  adjust- 
ment for  wear  is  made  by  wedge-blocks  and  set-screws,  as 
shown,  and  they  are  so  constructed  that  the  parts  cannot  get 
loose  and  cause  a  break-down.  The  cross-head  has  adjustable 
gibs  on  each  side,  turned  to  fit  the  slides,  which  are  cast  solidly 
in  the  frame,  and  bored  out  exactly  in  the  line  with  the  cylin 
der.  This  permits  it  freely  to  turn  on  its  axis,  and,  in  connec- 
tion with  the  adjustable  boxes  in  the  connecting-rod,  allows  a 
perfect  self-adjustment  to  the  line  of  the  crank-pin.  The  out- 
board bearing  may  be  moved  an  inch  or  more  out  of  position 
in  any  direction,  without  detriment  to  the  running  of  the 
engine,  all  bearings  accommodating  themselves  perfectly  to 
whatever  position  the  shaft  may  assume. 

The  ports  and  valve-passages  are  proportioned  as  in  loco- 
motive practice.  The  valve-seat  is  in  this  instance  adapted  to 
the  ordinary  plain  slide-  or  D-valve,  should  it  be  preferred  ;  but 
the  balanced-piston  slide-valve  works  with  equal  ease,  and  at  the 
same  time  gives  double  steam  and  exhaust  openings,  which 
greatly  facilitates  the  entrance  of  the  steam  to,  and  its  escape 
from,  the  cylinder.  The  vertical  direct-acting  engine  is  some- 
times, though  rarely,  built  of  very  considerable  size  ;  these  large 
engines  are  more  frequently  seen  in  rolling-mills  than  elsewhere. 

34.  The  Mill  or  Factory  Engine  of  latest  date  is  very 
generally  horizontal,  direct-acting,  with  a  detachable  expansion- 
valve,  a  governor  operating  by  adjusting  the  point  of  detach- 
ment and  closing  of  the  valve ;  which  latter  is  closed  quickly 
either  by  gravity  or  by  a  spring,  or,  sometimes,  by  steam- 
pressure.  In  a  few  instances,  engines  have  been  built  in  which 


A    MANUAL    OF   THE   STEAM-ENGINE. 


STRUCTURE   OF   THE   STEAM-ENGINE. 


97 


the  valve  continuously  rotates,  closing  without  reciprocation.* 
When  of  small  size,  the  stationary  is  made  non-condensing ; 
when  of  large  power,  it  is  very  frequently  a  condensing  engine. 
When  large  and  where  economy  is  very  essential,  it  is  frequently 
a  "compound,"  and  often  a  "triple-expansion,"  engine;  the 
steam-pressure  being  carried  higher  as  a  higher  ratio  of  expan- 
sion is  adopted.  In  many  cases,  as  in  cotton-mills  making  fine 
grades  of  product,  or  for  electric-lighting,  precise  regulation  of 
speed  is  required,  and  this  may  determine  the  choice  of  type 
of  engine. 

The  best-known  engine  of  this  class  is  the  Corliss  engine. 
It  is  very  extensively  used  in  the  United  States,  and  has  been 
copied  very  generally  by  European  builders.  Fig.  32  repre- 
sents the  Corliss  engine.  The  horizontal  steam-cylinder  is 
bolted  firmly  to  the  end  of  the  frame,  which  is  so  formed  as  to 
transmit  the  strain  to  the  main  journal  with  the  greatest  direct- 
ness. The  frame  carries  the  guides  for  the  cross-head,  which 
are  both  in  the  same  vertical  plane.  The  valves  are  four  in 
number,  a  steam-  and  an  exhaust-valve  being  placed  at  each 
end  of  the  steam-cylinder.  Short  steam-passages  are  thus 
secured,  and  this  diminution  of  clearance  is  a  source  of  some 
economy.  Both  sets  of  valves 
are  driven  by  an  eccentric  oper- 
ating a  disk  or  wrist-plate,  E 
(Fig.33),which  vibrates  on  a  pin 
projecting  from  the  cylinder. 
Short  links  reaching  from  this- 
wrist-plate  to  the  several  valves, 
D  D,  FF,  move  them  with  a  pe- 
culiarly varying  motion,  open- 
ing and  closing  them  rapidly, 
and  moving  them  quite  slowly 
when  the  port  is  either  nearly 
open  or  almost  closed.  This 

effect  is  ingeniously  secured  by    FIG  33  _CORLISS  ENGISE  VALVE.MOTJON. 
so  placing  the  pins  on  the  wrist- 

*  Report  on  Machinery  and  Manufactures  at  Vienna  in  1873;  R.  H.   Thurs- 
ton;  Washington,  Gov't  Printing  Office;  1875. 


98 


A    MANUAL    OF   THE   STEAM-ENGINE. 


plate  that  their  line  of  motion  becomes  nearly  transverse  to 
the  direction  of  the  valve-links  when  the  limit  of  movement  is 
approached.  The  links  connecting  the  wrist-plate  with  the 
arms  moving  the  steam-valves  have  catches  at  their  extremities, 
which  are  disengaged  by  coming  in  contact,  as  the  arm  swings 
around  with  the  valve-stem,  with  a  cam  adjusted  by  the  gov- 
ernor. This  adjustment  permits  very  perfect  regulation  by 
automatic  variation  of  the  ratio  of  expansion  by  the  governor. 
The  standard  form  of  Corliss  valve  is  very  well  exhibited 


FIG.  34.— THE  CORL 


NGINE-CYL1NDKF 


by  the  illustrations  here  given,  which  are  taken  from  the  draw- 
ings of  Mr.  Harris. 

Those  marked  A  are  the  steam-,  and  those  marked  B  are  the 
exhaust-valves.  Both  consist,  as  is  seen,  of  cylinders,  parts  of 
which  have  been  cut  away,  leaving  the  working  and  bearing 
surfaces  of  no  greater  extent  than  is  necessary  to  subserve  the 
purposes  of  the  valve.  These  surfaces  are  of  the  simplest 
possible  form  and  are  easily  fitted  up  in  the  lathe.  In  order 
that  they  may  come  to  a  bearing  with  certainty,  and  without 
regard  to  the  position  of  the  spindle  relatively  to  the  valve, 


STRUCTURE   OF    THE   STEAM-ENGINE. 


99 


they  are  made  with  a  longitudinal  slit  into  which  fits,  without 
jamming,  the  blade  of  the  rock-shaft.  The  valves  are  thus 
allowed  to  come  to  a  bearing,  and  even  to  wear  down  in  their 
seats  without  causing  leakage. 

The  next  figure  shows  the  arrangement  of  this  valve  as 
seen  in  longitudinal  section  of  the  chest.  As  this  maker  con- 
structs it,  the  stem  goes  through  a  fitted  opening,  without 
stuffing-box,  and  the  slight  drip  is  carried  off  from  the  closed 


FIG.  35. — HAJUUS-CORIJSS  VALVES. 

space  at  D\  thus  none  escapes  into  the  engine-room.  The 
steel  collar  at  F%  which  is  shrunk  on  the  stem,  fits  into  the 
recess  at  a  and  serves  as  a  packing.  As  the  tendency  of  the 
stem  to  shift  outward  always  causes  the  collar  to  wear  to  a  fit, 
it  is  not  likely  often  to  wear  leaky. 

Another  detail  of  interest  in  the  Corliss  engine  is  the  "  dash- 
pot."  When  the  valve  is  suddenly  closed,  some  device  is 
necessary  to  prevent  jar  at  the  instant  of  its  coming  to  rest. 
This  device  is  the  dash-pot.  The  form  adopted  by  Corliss  con- 
sists of  a  shallow  cup  into  which  a  piston  on  the  valve-stem  fits, 


100 


A    MANUAL    OF    THE   STEAM-ENGINE. 


cushioning  the  enclosed  air,  and  thus  checking  the  motion  of 
the  valve  without  shock.  This  dash-pot,  made  by  Watts, 
Campbell  &  Co.,  who  have  successfully  introduced  Corliss  en- 
gines into  electric-light  establishments  in  New  York  City  and 
elsewhere,  is  that  seen  in  the  figures. 

The  annular  piston,  E,  E,  fits  the  cylinder,  D,  D,  £,  E,  and 
a  space,  seen  above  B,  forms  a  vacuum-chamber  which  assists 
the  spring  or  weight,  closing  the  valve  by  the  formation  of  a 
more  or  less  complete  vacuum,  as  the  piston  is  raised  while  the 
valve  is  opening.  A  small  cock,  not  seen,  is  arranged  to  adjust 
the  degree  of  exhaustion  of  this  chamber.  When  the  valve 
has  nearly  reached  its  seat,  the  piston,  D,  passes  the  opening 


FIG.  36. — HARRIS-CORLISS  VALV 


from  F  into  the  outer  space  and  the  enclosed  air  then  acts  as  a 
cushion,  checking  the  movement  of  the  valve. 

The  "  dash-pot "  was  invented  originally  by  F.  E.  Sickels. 
In  the  original  water  dash-pot  of  Sickels,  the  cylinder  is 
vertical,  and  the  plunger  or  piston  descends  upon  a  small  body 
of  water  confined  in  the  base  of  the  dash-pot.  Corliss's  air 
dash-pot  is  now  often  set  horizontally. 

The  Corliss  engine  is  the  prototype,  of  a  large  number  of 
engines  constructed  in  Europe  and  America,  having  the  same 
or  very  similar  structure  and  methods  of  operation. 

The  leading  features  of  this  machine  are  thus : 

(i)  The  use  of  four  valves— two  steam  and  two  exhaust — 
so  placed  as  to  reduce  "clearance"  to  a  minimum. 


STRUCTURE   OF    THE    STEAM-ENGINE. 


101 


(2)  The  use  of  a  rotating  valve,  capable  of  being  cheaply 
and  readily  fitted  up,  of  being  easily  moved,  and  of  being  con- 
veniently worked  by  connections  outside  the  steam-spaces. 

(3>  The  use  of  a  "  wrist-plate,"  caused  to  oscillate  by  a  sin- 
gle eccentric,  and  directly  so  connected  with  all  four  valves 
that  each  may  be  given  a  rapid  opening  and  closing  movement, 
and  be  held  open  and  nearly  still,  at  either  end  of  its  range,  by 
swinging  the  line  of  connection  nearly  into  the  line  between 
centres,  thus  permitting  nearly  a  full  opening  of  port  to  be 


FIG.  37. — THE  DASH- 


maintained  during  an  appreciable  interval,  and  a  free  and  com- 
plete steam  supply  and  exhaust. 

(4)  A  beautifully  simple  and  effective  method  of  detaching 
the  steam-valve  from  the  driving  mechanism,  and  of  insuring 
its  rapid  and  certain  closure  at  the  proper  moment,  to  produce 
any  desired  expansion  of  steam. 

(5)  A  direct  connection  of  the  governor,  so  as  to  determine 
the  ratio  of  expansion,  while  so  adjusting  the  power  of  the 
engine  to  the  work  to  be  done  that  the  variation  of  speed  with 
changing  loads  becomes  a  minimum. 

(6)  Making  this  latter  adjustment  in  such  away  as  to  throw 
the  least  possible  work  on  the  regulating  mechanism,  and  thus 


IO2 


A    MANUAL   OF   THE    STEAM-ENGINE. 


to  give  the  governor  the  greatest  possible  sensitiveness  and 
accuracy  of  action. 

(7)  A  form  of  frame  and  general  design  of  engine  which 
gives  maximum  strength  and  stiffness,  with  least  cost  and 
weight. 

All  these  features  are  combined  to  form  a  steam-engine 
essentially  different,  in  general  and  in  detail,  from  all  earlier 
engines.  In  operation,  the  engine  was  found  to  exhibit  a 
remarkable  economy  of  fuel,  and  a  singularly  perfect  regula- 


FIG.  38.—  GREENE  ENGINE. 


tion,  and  to  be  far  more  durable  and  more  economical  in  cost 
of  repairs,  on  the  average,  than  was  generally  supposed  possible. 
The  Greene  Strain-engine  (Fig.  38)  has  four  valves,  as  in  the 
Corliss.  The  cut-off  gear  consists  of  a  bar,  A,  moved  by  the 
steam-eccentric  in  a  direction  parallel  with  the  centre-line  of 
the  cylinder  and  nearly  -coincident  as  to  time  with  the  piston. 
On  this  bar  are  tappets,  C  C,  supported  by  springs  and  adjustable 


104  A   MANUAL    OF   THE   STEAM-ENGINE. 

in  height  by  the  governor.  These  tappets  engage  the  arms,  B  B, 
on  the  ends  of  rock-shafts,  E  E,  which  move  the  steam-valves 
and  remain  in  contact  with  them  a  longer  or  shorter  time,  and 
holding  the  valve  open  during  a  greater  or  less  part  of  the 
piston-stroke,  as  the  governor  permits  the  tappets  to  rise  with 
diminishing  engine-speed,  or  forces  them  down  as  speed  in- 
creases. The  exhaust-valves  are  moved  by  an  independent 
eccentric-rod,  which  is  itself  moved  by  an  eccentric-set,  as  is 
usual  with  the  Corliss  and  with  other  engines  generally,  at 
right  angles  with  the  crank.  This  engine,  in  consequence  of 
the  independence  of  the  steam-eccentric,  and  of  the  contem- 
porary movement  of  steam  valve-motion  and  steam-piston,  is 
capable  of  cutting  off  at  any  point  from  beginning  to  nearly 
the  end  of  the  stroke.  The  usual  arrangement,  by  which  steam 
and  exhaust  valves  are  moved  by  the  same  eccentric,  only  per- 
mits expansion  with  the  range  from  the  beginning  to  half-stroke. 
In  the  Corliss  engine  the  latter  construction  is  retained,  with 
the  object,  in  part,  of  securing  a  means  of  closing  the  valve  by 
a  "  positive  motion,"  should,  by  any  accident,  the  closing 
not  be  effected  by  the  weight  or  spring  usually  relied  upon. 

There  are  other  engines  belonging  to  the  class  here  con- 
sidered— engines  having  a  detachable  cut-off  valve  closed 
independently  of  the  motion  of  the  valve-gear, — of  which  space 
will  not  permit  description.  Among  these  are  the  Wright 
engine,  constructed  by  one  of  the  oldest  and  best  known 
designers  in  the  United  States;  the  Brown  engine,  a  machine 
which  has  been  extensively  adopted  for  driving  mills  in  New 
England,  and  is  famous  for  the  excellence  of  its  workmanship 
and  finish,  as  well  as  for  its  durability  and  efficiency  ;  the  Fitch- 
burg  engine,  and  others. 

An  ingeniously  arranged  engine  of  the  class  considered  in 
this  division  of  the  subject,  the  Wheelock  engine,  is  seen  in 
the  accompanying  engraving. 

The  steam-chest  is  placed  below  the  cylinder,  and  the  steam- 
and  exhaust-valves  are  set  side  by  side,  the  latter  serving  both 
as  induction  and  eduction  valve,  and  having  the  same  action, 
nearly,  as  the  common  three-ported  slide-valve  ;  while  the  func- 


STRUCTURE   OF   THE   STEAM-ENGI.VE. 


105 


IO6  A   MANUAL   OF   THE    STEAM-ENGINE. 

tion  of  the  former  is  principally  that  of  a  cut-off  valve.  The 
latter,  or  main  valve,  is  set  nearest  the  end  of  the  cylinder,  and 
the  exhaust  steam  is  thus  permitted  to  escape  directly,  and 
promptly  from  the  engine.  The  valve  and  seat  are  independent, 
and  coned  slightly,  and  may  be  adjusted  to  take  up  wear,  or 
to  relieve  pressure  on  the  seats.  These  valves  are  carried 
on  steel  trunnions,  and  with  hardened  surfaces  of  contact  are 
but  little  subject  to  wear.  The  steam  or  cut-off  valve  is  set 
farther  away  from  the  cylinder  than  in  the  standard  arrange- 
ments of  Corliss  and  other  builders  of  that  class  of  engines, 
and  this  enables  the  maker  of  this  engine  to  secure  a  single 
port  with  reduced  clearance  and  less  liability  to  leakage,  should 
the  expansion-valve  leak.  In  the  later  engines  of  this  class  a 
gridiron  valve  is  used  in  a  shell  of  the  same  general  form,  as 
illustrated  in  Volume  II.  In  this  engine — and  it  should  be 
the  case  in  every  engine  in  which  the  regulator  is  driven  by 
belt — the  connection  from  shaft  to  governor  is  so  made  that 
the  breaking  of  the  belt  permits  an  automatic  closing  of  the 
valve  and  the  stopping  of  the  engine.  The  regularity  of 
motion  of  the  class  of  engines  described  in  this  section  may  be 
inferred  from  the  fact  stated  in  regard  to  the  engine  here 
studied,  that  it  has  been  known  to  vary  but  a  half-revolution 
per  minute  when  five  sixths  of  the  load  was  thrown  off. 

Simple  and  Compound  Stationary  Engines  are  both  in  com- 
mon use  as  mill-engines ;  and  all  the  familiar  classes  of  engines 
are  constructed  in  both  forms.  Until  recently  the  mill-engine 
has  been  very  generally  a  single-cylinder  engine,  or  a  pair  of  sim- 
ple engines  coupled  with  cranks  at  right-angles  where  great 
power  was  demanded  ;  but  the  Corliss  and  other  mill-engines  are 
now  often  "compounded,"  and  it  is  not  unusual  to  compound 
comparatively  small  high-speed  engines.  In  such  cases  the 
elements  of  the  combination  are  commonly  similar  in  design 
to  the  simple  form  of  the  same  engine.  The  combination  is  often 
made  by  constructing  a  "  tandem  "  engine,  in  which  the  cylin- 
ders are  placed  in  the  same  line,  end  to  end,  and  often  with 
their  pistons  on  the  same  rod.  In  other  cases,  the  engines  are 
set  side  by  side,  actually  constituting  each  a  complete  engine, 


STRUCTURE  OF   THE   STEAM-ENGINE  IOJ 

with  their  cranks  set  at  right-angles  for  a  two-cylinder  com- 
pound, or  at  angles  of  120°  for  a  "  triple-expansion,"  engine, 
and  with  a  common  frame.  In  such  cases,  as  will  be  seen  later, 
an  intermediate  "  receiver  "  is  introduced  into  which  the  high- 
pressure  cylinder  exhausts  and  from  which  the  low-pressure 
cylinder  takes  its  supply  without  seriously  affecting  the  work- 
ing of  the  fluid. 

Nearly  all  the  engines  to  be  described  are  thus  built  "  com- 
pound," and  some  are  "  triple  expansion." 

The  Stationary  Multiple-cylinder  Engine  is  rarely  given  the 
_ne  form  as  the  marine  engine.  The  necessity  of  having  a 
!_  .ar  of  cranks,  and  the  objection  to  the  employment  of  the 
fly-wheel,  do  not  here  exist ;  nor  does  either  the  volume  or  the 
weight  of  the  machine  become  so  vitally  important  a  matter 
as  at  sea.  The  design  adopted  is,  for  these  reasons,  one  which 
will  be  of  minimum  first  cost,  irrespective  of  these  considera- 
tions. 

Tke"Tandem  "  Engine  is  perhaps  the  most  common  form  of 
stationary  compound  engine.  In  this  type,  as  shown  in  the 
accompanying  illustration,  the  two  cylinders  are  set  in  line, 
have  a  common  piston-rod,  and  drive  the  same  crank.  The 
high-pressure  cylinder  is  commonly  placed  behind  the  low- 
pressure,  and  the  latter  is  directly  attached  to  the  frame  of  the 
engine.  The  exhaust  of  the  smaller  cylinder  is  carried  in  any 
convenient  manner  to  the  large  engine ;  but  the  more  direct 
and  the  larger  the  conduits  employed,  the  better.  In  some 
cases,  the  two  cylinders  are  set  directly  in  contact.  This  plan 
involves  a  difficulty,  usually,  in  packing  the  rod  between  them, 
but  it  has  the  advantage  of  great  compactness. 

The  Compound  Corliss  Engine  was  first  introduced  by  other 
builders ;  but  no  ore  was  more  successful  in  the  economical 
working  of  the  machine  than  was  its  great  originator,  the  late 
George  H.  Corliss.  The  usual  method  of  compounding  this 
engine  for  stationary  purposes  is  that  known  as  the  "  tandem  " 
system,  in  which  the  high-pressure  cylinder  is  set  behind  the 
low-pressure,  both  pistons  having  a  common  rod  and  driving  a 
common  set  of  reciprocating  parts  and  having  valve-gearing 


io8 


A    MANUAL   OF   THE   STEAM-ENGINE. 


actuated  by  the  same  eccentric  and  rod.  The  plan  is  simple, 
inexpensive,  convenient,  and  compact,  and  is  found  to  be  very 
satisfactory  in  operation,  the  economy  attained  by  it  being 
about  as  high  as  that  of  any  other  arrangement  yet  devised. 


This  method  is  illustrated  by  Fig.  41,  which  exhibits  a  form  of 
the  engine  designed  by  Mr.  Edwin  Reynolds.  It  is  readily  seen 
that  it  would  probably  be  impossible  to  find  a  better  method 
of  combining  maximum  efficiency  with  minimum  cost  of  con- 


STXUCTUXE  OF  THE  ST£AM£A'G/y£.  :  ;.:. 

struct  ion  than  this,  or  to  make  a  more  compact:  disposition  of 
parts.  It  is  necessarily  of  considerable  length ;  but  in  other 
directions  has  no  greater  dimensions  than  the  single  engine  of 
the  simple  type. 

The  performance  of  this  type  of  engine  has  been  most 
excellent.  For  example,  the  engines  of  the  Xourse  steam- 
mfll,  as  constructed  by  Mr.  Corliss,  were  found  to  demand  no 
more  than  1.62  pounds  of  good  fuel  per  horse-power  and  per 
hour.  The  same  engine  as  a  simple  engine,  the  high-pressure 
cylinder  disconnected.,  if  equal  to  the  best  of  its  class,  under 
TJmflar  conditions  of  operation,  would  probably  not  require  less 
than  two  pounds ;  which  may  be  taken  as  about  the  limit  of 
economical  working  for  that  type  of  engine,  with  a  good  con- 
denser and  dry  steam. 

One  disadvantage  of  this  type  of  engine — the  *•  tandem"" — is 
the  length  of  passage  between  the  exhaust-port  of  the  high- 
pressure  and  the  induction-passage  of  the  low-pressure  cvlin- 
der  when  the  former  is  taking  steam  in  the  backward  stroke ; 
but  this  is  partly  compensated,  at  least,  by  the  very  short  pas- 
sage obtainable  for  the  opposite  movement.  The  valve-gearing; 
is  commonly  the  same  on  both  cylinders ;  but  it  is  often  so 
arranged  that  the  governor  operates  on  the  one  cylinder  onlv. 
leaving  the  ratio  of  expansion  of  the  other  to  be  determined 
by  the  measure  of  expansion  in  the  first. 

Another  not  uncommon  system  of  compounding  this  engine, 
especially  for  large  powers,  is  oftener  practised  in  Europe  than 
in  the  United  States.  This  is  the  coupling  of  two  engines, 
side  by  side,  as  in  common  marine  practice;  while  another 
method  sometimes  adopted  is  the  adaptation  of  two  independ- 
ent engines  of  properly-adjusted  sizes  to  act,  the  one  as  the 
high-,  the  other  as  the  low-pressure  engine  of  a  compound  sys- 
tem. These  engines  are  occasionally  set  at  some  distance 
apart,  when  the  local  conditions  make  that  a  more  convenient 
disposition.  The  efficiencies  of  these  several  types  of  com- 
pound Corliss  engines  are  substantially  the  same.  They  are  all 
subject  to  about  one  half  the  internal  wastes  of  the  simple 
engine  of  qffiilar  dimensions,  to  about  doable  the  external 


STRUCTURE:  OF  THE  STEAM-ENGINE.  in 

wastes  of  heat,  and  have  a  trifle  more  friction.  On  the  whole, 
they  will  ordinarily  give  an  increased  economy  amounting  to 
about  twenty  per  cent  of  the  heat  and  fuel  consumption  of 
the  simple  engine. 

In  some  cases  the  arrangement  of  a  pair  of  complete 
engines,  of  properly  selected  sizes,  in  such  manner  that  either 
the  exhaust  of  one  may  be  used  in  the  other,  or  steam  may  be 
taken  direct  from  the  boiler  to  either,  is  found  advantageous. 
When  less  power  is  demanded,  or  when  one  is  disabled,  the 
available  engine  may  then  be  used  alone.  Economy  has  been 
attained  by  this  plan,  even  when  the  two  engines  are  placed  at 
considerable  distances  apart,  the  precaution  being  taken  to 
carefully  guard  against  loss  of  heat  between  them. 

The  "Cross-compound"  type  of  Corliss  engine  is  illustrated  by 
the  accompanying  sketch  of  a  pair  designed  by  Mr.  Reynolds 
and  built  by  Allis  &  Co.  for  the  Namquit  Mills.  The  cranks  are 
set  at  right-angles,  and  the  receiver  is  placed  beneath  the  floor. 
This  is  a  less  common  variety  than  the  "  tandem  "  form  ;  but 
is  still  often  adopted. 

The  general  arrangement  and  disposition  of  the  parts  of  a 
triple-expansion  engine,  as  built  by  the  Corliss  Co.,  is  seen  in 
Fig.  43.  Here  the  low-pressure  cylinder  is  divided,  one  of  its 
two  elements  being  coupled  with  the  high-pressure  cylinder 
on  the  right,  and  the  twin  with  the  intermediate  cylinder  on 
the  left.  The  cranks  are  set  at  90°.  These  engines  have 
cylinders  20,  34,  36,  and  36  inches  diameter  and  5  feet  stroke 
of  piston.  All  cylinders  are  completely  steam-jacketed, 
heads  included,  and  the  steam  is  somewhat  superheated. 
Jet-condensers  are  used.  The  capacity  of  the  engine  is 
1000  I.  H.  P.  or  more,  and  its  "duty"  is  about  135,000,000 
pounds ;  the  fuel  used,  when  of  good  quality,  amounting, 
on  test,  to  1.44  pounds  per  horse-power  per  hour. 

"Compounding"  simple  engines  is  often  a  very  economical 
and  profitable  plan.  The  method  depends  mainly  upon  the 
design  of  the  engine  to  be  so  altered.  The  common  forms  of 
stationary  beam-engine  are  commonly  improved  by  what  is 
called  "  McNaughting,"  placing  a  ne-  /  high-pressure  cylinder 


112 


A   MANUAL   OF   THE   STEAM-ENGINE. 


STRUCTURE   OF   THE   STEAM-ENGINE. 


beside  the  old  cylinder  and  connecting  it  to  the  beam  either 
at  the  old  air-pump  centre,  if  condensing,  or  to  the  point  at 
which  the  air-pump  would  have  been  attached,  if  the  engine 


be  non-condensing.  The  vertical  marine  engine  may  sometimes 
be  altered  into  the  compound  form  by  placing  the  new  cylin- 
der above  the  old  and  the  two  pistons  on  a  common  rod. 


114  A  MANUAL   OF   THE   STEAM-ENGINE. 

Many  engines  cannot  be  satisfactorily  compounded,  and  others 
only  by  the  establishment  of  a  separate  complete  high-pres- 
sure engine  in  close  proximity  to  the  old  and  arranging  the 
latter  to  take  its  steam  from  the  former. 

The  gain  to  be  anticipated  by  such  improvement  and  alter- 
ation of  type  will  depend  upon  the  character  of  the  altered 
machine.  Should  it  be  a  very  wasteful  engine,  enormous 
gains  may  be  anticipated  if,  while  adding  the  new  construction, 
the  old  is  put  in  good  order.  For  cases  in  which  the  old  en- 
gine is  reasonably  economical,  the  gain  is  simply  that  due  to 
reduction  of  cylinder-condensation,  and  this  is  at  least  partly 
compensated  by  the  friction  of  the  added  parts.  Savings  as 
great  as  one  half  are  not  unusual  in  such  cases  as  the  first,  and 
as  little  as  ten  per  cent,  in  cases  like  the  second,  are  common. 
Whether  such  a  gain  is,  on  the  whole,  financially  advantageous 
is  still  another  question  to  be  settled  for  each  case. 

Rolling-mill  Engines  are  often  constructed  especially  for 
their  work.  For  heavy  mills  they  are  often  made  to  reverse. 
The  last  figure  illustrates  a  common  form  of  reversing-engine. 
The  engine  frames  are  heavy  cast-iron  girders  having  a  bearing 
the  entire  length  on  the  foundation.  On  the  top  side  of  the 
frames  are  the  main  journals.  These  journals  are  provided 
with  means  for  taking  up  wear  and  adjusting  the  helical  gears 
which  transmit  motion  from  one  shaft  to  the  other. 

The  main  valves  are  placed  under  the  cylinders,  the  valve- 
chambers  forming  a  part  of  the  cylinder  casting,  thus  bringing 
the  steam-ports  on  the  lower  side  of  the  cylinder,  to  allow 
water  of  condensation  to  pass  out  through  the  exhaust-ports 
without  danger  to  either  cylinder  or  head.  As  an  additional 
means  of  safety  the  builders  often  use  "  snifting-valves "  on 
each  end  of  the  cylinder. 

Where  very  heavy  rolls  are  employed,  as  in  making  armor- 
plate,  for  example,  an  engine  is  often  demanded  which  may 
be  instantly  reversed,  driving  with  equal  facility  in  either  di- 
rection. Fig.  45  exhibits  such  an  engine  as  built  by  the  Allis 
Co.,  from  Mr.  Reynolds's  plans,  for  Messrs.  Carnegie,  Phipps 
&  Co.  of  Pittsburgh.  The  fly-wheel  is  here,  also,  dispensed 


STRUCTURE   OF   THE   STEAM-ENGINE.  11$ 

with,  and  the  engines  are  designed  for  high  speeds  of  rotation 
and  very  heavy  work. 

The  steam-cylinders  are  forty  inches  diameter  by  fifty-four 


inches  stroke,  with  Reynolds'  Corliss  valve-gear  without  the 
drop  cut-off  mechanism  ;  the  speed  of  the  engines  is  controlled 
by  the  operator,  and  is  varied  in  every-day  practice  from  5 


Il6  A    MANUAL   OF   THE   STEAM-ENGINE. 

revolutions  to  120  revolutions  per  minute.  Power  from  the 
crank-shaft  is  transmitted  to  the  roll-shaft  by  means  of  a  pair 
of  shrouded  helical-tooth  steel  gears. 

The  reversing  mechanism,  operated  by  steam,  is  controlled 
by  a  lever  on  the  engineer's  platform;  from  this  position  he 
has  unobstructed  view  of  all  parts  of  the  engine  and  roll-train. 

35.  High  and  Low  Speed  distinguish  a  more  modern  type 
from  those  engines  already  described.  Classified  with  refer- 
ence to  their  method  of  driving  machinery,  we  may  thus  desig- 
nate the  two  classes : 

(1)  Engines  which   may  be  used  in    driving  by  belt,  and 
which  are  not  adapted  for  direct  connection. 

(2)  Engines   especially   designed    and    constructed    to    be 
coupled  directly  to  the  "  dynamo." 

The  first  class  of  engines  is,  by  many  of  the  more  conservative 
engineers,  still  preferred  to  the  second.  The  latter  constitute 
the  so-called  modern  "  high-speed  "  type  of  engine,  and  are 
gradually  coming  into  use  ;  some  engineers  adopting  them  both 
for  direct  and  for  indirect  connection.  The  most  experienced 
engineers  are  not  yet  fully  in  accord  in  regard  to  the  question 
whether  they  have  passed  the  experimental  stage  in  such 
general  application. 

One  of  the  methods  of  securing  economy  in  the  working 
of  steam  has  been  stated  to  be  the  driving  of  the  engine  up  to 
the  highest  safe  velocity  of  piston,  and  giving  it  maximum 
speed  of  rotation.  The  time  allowed  for  "  initial  "  condensa- 
tion of  each  charge,  and  for  the  necessary  change  of  tempera- 
ture preceding  such  condensation,  is  thus  reduced,  and  the 
amount  of  steam  condensed  within  the  cylinder  being  thus 
made  a  minimum,  in  any  given  time,  the  percentage  of  loss 
of  the  increased  quantity  of  steam  worked  off  by  the  engine 
becomes  correspondingly  less. 

Engines  of  this  class  have  a  number  of  advantages,  consequent 
upon  their  high  speed  :  they  are,  other  things  being  equal,  more 
economical  in  the  use  of  steam  ;  they  can  be  given  a  very  much 
smaller  fly-wheel ;  they  have,  in  consequence  of  the  enormously 
reduced  weight  of  wheel,  less  friction ;  they  are  more  easily 


STRUCTURE  OF   THE   STEAM  EXCISE.  IIJ 

held  to  their  speed  by  the  governor ;  they  are  less  subject  to 
variation  of  speed  between  beginning  and  end  of  any  one 
stroke :  and  they  are  often  less  troublesome  and  expensive  to 
connect  to  the  load  than  slow- running  engines.  These  ad  van- 
tages are  common  to  all  classes  of  engines,  if  they  can  be 
driven  up  to  high  speeds.  The  class  here  considered  is  better 
fitted  to  realize  these  advantages  than  the  older  forms  of 
engines,  because  they  are  especially  designed  for  high  speed. 

The  objection  to  this  type  of  engine  is  the  increased  risk 
of  wear,  and  of  accident,  due  to  their  rapid  motion,  and  espe- 
cially the  danger  that  when  accidents  do  occur  they  may  be 
more  serious  than  with  engines  working  at  ordinary  speeds. 
The  precautions  taken  by  builders  of  fast  engines  are  all 
directed  toward  meeting  this  contingencj-,  making  their  ma- 
chines safe  against  accident.  These  precautions  are  seen  to 
be  the  strengthening,  and  especially  the  stiffening,  of  all  the 
parts  exposed  to  the  stresses  due  to  the  action  of  inertia  in  the 
reciprocating  pieces  :  the  adjustment  of  all  parts  to  each  other 
in  such  a  manner  as  to  avoid  spring;  the  use  of  the  best 
material,  and  of  an  effective  system  of  lubrication  :  and  the 
securing  of  the  most  perfect  workmanship. 

As  actually  constructed,  they  are  of  proportionallj-  shorter 
stroke  than  the  preceding  types,  and  are  consequently  more 
subject  to  internal  waste  by  cylinder-condensation  and  have 
large  clearance  and  "  dead  "  spaces,  and  thus,  also,  both  exag- 
gerate internal  heat-waste,  and  become  liable  to  greater  loss 
of  cushion-steam.  As  a  rule,  in  actual  work,  this  class  of 
engine  is  not  usually  distinguished  by  peculiarly  high  economi- 
cal results,  in  competition  with  the  "  low-speed  "  engines. 

The  latter,  on  the  other  hand,  usually  are  at  a  disadvantage 
for  fast  running,  both  through  complication  of  parts  and  the 
use  of  a  detachable  valve. 

TJu  Porttr-Allcn  Engine  was  the  first  of  the  class  known 
as  *•  high-speed  "  engines.  Its  designers  were  Mr.  C.  T.  Porter 
and  Mr.  J.  F.  Allen,  the  latter  being  the  inventor  of  its  valve- 
gear  :  while  the  former  was  the  pioneer  in  the  introduction  of 
engines  of  this  class. 


riS 


MANUAL   OF    THE    STEAM-ENGINE. 


STRUCTURE  OF  THE  STEA31-EXGIXS.  119 

In  the  Allen  engine  (Fig.  46),  the  cylinder  and  frame  are 
connected  as  in  the  engine  seen  in  Fig.  25,  and  the  crank-disk, 
shaft-bearings,  and  other  principal  details  are  not  essentially 
different.  The^  valve-gear  differs  in  having  four  valves,  one  at 
each  end  on  the  steam  as  well  as  on  the  exhaust  side,  all  of 
which  are  balanced  and  worked  with  very  little  resistance. 
These  valves  are  not  detachable,  but  are  driven  by  a  link 
attached  to  and  moved  by  an  eccentric  on  the  main  shaft ;  the 
position  of  the  valve-rod  attachment  to  which  link  is  deter- 
mined by  the  governor,  and  the  degree  of  expansion  is  thus 
adjusted  to  the  work  of  the  engine.  The  engine  has  usually  a 
short  stroke,  not  exceeding  twice  the  diameter  of  cylinder,  and 
is  driven  at  very  high  speed,  generally  averaging  from  600  to 
800  feet  per  minute.*  This  high  piston-speed  and  short 
stroke  give  high  velocity  of  rotation.  The  effect  is,  therefore, 
to  produce  an  exceptional  smoothness  of  motion,  while  per- 
mitting the  use  of  small  fly-wheels.  Its  short  stroke  ^-n^M*^ 
solidity  to  be  attained  in  a  bed  of  rigid  form,  making  it  a  self- 
contained  engine,  adapted  to  heavy  work,  and  requiring  but 
a  small  foundation. 

The  journals  of  the  shaft,  and  all  cylindrical  wearing-sur. 
faces  of  such  engines,  are  finished  by  grinding,  and  are  thus 
made  perfectly  cylindrical.  The  crank-pin  and  cross-head  pin 
are  hardened  before  being  ground.  The  joints  of  the  valve- 
gear  consist  of  pins  turning  in  solid  ferrules  in  the  rod-ends, 
both  hardened  and  ground.  After  years  of  constant  use  thus, 
no  wear  occasioning  appreciable  lost  time  in  the  valve-move- 
ments occurs. 

Where  great  steadiness  of  motion  is  desired,  the  expense  of 
coupled  engines  is  often  incurred.  Quick-running  engines  do 
not  often  require  to  be  coupled ;  a  single  engine  may  give 
greater  uniformity  of  motion  than  is  usually  obtained  with 
coupled  engines  at  ordinary  speeds. 

The  governor  used  on  this  engine  is  known  as  the  Porter 
governor.  It  is  given  power  and  delicacy  by  weighting  it 

*  Or  not  fer  from  600  limes  the  cube  root  of  the  length  of  stroke,  mil  mi 
in  feet. 


120  A    MANUAL    OF    THE    STEAM-ENGINE. 

down,  and  thus  obtaining  a  high  velocity  of  rotation,  and  by 
suspending  the  balls  from  forked  arms,  which  are  given  each 
two  bearing-pins  separated  laterally  so  far  as  to  permit  consid- 
erable force  to  be  exerted  in  changing  speeds  without  cramping 
those  bearings  sufficiently  to  seriously  impair  the  sensitiveness 
of  the  governor. 

In  "high-speed"  engines,  the  possibilities  in  the  direction  of 
increasing  speeds  are  sought  to  be  made  the  most  of.  Their 
market  is  not  only  to  be  found  in  the  domain  of  the  electrical 
generation  of  light,  and  electrical  transmission  of  power,  but  in 
older  fields  of  work  as  well.  The  loss  of  power  in  the  "  jack- 
shafts,"  or  "  first-motion  shafts,"  of  mills  and  workshops  driven 
by  the  low-speed  engines  is  an  item  of  no  inconsiderable  amount 
in  many  cases.  The  tendency  is  now  observable  toward  the 
adoption  of  the  higher  speed  of  engine,  in  direct  connection 
with  the  main  line  of  shafting,  even  where  not  quite  as  econom- 
ical in  the  use  of  steam,  through  the  intermediary  of  a  single 
belt  or  pair  of  gears,  or  even  by  directly  attaching  the  crank- 
shaft of  the  engine  to  the  main  line  by  a  coupling. 

Mr.  Allen's  invention  of  a  valve-gear  placed  in  the  hands  of 
Mr.  Porter,  who  was  endeavoring  to  design  a  "  high-speed  " 
engine,  the  device  needed  to  carry  out  the  idea. 

This  arrangement  consists  of  a  single  eccentric  driving  a 
link-motion  to  operate  the  steam-valve  and  to  work  the 
exhaust  at  the  same  time.  The  link  is  controlled  by  a  Porter 
governor,  and  is  so  connected  and  driven  that  the  gear  may  be 
readily  and  quickly  adjusted  by  the  governor  to  any  desired 
point  of  cut-off.  The  eccentric  and  link  are  shown  in  the  next 
illustration.  The  eccentric  is  set  on  the  shaft  in  such  a  position 
that  its  motion  is  coincident  with  that  of  the  crank.  The  link 
is  a  slotted  curved  arm,  forming  one  piece  with  the  eccentric- 
strap,  pivoted  at  the  middle  on  trunnions  sustained  by  an  arm 
rocking  about  a  pin  set  in  the  bed  of  the  engine.  The  upper 
end  of  the  link  carries  a  pin,  from  which  a  rod  leads  off  to  the 
exhaust,  which  is  driven  without  variable  connections.  The 
link-block  is  fitted  to  work  in  the  slot  of  the  link,  from  the  end 
nearest  the  exhaust-rod  pin,  down  to  the  point  opposite  the 


STRUCTURE   OF   THE   STEAM-ENGIXE. 


121 


pivotal  point  at  which  the  trunnions  are  set.  \Yhen  it  is  at 
the  upper  end,  the  throw  of  the  valve  is  a  maximum ;  when  at 
the  lower  point,  it  is  a  minimum.  As  the  link-block  is  moved 
up  and  down  in  the  slot,  the  motion  of  the  valve  is  varied,  and 
the  ratio  of  expansion  correspondingly  altered.  By  an  in- 
genious adjustment  of  a  still  more  ingenious  form  of  valve- 
motion,  it  is  thus  possible  to  obtain  a  valve  movement  of  perfect 
precision  at  all  speeds,  and  on  both  the  forward  and  the  back- 


FIG.  47. — THE  ALLEN    LINK.    (Scale  -ft-) 

ward  stroke,  with  a  quicker  closing  action,  as  the  cut-off  is 
later.  The  steam  is  allowed  to  enter  the  cylinder,  at  nearly 
boiler  pressure,  almost  up  to  the  point  of  cut-off,  and  the  ex- 
pansion line  is  a  smooth  curve  very  nearly  from  the  junction 
with  the  steam  line. 

The  four  valves  are  shown  in  the  next  figure,  which  is 
a  section  through  the  steam-cylinder  showing  valve,  ports,  and 
general  construction.  The  two  valves  at  the  upper  side  of  the 
cylinder  are  the  steam-valves ;  the  lower  are  the  exhaust- 
valves.  This  section  is,  however,  horizontal,  the  valves  being 
set  on  their  edges  at  either  side  of  the  cylinder.  The  exhaust- 


122 


A  MANUAL    OF    THE   STEAM-ENGINE. 


valves  are  so  placed  as  to  drain  the  cylinder  of  any  water  that 
may  have  entered  with  the  steam,  or  may  have  been  produced 
by  internal  condensation.  Both  sets  of  valves  are  so  made, 


and  set,  as  to  be  well  balanced,  and  so  as  to  be  capable  of  hav 
ing  the  wear  taken  up  when  it  occurs.  The  steam-valves  are 
provided  with  packing-plates,  which  are  adjustable  by  hand,  to 


STRUCTURE   OF   THE   STEAM-ENGINE.  123 

make  them  steam-tight,  as  well  as  to  secure  a  perfect  balance. 
Each  valve  is  placed  in  a  separate  valve-chest,  and  can  be  in- 
dependently  adjusted.  Each  valve  opens  four  ports;  each  is  so 
set  that  it  is  actuated  by  a  rod  in  the  line  of  its  own  centre ; 
and  all  are  thus  rendered  but  little  liable  to  either  wear  or 
leakage.  The  rock-shaft  arm  on  the  intermediate  rock-shaft, 
between  the  eccentric  and  the  steam-valve  stem,  assists  in  secur- 
ing the  quick  opening  and  closing  motion  essential  to  a  satis- 
factory distribution  of  the  steam. 

The  features  which  have  been  described  are  not  necessarily 
distinctive  of  a  "  high-speed  engine."  A  positive-motion  valve- 
gear,  and  a  good  steam-distribution,  are  desirable  in  such 
engines,  and  the  first  point  is,  in  fast-running  machines,  an 
essential  requisite ;  but  the  engine,  so  far  as  it  has  been  de- 
scribed, may  be  as  well  considered  a  slow  as  a  fast  engine. 
There  are  some  details  which  are  essentially  and  peculiarly 
characteristic  of  the  class  to  which  this  machine  is  assigned. 
Among  these  points  are  the  strength  and  rigidity  of  parts 
which  distinguish  such  engines ;  the  great  nicety  of  fitting ;  the 
excellence  of  all  material  in  every  part  exposed  to  the  straining 
action  of  inertia,  and  the  minor  modifications  of  details  to 
adapt  them  to  service  in  a  machine  in  which  play  in  joints  or 
bearings  will  make  trouble. 

The  bed  is  stiff  and  solid,  especially  in  those  parts  which 
take  the  stresses  of  the  reciprocating  pieces.  It  is  broad  and 
deep,  with  the  line  of  thrust  of  piston-rod  carried  close  to  its 
surface  between  the  guides,  and  with  a  box  form  which  gives 
great  resistance  to  forces  tending  to  twist  it.  The  steam-cylin- 
der is  secured  to  the  bed  by  the  end,  a  construction  adopted 
by  Corliss  many  years  ago,  and  one  which  gives  all  desirable 
strength,  with  freedom  from  those  strains  which  come  of  con- 
nection of  two  large  masses  at  different  and  constantly  varying 
temperatures.  The  main  journal-boxes  are  made  in  four 
pieces,  and  are  set  up  by  adjustable  wedges,  so  set  as  to  avoid 
the  springing  of  the  shaft  that  is  sometimes  found  to  occur  with 
a  less  effective  arrangement.  The  main-shaft  journals,  and  the 
journals  of  the  crank-pins,  are  made  with  especial  care,  skil- 


124  A    MANUAL   OF   THE   STEAM-ENGINE. 

fully  ground  to  size  and  form,  and  nicely  finished  before  the 
engine  is  assembled.  The  pin  is  of  "  mild "  steel,  carefully 
case-hardened  to  give  it  a  surface  that  will  wear  well  and  will 
not  "  cut."  The  provisions  for  lubrication  in  such  engines  are 
among  the  most  important  of  its  details. 

The  action  of  inertia  in  the  moving  parts  is  made  by 
Mr.  Porter  the  means  of  securing  smoothness  in  working  and 
evenness  of  crank-pin  pressures.  At  the  beginning  of  the 
stroke  the  inertia  of  the  piston,  its  rod,  the  cross-head,  and  to 
a  certain  extent  the  connecting-rod,  of  all  reciprocating  parts, 
causes  them  to  offer  a  certain  resistance  to  the  accelerated 
motion  which  they  are  compelled  to  take  up.  This  resistance 
becomes  less  and  less  up  to  zero  at  half-stroke,  the  point  at 
which  their  velocity  is  a  maximum.  Passing  this  point,  they  are 
rapidly  retarded,  and  this  same  property  of  inertia  causes 
them  to  offer  a  resistance  to  retardation,  which  resistance  now 
is  felt  as  an  impelling  force  at  the  crank-pin.  Thus,  the 
effect  of  the  presence  of  these  heavy  masses  in  the  line  of 
connection  produces  a  reduction  of  pressure  upon  the  pin  at 
the  commencement,  and  an  increase  of  pressure  at  the  end,  of 
stroke.  But  in  consequence  of  the  varying  action  of  the 
steam,  producing  an  excess  of  pressure  at  the  beginning  and 
a  deficiency  of  pressure  at  the  end  of  stroke,  we  may  combine 
these  two  effects,  and  the  result  is  a  comparatively  uniform 
load  upon  the  crank-pin  throughout  the  stroke.  This  com- 
pensation is  capable  of  being,  in  many  cases,  very  nicely 
adjusted  by  properly  proportioning  the  weight  of  the  recipro- 
cating parts.  It  is  evident,  however,  that  at  some  higher 
speed,  the  weight  of  these  parts,  as  proportioned  for  strength 
simply,  would  be  sufficient  to  give  this  desirable  adjustment 
of  the  load  on  the  crank-pin.  There  is  no  reason  to  suppose 
that  this,  which  would  seem  to  be  a  natural  speed  of  the  steam- 
engine,  may  not,  at  any  time,  be  attained. 

The  Porter-Allen  engine,  the  earliest  of  the  "  high-speed  " 
engines,  was  also  one  of  the  first  of  its  class  to  be  constructed 
as  a  compound  engine.  Since  the  best  engines  of  this  type 
have  about  the  efficiency  of  good  Corliss  engines,  it  is  evident 


STRUCTURE   OF   THE   STEAM-ENGINE.  12$ 

that  the  opportunity  offered  for  economical  improvement  is 
here  equal,  and  the  result  of  the  experiment  has  been  as  sat- 
isfactory. The  usual  methods  of  compounding  are  substan- 
tially the  same  as  those  familiar  in  the  case  of  the  Corliss  en- 
gine, and  they  may  be  expected  to  exhibit  a  similar  ratio  of 
improvement  when  compared  with  the  corresponding  simple 
machine.  In  some  cases  this  gain  is  not  sufficient  to  compen- 
sate the  increased  cost  and  complication,  added  expense  of 
maintenance,  and  greater  weight  and  volume  ;  but  at  pressures 
exceeding  sixty  or  seventy-five  pounds  it  is  found  that  they 
give  real  advantage,  and  the  more  as  the  pressures  and  ratios 
of  expansion  are  increased.  At  still  higher  pressures,  as  for 
those  exceeding  125  or  150  pounds,  it  is  probable  that  still 
further  subdivision  of  the  total  expansion-ratio,  and  the  con- 
struction of  the  triple-expansion  engine,  would  prove  to  be  an 
improvement ;  while  at  pressures  exceeding  200  or  225  pounds 
the  quadruple-expansion  machine  would  be  as  profitable,  com- 
paratively, as  in  those  departments  of  application  in  which 
they  have  been  already  set  at  work.  A  maximum  ratio  of  ex- 
pansion of  about  three  in  each  cylinder  is  probably  advisable. 

Another  engine  of  this  class  is  that  first  designed  by  Mr. 
J.  W.  Thompson,  and  known  as  the  "  Buckeye  engine."  This 
engine  was  not  a  radical  competitor  of  the  pioneer  engine ; 
but  was,  from  the  beginning,  a  moderately-high-speed  engine. 
It  was  fitted  with  a  positive  motion,  "  automatic  "  or  self- 
adjusting  valve-gear,  and  a  balanced  valve,  and  had  sufficient 
stability  and  excellence  of  workmanship  to  make  it  safe  at 
high  speeds ;  while  the  peculiarities  of  its  construction  were 
such  as  gave  it  a  very  high  place  as  an  economical  machine. 
In  this  case  the  cylinder  is  carried  on  a  pedestal,  as  is  that  of 
the  Corliss  engine,  usually;  the  frame  consists  of  a  girder  unit- 
ing the  cylinder  and  the  main  pillow-block  and  carrying  the 
guides ;  the  crank-shaft  end  is  carried  by  another  pillow-block. 
The  main  frame  is,  however,  supported  by  a  strut  which  is 
now  usually  seen  in  other  engines,  and  which  takes  the  load 
tending  to  spring  the  girder  under  the  guides. 

The  valves  are  so  constructed  that  the  steam  enters  balance- 


126 


A   MANUAL   OF   THE   STEAM-ENGINE. 


pistons,  through  which  it  passes  to  the  interior  of  the  valve, 
where  the  boiler-pressure  is  constantly  maintained  when  the 
engine  is  at  work.  The  balance-pistons  are  packed  with 
sprung  rings  and  followers,  and  fitted  to  work  steam-tight  on 
faces  on  the  cover-plates  of  the  valve.  Coiled  steel  springs 
serve  to  hold  the  pistons  to  their  seats  on  the  valve  when 


FIG.  49. — PLAN  OF  VALVES. 

steam  is  shut  off.  From  the  interior  of  the  valve  the  steam  is 
admitted  to  the  cylinder  through  ports  in  its  faces  as  they  are 
alternately  brought  by  its  movement  to  coincide  with  the 
cylinder-ports. 

The  cut-off  valve  is  formed  by  two  plates  shown  at  v  v,  Fig. 
49,  rigidly  connected  by  rods  h  h  h'  h'.  These  plates  work  on 
seats  surrounding  the  valve-ports,  which  ports  they  alternately 
cover  at  times  relatively  to  the  piston-travel,  determined  by  the 


STRUCTURE  OF   THE  STEAM-EtfGWE.  12" 

governor.  The  governor  is  of  a  type  that  has  not  been  seen 
in  engines  previously  described.  In  the  common  "fly-ball 
governor "  the  two  balls  revolve  about  a  vertical  spindle,  to 
which  they  are  attached  by  a  pair  of  arms  in  such  a  manner 
that  they  may  take  any  position  that  the  resultant  action  of 
gravity,  centrifugal  force,  and  the  pull  on  the  supporting  arms 
may  give  them.  A  defect  common  to  all  governors  of  this 
class  is  that  the  force  tending  to  pull  the  balls  downward  is 
perfectly  uniform.  The  position  taken  by  the  balls,  at  any 
fixed  speed  of  engine,  is  always  the  same ;  the  connection  of 
the  balls  with  the  regulating  mechanism  is  one  which  alwavs 
preserves  a  fixed  relation  between  the  position  of  the  governor- 
balls  and  the  position  of  the  regulating  apparatus.  Thus  it 
happens  that  the  engine  can  never  be  kept  precisely  at  speed, 
unless  the  speed  is  such  as  will  give  the  governor  exactly  its 
normal  position  and,  at  the  same  time,  such  that  the  valves 
shall  supply  just  the  normal  quantity  of  steam  to  the  engine. 
If  we  can  substitute  for  the  action  of  gravity  a  force  which 
can  be  made  to  vary  with  change  in  the  position  of  the  balls, 
in  such  a  way  that  the  variation  in  the  opening  of  the  throttle, 
or  in  position  of  the  point  of  cut-off,  shall  go  on  until  the  en- 
gine comes  to  speed,  irrespective  of  all  other  conditions,  we  shall 
have  what  is  known  as  an  "  isochronous  "  governor,  and  shall  be 
able  to  secure  the  right  speed,  whatever  changes  occur  in 
steam-pressure  or  in  load,  provided  that  there  is  steam  enough 
to  drive  the  load  at  that  speed  with  the  least  expansion  for 
which  the  engine  is  designed.  Such  a  result  can  be  reached 
by  substituting  the  tension  of  a  spring,  properly  set,  for  the 
action  of  gravity.  The  form  of  governor  here  illustrated  is. 
or  can  be  made  to  be.  of  this  class.  It  simply  requires  that 
the  spring  tension  shall  be  given  a  certain  easily  determined 
relation  to  the  effort  of  centrifugal  force. 

A  governor  of  this  character,  when  well  made  and  adjusted, 
will  open  the  throttle-valve,  or  will  increase  the  ratio  of  ex- 
pansion, as  the  steam-pressure  diminishes  or  as  the  load  is  in- 
creased, and  will  continue  to  move  in  the  proper  direction  in- 
definitely, or  until  the  machine  comes  to  speed,  or  until  the 


128  A   MANUAL   OF   THE   STEAM-ENGINE. 

engine  is  doing  all  that  it  can  do.  In  this  governor  (Fig.  50) 
two  levers  are  set  on  either  side  the  crank-shaft,  in  a  frame  or  a 
pulley  to  which  they  are  pivoted  at  b,  b.  These  rods  carry 
weights,  A,  A,  which  may  be  adjusted  to  any  desired  position 
by  means  of  the  bolts  seen  in  the  cut.  The  outer  end  of  each 
rod  is  linked  to  the  loose  eccentric,  C,  C,  by  the  rods  B,  B, 
and  is  controlled  by  the  springs  F,  F,  which  resist  the  effort 
of  centrifugal  force  tending  to  throw  the  weights  outward. 
As  the  weights  swing  outward  or  inward,  as  the  one  or  the 
other  of  the  two  opposing  forces  predominates,  the  eccentric 
is  turned  on  the  shaft  in  such  a  manner  as  to  give  the  valves 
that  motion  which  is  necessary  to  produce  the  proper  distri- 


FIG.  50. — THOMPSON'S  GOVER 


bution  of  steam  to  bring  the  engine  to  its  speed.  The  ad- 
justment of  this  regulator  to  its  work  is  easily  obtained  by 
the  shifting  of  the  weights  along  the  levers,  or  by  increasing 
or  diminishing  their  amount,  as  is  found  necessary. 

The  general  arrangement  of  this  system  and  the  appearance 
of  an  engine  of  this  class  are  illustrated  in  the  accompanying 
engraving. 

A  dash-pot  has  sometimes  been  used  on  the  governor  to 
correct  the  tendency  to  violent  fluctuation  when  nearly  isochro- 


STRUCTURE  OF   THE   STEAJt-EJCGIJCE. 


tag 


nous,  and  this  was  probably  the  first  case  of  its  use  on  this 
class  of  engines. 

The  independence  of  the  cut-off  and  main  valves,  in  con- 
sequence of  the  use  of  two  eccentrics,  permits  any  ratio  of 
expansion  to  be  adopted  that  may  be  desired,  and  the  fact  that 
the  cut-off  eccentric  is  set,  at  starting,  nearly  "  with  the  crank." 
gives  a  wide  range  detenninable  by  the  governor,  nearly  from 
full-stroke  to  complete  suppression.  As  the  governor  shifts  the 
eccentric  about  the  shaft,  it  gives  increased  angular  advance 
and  a  shorter  and  shorter  cut-off. 

Here  the  main  valve  is  actuated  as  in  the  common  forms  of 
valv«:  but  its  eccentric,  instead  of  being  set  ahead  of  the 


crank,  follows,  the  exhaust-  and  steam-openings  being,  by  the 
structure  of  the  valve,  reversed,  and  their  acting  edges  trans- 
posed. 

By  carrying  the  pivot  of  the  cut-off  rock-shaft  on  the  main 
rock  shaft  arm,  uniform  travel  of  the  cut-off  valve  on  the  back 
of  the  main  valve  is  secured,  whatever  the  variation  of  cut-off. 
This  insures  uniform  wear.  In  this,  as  in  all  engines  similarly 
regulated,  any  mishap  to  governor  or  its  connections  stops  the 
engine,  a  "  run-away  engine ""  being  thus  impossible. 

In  some  cases,  the  use  of  an  independent  cut-off  valve  actu- 
ated by  an  "  automatic  "  regulation  system  is  adopted  with 
the  simpler  forms  of  valve.  The  following  figure  illustrates 


STRUCTURE  OF  THE  STEA3t-EXGI&E.  IJI 

such  a  plan,  as  constructed  by  Stnrtevant,  for  all  powers  up  to 
150  H.  P.  Here  the  passages  in  the  main  valve,  for  the 
admission  of  steam,  do  not  extend  through  the  entire  thickness 
of  the  valve.  Within  the  main  valve  is  a  cylindrical  seat  in 
which  nuts  a  piston-valve,  which  receives  from  its  eccentric  a 
differential  movement  relatively  to  that  of  the  main  valve, 
just  before  the  beginning  of  the  stroke,  opening  the  passage 
into  the  cylinder.  The  valve  returns  to  cut  off  the  steam  at  a 
time  determined  by  the  governor.  As,  at  this  time,  the  two 
valves  are  moving  in  opposite  directions,,  this  action  is  very 
prompt. 

This  form  of  cut-off  valve  has  very  little  motion  in  its  seat. 
and  is  subject  to  no  lateral  pressure.  The  main  valve  is  set  to 
cut  off  at  three-quarters  stroke.  The  main  valve  is  habtw^J 
by  pressure-plates  upon  its  back. 

The  SlTaigklJim*  E*gi*e  differs  as  radically  from  the  two 
preceding  as  do  they  from  each  other.  In  this  engine  we  find 
but  a  single  valve,  which  does  duty  both  as  a  distributing  and  as 
a  cut-off  valve. 

This  engine  is  the  invention  of,  and  is  designed  by,  Prof. 
J.  E.  Sweet,  and  has  some  interesting  points,  which  wffl  bear 
much  more  extended  study  than  they  can  be  given  in  the  space 
which  can  here  be  allowed. 

The  engine  takes  its  name  from  its  peculiar  form  of  frame, 
which  is  seen  to  consist  of  two  perfectly  straight  diverging 
struts  extending  from  the  end  of  die  cylinder  directly  to  the 
two  main  bearings,  thus  carrying  the  fine  of  resistance  to 
the  puM  and  push  of  die  connections  exactly  along  its  own 
central  line.  The  engine  is  carried  on  three  points  as  is  the 
practice  with  "  surface-plates,'"'  which  must  have  an  absolntdly 
invariable  system  of  supports,  to  avoid  danger  of  ""spring. 
These  are  under  the  main  bearings,  and  beneath  the  steam- 
cylinder.  The  two  journals  receive  equal  loads;  the  crank-pin 
is  not  subject  to  the  deflecting  forces  met  with  where  a  crank 
is  overhung:  danger  of  unequal  wear  of  journals,  and  of  spring- 
ing the  pin,  is  thus  avoided.  The  fly-wheel  is  placed  in  twin 
form  between  the  fVE***  bearings,  and  also  serves  as  a  crank  as 


STRUCTURE  OF  THE  STEAM-fJSfGIA'E.  1JJ 

wdl  as  balance-wiled.  By  its  action  at  this  point  it  intercepts 
heavy  and  objectionable  stresses,  which,  otherwise,  might  he 
transmitted  to  the  mam  shaft ;  and  the  reciprocating  action  of 
counterweights  and  equilibrating  parts  is  dins  only  felt  within 
a  mass  of  metal  which  can  resist  them  with  safety  and  without 
affecting  the  main  journal;  which  is  also  less  liable  to  spring 
under  the  loads  transmitted  through  ft.  To  secure  better  dis- 
tribution of  wear,  the  crank-shaft  is  allowed  some  end-play. 

The  steam-cylinder  has  the  valve-chest  placed  at  the  end 
nearest  the  crank,  and  the  ports  and  passages  are  carried  as  in 
those  engines.  The  valve-stems  have  no  stuffing-boxes,  but 
pass  into  the  chest  through  unusually  long  and  carefully  fitted 
holies  in  a  hub,  made  about  five  one-thousandths  of  an  inch 
larger  than  the  rod  inside  the  Babbitt-metal  bushing,  for  a 
length  of  six  diameters,  or  more.  The  hub  is  loose  in  the  hole 
in  the  end  of  the  valve-chest,  and  is  packed  at  the  ends  by  a 
washer  fitted  on  a  flat  seat  on  the  inside.  The  piston-rod  is 
similarly  fitted. 

Ira  this  engine,  wear  is  a  voided  at  the  cross-head  pin  by  cutting 
away  the  surfaces  which  do  little  or  no  work,  and  thus  securing 
overrunning  surfaces,  which  are  not  subject  to  this  distorted 
wear  to  so  great  an  extent. 

The  valve  is  what  may  be  called  a  "  piston-valve  ~  of  rect- 
angular section,  the  space  in  which  it  slides  having,  therefore, 
also  a  rectangular  section. 

Tk*  wmpntmd  form  of  the  Sweet  engine  is  one  of  the  best 
of  illustrations  of  the  compactness  which  may  be  given  the 
"tandem  ™  type  of  the  machine.  The  engine  is  buflt,  as  to  its 
high-pressure  cylinder  and  working  parts,  precisely  like  the 
standard  type  of  the  simple  engine  of  the  same  design.  It  has 
exactly  the  same  characteristic  form  of  frame  and  methods  of 
connection  and  of  steam-distribution  and  governor.  Directly 
behind  the  high-pressure  cylinder,  however,  is  placed  the  larger, 
low-pressure,  cylinder,  the  whole  forming,,  practically,  one  struc- 
ture. The  whole  machine  can  be  taken  apart  and  reassembled 
without  disturbing  the  cylinders  or  the  frame.  Both  pistons, 
which  are  mounted  on  one  rod,  can  be  removed  and  replaced ; 


134 


A   MANUAL   OF   THE   STEAM-ENGINE. 


the   intermediate  head   coming    away  with    its   stuffing-box 
through  the  larger  cylinder.     The  packing  of  the  rod  between 


the  two  cylinders  is  a  metallic  sleeve,  solid  and  free  from  liability 
to  produce  trouble  or  to  require   readjustment,  once  in  place 


STRUCTURE   OF   THE   STEAM-ENGINE.  135 

and  properly  fitted.  It  is  /ree  from  liability  to  wear  or  to  bear 
upon  the  rod  in  such  a  manner  as  to  produce  undue  friction 
and  heating,  while  it  is  loose  enough  to  work  smoothly  and  yet 
tight  enough  to  prevent  leakage  of  steam  past  its  shell.  The 
valve  of  the  low-pressure  cylinder  is  worked  by  an  independent, 
fixed,  eccentric,  and  the  expansion  is  adjusted  by  the  action  of 
the  governor,  affecting  the  point  of  cut-off  on  the  high-pressure 
cylinder,  precisely  as  in  the  simple  engine.  Where  the  load  is 
fairly  steady  this  arrangement  is  perfectly  satisfactory.  The 
inventor  has  also  planned  a  triple-expansion  vertical  engine  of 
equal  simplicity. 

TJie  Armington  arid  Sims  Engine  is  of  the  same  general 
class  with  the  last  described  forms  of  engine,  but  differs 
from  them  in  its  details  and  in  its  proportions,  somewhat, 
and  especially  in  the  form  of  its  valve,  and  in  the  devices  in- 
termediate between  governor  and  valve.  In  this  engine  the 
"  piston "  valve  is  used,  combined  with  a  double  port.  The 
following  engraving,  Fig.  55,  presents  a  view  of  this  en- 
gine. The  bed,  or  frame,  is  seen  to  be  similar  to  that  of  the 
Porter-Allen  engine,  heavy,  solid,  stiff,  taking  the  bending 
stresses  of  the  guides  at  its  upper  surface,  and  insured  against 
twisting  strains  by  the  box  form  of  its  section.  Two  main 
pillow-blocks  carry  its  steel  crank-shaft,  and  support  the  two 
wheels,  one  of  which  is  a  balance-wheel,  and  the  other  of 
which  is  the  pulley,  from  which  the  engine  is  belted  to  its  work ; 
or,  perhaps  oftener,  both  being  used  in  driving,  thus  equalizing 
the  load  on  the  shaft  and  preventing  tendency  to  wear  out  of 
line.  The  steam-cylinder  is  overhung,  and  the  exhaust-pipe  is 
carried  down  below  the  floor,  clear  of  the  foundation,  which 
latter  has  a  minimum  extent  and  cost,  while  sufficiently  heavy 
and  strong  enough  to  carry  the  engine  steadily.  In  some  cases 
the  frame  is  made  with  but  one  pillow-block,  and  the  crank  is 
overhung. 

The  journals  are  calculated  for  the  speeds  and  pressures 
adopted.  The  lubrication  is  a  matter  of  vital  importance  in  all 
engines  of  this  class.  In  this  engine  the  "sight  feed  "  is  used, 
in  which  each  drop  of  oil  falls  through  a  clear  space,  on  its  way 


136  A    MANUAL    OF    THE    STEAM-ENGINE. 

to  the  point  to  be  oiled,  in  full  view  of  the  man  in  charge,  and 
any  failure  of  the  oil  to  "  feed "  is  thus  promptly  detected. 
The  crank-pin  is  supplied  by  a  "wiper,"  which  takes  its  supply 
of  the  lubricant  from  the  oil-cup  at  every  revolution  of  the 
crank.  This  device  has  been  used,  in  very  similar  form,  by  the 
Author,  on  fast  marine  engines,  with  perfect  satisfaction. 

A  governor,  of  the  same  type  as  that  exhibited  in  the  arti- 
cles describing  the  "  Buckeye "  and  the  "Straight  Line  "en- 
gines, is  secured  to  the  arms  of  the  pulley  on  the  frame,  and 


FIG.  55. — AKMINGTON  &  SIMS  ENGINE. 

adjusts  the  position  of  the  eccentrics  which  give  motion  to  the 
valve  through  a  rod  and  valve-stem,  the  connection  between 
which  two  parts  is  made  at  a  point  at  which  they  can  be  conve- 
niently supported  by  a  rock-shaft  and  arm  carried  at  the  middle 
of  the  length  of  the  frame.  The  cranks  are  two  disks  in  which 
the  balancing  mass  can  be  secured  at  any  desired  point. 

The  cylinder,  steam-chest,  and  valve-seat  are  all  in  one  cast- 
ing. 

The  steam-chest  is  in  direct  communication  with  the  boiler, 
and  the  valve,  which  is  of  the  piston  form  with  a  double  steam- 


STRUCTURE  OF   THE   STEAM-EXGIffE.  Itf 

port,  is  surrounded  by  the  "  live  steam,"  thus  taking  steam  at 
the  middle  and  exhausting  it  at  the  ends  of  the  chest.  The 
valve  moves  precisely  as  does  the  ordinary  locomotive  slide- 
valve,  and  the  steam  is  introduced,  at  the  beginning  of  the 
stroke,  through  a  double  length  of  port,  and  hence  with  un- 
usual promptness  when  the  engine  is  running  at  high  speed. 

The  total  "  dead  space  "  in  these  engines,  including  piston- 
clearance,  is  sometimes  as  low  as  5  per  cent  on  large  gfags, 
In  all  cases,  compression  should  fill  this  space  at  ever}*  stroke. 
This  piston-valve  possesses  a  novelty  in  the  double  port.  Its 
advantages  are  the  ease  and  cheapness  with  which  it  can  be 
made  and  fitted,  and  with  which  it  can  be  replaced  when  worn  ; 
its  perfect  balance  and  ease  of  working  under  any  practicable 
steam-pressure,  its  permanence,  tightness,  and  remarkable 
durability  when  properly  cared  for  and  used  with  boilers  sup- 
plied with  good  water.  Its  disadvantages  are  the  rapidity 
with  which  it  sometimes  wears,  when  it  is  not  kept  well  lubri- 
cated, or  when  it  is  exposed  to  the  action  of  steam  carrying 
over  from  the  boiler  acidulated  or  dirty  water,  the  danger  of 
injury  to  the  cylinder  or  its  heads  when  priming  occurs,  and 
the  proneness  of  the  attendant  to  neglect  its  repair. 

The  governor  is  the  same,  in  principle,  as  those  already  de- 
scribed as  adapted  to  the  adjustment  of  the  eccentric  on  the  main 
or  the  governor  shaft.  It  has  the  two  weights  carried  on,  and 
forming  a  part  of  arms  pivoted  to  the  governor  pulley,  and  re- 
volving in  the  vertical  plane  as  usual  in  that  class  of  governors, 
The  position  of  these  weights,  as  determined  by  the  speed  and 
the  action  of  the  springs,  determines  the  position  of  the  eccen- 
trics, and  thus  the  position  and  motion  of  the  valve,  and  the 
point  of  cut-off,  flying  out  and  giving  a  higher  ratio  of  expan- 
sion as  the  load  on  the  engine  is  diminished,  or  as  steam-pres- 
sure rises  in  the  slightest  degree,  and  a  lower  ratio  as  these 
conditions  are  reversed.  In  the  device  here  adopted,  however, 
the  valve  is  driven  by  an  eccentric  which  is  •*  duplex."  One 
eccentric  is  set  inside  another,  and  connected  to  the  governor 
arms  in  such  a  way  that,  as  the  weights  separate  with  increas- 
ing speed  of  engine,  both  eccentrics  are  turned  on  the  shaft  so 


138  A    MANUAL    OF   THE   STEAM-ENGINE. 

as  to  cause  their  "  throws  "  to  coincide,  or  to  separate  as  may  be 
necessary.  When  they  coincide,  the  travel  of  the  valve  is  due 
to  a  greater  total  throw,  and  is  a  maximum  ;  when  they  are 
separated  as  far  as  possible  the  travel  is  reduced  to  a  mini- 
mum. The  action  is  almost  precisely  the  same  as  that  of  a 
"  Stephenson  link,"  worked  between  full  and  mid-gear.  When 
the  two  eccentrics  give  maximum  travel,  the  action  is  that  of 
the  link-motion  in  full  gear ;  when  they  are  at  opposite  sides 
of  the  shaft,  the  action  is  that  of  a  link  in  mid-gear.  By  set- 
ting them  at  intermediate  points,  the  throw  is  made  that  is 
required  to  give  an  intermediate  action  of  the  valve,  and  thus 
the  distribution  of  steam  is  made  to  accord  with  the  demands 
of  the  work  by  such  a  variation  of  the  ratios  of  expansion  and 
of  compression  as  is  obtained  by  the  link-motion,  and,  in  this 
case,  with  the  advantage  in  promptness  of  opening  and  of 
closure  obtainable  with  a  double-ported  valve.  The  range  of 
action  given  in  this  engine  is  sufficient  to  permit  a  range  of 
cut-off  from  o  to  about  three-quarters  stroke.  The  lead  re- 
mains unchanged,  and  the  compression  increases  as  the  ratio  of 
expansion  is  increased.  The  springs  of  the  governor  are  used 
in  compression. 

Among  the  first  of  the  "  single-valve  automatic  "  engines 
to  find  a  place  in  electric  lighting  was  the  Armington  &  Sims 
engine,  which  was  also  one  of  the  earliest  to  be  built  as  a 
compound  engine.  An  experimental  engine  was  built  about 
1880  ;  but  the  engine  was  not  constructed  as  a  multiple-cylinder 
engine  regularly  and  as  a  standard  type  until  some  years  later. 
The  form  given  this  engine  is  seen  in  the  accompanying 
illustration,  which  represents  the  machine  as  constructed  to 
give  100  horse-power  at  high  speed.  The  regulation  and  the 
general  construction  of  each  of  the  two  elements  of  the  com- 
pound engine  are  similar  to  those  already  described  in  the 
simple  engine.  The  two  cranks  are  placed  opposite,  and  this 
gives  that  perfection  of  balance  which  cannot  be  secured  by 
any  other  device.  It  is  also  the  best  method  of  obtaining 
transfer  of  steam  from  the  one  engine  to  the  other  with 
minimum  loss  of  pressure.  The  attainment  of  a  speed  of  800 


STRUCTURE   OF  THE   STEAX-EXGIXE,  159 

revolutions  a  minute  is  not  unusuaL  Both  cylinders  are  steam- 
jacketed.  Such  engines  are  usually  made  up  to  about  200 
horse-power.  In  the  type  here  shown,  the  cranks  being 
opposite,  the  engine  balanced,  it  can  safely  be  run  at  a  high 
speed :  the  peculiar  form  of  the  valve  provides  for  quick  ad  mis- 


sion  of  steam,  and  the  large  wearing  surfaces  insure  it  more  or 
less  fully  against  leakage :  the  pistons  and  stuffing-boxes  used 
are  more  easily  got  at  than  ordinarily  with  engines  of  the 
"  tandem  "  type. 


140 


A    MANUAL    OF    THE   STEAM-ENGINE. 


In  the  Idc  engine,  of  this  class,  shown  herewith,  a  similarly 
compact  form  of  "  automatic  "  engine  is  illustrated ;  with  its 
shaft-governor,  and  peculiarly  solid  frame. 

The  top  of  the  frame  extends  from  cylinder  to  main  bear- 
ing, the  full  width  of  bearing.  The  caps  are  put  on  at  an 
angle,  which  gives  an  adjustment  in  line  with  the  wear  of  the 


parts.  The-  adjustment  is  given  by  reducing  the  thickness  of 
the  liner  plates,  and  the  cap  is  always  drawn  up  solid. 

A  straight  vertical  web  of  metal  connects  the  upper  and 
lower  portions  of  the  frame,  and  forms  a  stiff  girder.  This 
web  extends  from  the  cylinder  to  the  front  side  of  bearing, 
close  to  the  crank-disk. 

The  fly-wheel  is  set  as  close  as  possible  .to  the  crank,  in 
order  to  reduce  the  strain  on  the  shaft.  The  base  of  the  frame 
is  rectangular,  and  forms  a  box  girder,  the  top  of  which  forms 


STRUCTURE  OF   THE   STEAM-ENGINE.  14! 

the  bearing  for  the  lower  guide,  which  receives  the  pressure  of 
the  connecting-rod. 

Piston-valves  are  used,  and,  in  this  engine,  the  steam-chest  is 
bored  out  and  fitted  with  bushings  which  have  supporting  bars 
to  prevent  the  valve  catching  upon  the  ports.  When  worn 
they  can  be  withdrawn  and  new  ones  inserted,  and  a  new  valve 
introduced,  without  delay. 


FIG.  58.—"  CROSS  "  COMPOUX-D  TXGIXE. 

Fig.  58  represents  an  automatic  compound  engine  de- 
signed by  Mr.  F.  H.  Ball,  especially  for  use  in  driving  dynamo 
electric  machinery. 

The  illustration  represents  engines  using  steam  at  125 
pounds  pressure,  and  of  250  horse-power  each. 

It  was  thought  best  to  build  these  engines  in  the  form  of  a 
double  engine  rather  than  the  "  tandem  "  type  of  compound, 
because  it  was  believed  that  higher  rotative  speed  could  be 
successfully  used  where  the  work  was  distributed  over  twc  sets 
of  crank-pins  and  journals  of  smaller  sizes,  rather  than  with 
the  use  of  a  single  set  of  bearings  of  larger  size,  as  in  the  case 
of  a  tandem  engine  developing  the  combined  power  of  the 
double  compound. 


142 


A    MANUAL    OF    THE   STEAM-ENGINE. 


The  cylinder-dimensions  selected  after  working  up  a  large 
number  of  provisional  diagrams  were  as  follows: 

High-pressure  cylinder:  diameter  13";  stroke  16".  Low- 
pressure  cylinder :  diameter  25";  stroke  16". 

The  maximum  power  attained  on  trial  was  325  I.  H.  P. 

The  next  figure  illustrates  the  same  make  of  engine  com- 
pounded in  the  more  usual  way,  a  "  tandem,"  compound, 
high-speed  engine,  for  electric-lighting  or  other  purposes,  which 
is  found  to  be  one  of  the  best  combinations  of  efficiency  with 
simplicity  and  small  cost. 


FIG.  59.— TANDKM  COMPOUND  HIGH-SPEED  ENGINE. 

Nearly  all  makers  now  use  this  method  of  compounding 
for  all  cases  except  where,  as  in  marine  engines,  a  double 
engine  with  cranks  at  right-angles  is  considered  desirable  on 
other  grounds.  They  are  nearly  as  simple  in  form,  as  cheap 
of  construction,  and  as  inexpensive  in  repairs  as  the  simple 
engine. 

An  engine  designed  by  Mr.  Ide,  Fig.  60,  illustrates  both 
the  "  tandem  "  form  of  compound  high-speed  engine,  and  some 
features  of  design  of  peculiar  interest.  This  engine  has  its 
running  parts  covered  in  to  insure  that  the  oil,  which  is  freely 
supplied,  may  not  be  wasted  or  spattered  about,  to  the  injury 
of  surrounding  objects,  while  thus  also  obtaining  thoroughness 


STRUCTURE  OF  THE  STEAM-EKGIKE.  143 


144  A   MANUAL    OF   THE   STEAM-ENGINE. 

of  lubrication  approximating  that  of  the  "oil-bath."  This 
gives,  when  fully  effected,  very  great  decrease  in  the  wasted 
energy  of  internal  friction  of  engine  and  corresponding  increase 
of  efficiency.  The  design  is  simple,  inexpensive  of  con- 
struction, and  embodies  details  of  construction  coming  to  be 
generally  recognized  as  essential  to  high  efficiency.  The 
engine  has  a  shaft-governor,  controlled  by  a  dash-pot,  and  thus 
enabled  to  regulate  more  closely.  Its  running  parts  are  usually 
of  steel. 

The  low-pressure  cylinder  is  bolted  direct  to  the  engine- 
bed,  and  to  the  head  of  this  cylinder  is  cast  the  high-pressure 
cylinder.  By  this  arrangement  steam  from  the  high-pressure 
cylinder  has  a  short,  direct  passage  into  the  low-pressure 
cylinder,  and  four  stuffing-boxes  are  dispensed  with  on  the 
rods  between  cylinders,  reducing  friction  and  dispensing  with 
considerable  external  radiating  surface. 

The  cylinders  and  steam-chests  are  encased  with  a  finished 
iron  jacket,  with  two-inch  air-space,  between  cylinder  and 
jacket,  filled  with  non-conducting  material.  Both  cylinder- 
heads  are  protected  in  the  same  manner. 

The  head  between  the  cylinders  is  cored  out  leaving  a  space, 
which  is  filled  with  non-conducting  materials. 

The  next  figure  exhibits  the  same  type  of  engine  as 
arranged  for  a  "  cross-compound  "  by  the  Harrisburg  Co. 
The  "  tandem  "  engine  has  an  advantage  in  small  cost,  in  com- 
pactness, and  small  friction  ;  but  the  cross-compound,  with 
cranks  at  90°,  has  no  "  dead-centres,"  is  somewhat  steadier  in 
its  revolution,  and  has  lighter  stresses  on  its  running  parts.  A 
receiver  is  here  needed,  and  is  seen  between  the  two  engines. 
It  is  made  an  expansion-piece  to  avoid  temperature-strains. 

In  designing  the  twin  form,  or  cross-compound  engine,  it  is 
advisable  to  secure  compactness  without  sacrificing  accessi- 
bility; independence  of  parts  exposed  to  independently  vary- 
ing temperatures,  and  a  nice  adjustment  of  steam-distribution 
with  respect  to  both  the  cylinders  and  the  intermediate  re- 
ceiver. The  next  figure  illustrates  the  arrangement  of  the 
Harrisburg  engine  as  seen  from  behind  the  cylinders. 


146 


A   MANUAL   OF   THE   STEAM-ENGINE. 


In  the  plans  it  is  to  be  noted  that  the  power  to  be  given 
off  by  the  engines  is  transferred  through  the  intermediately 
situated  pulley  fly-wheel,  which  is  the  only  element  separating 
the  two  machines.  The  shaft  is  made  of  minimum  length  ;  the 
space  afforded  by  the  mounting  of  the  wheel  in  this  manner 
also  serves  to  admit  the  two  valve-chests  and  a  very  short 


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I           : 

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1     : 

1 

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t    ; 

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iFio.  fa. — SECTION  :  CROSS-COMPOUND  ENGINE. 

connection  serving  as  receiver  and  constructed  with  an  ex- 
pansion-piece, to  avoid  introduction  of  strains.  The  whole 
design,  which  is  now  a  not  uncommon  one,  illustrates  well  the 
most  compact  possible  form  of  this  engine. 

These  points  are  also  observable  in  the  next  illustration,  in 
which  a  plan  of  the  Porter  compound  is  given.     Where,  as 


STRUCTURE   OF   THE   STEAM-ENGINE.  147 

in  this  case,  the  valve  is  on  a  level  with  the  centre-line  of  the 
engine,  care  must  be  taken  to  secure  immunity  from  danger 


FIG.  «3.-Puwc  or  Ri 


from  water  entering  the  cylinders,  by  the  use  of  an  automatic 
relief-valve,  or  a  "  breaking-cap." 


OF  T£f£  $TEAM-EJTGaC£.  149 

Tlie  engraving  on  page  146  shows  the  usual  construction  of 
foundation,  which  may  be  either  brick  or  stone,  but  is  com- 
monly prefened  of  brick  with,  often,  stone  blocks  on  which 
the  engine  is  immediately  supported. 

Where,,  as  often  in  rolling-mills,  the  power  of  the  engine 
must  be  transmitted  along  the  shaft,  a  fly-wheel  of  the  simpler 
kind  may  be  placed  between  the  cylinders,  and  still  greater 
compactness  thus  sometimes  attained.  Thus,  in  Fig.  63,  the 
plan  of  a  Porter- Afflen  rolling-mill  engine,  this  arrangement 
is  made,  the  shaft  being  extended  to  the  right,  toward  the 
roIl-iraitnL  to  which  ft  is  coupled  as  shown.  The  arrangement 
of  die  machine,  in  detail,  illustrates  the  special  methods  of 
combining  two  engines  of  this  type,  as  dictated  by  its  ^pp**-"! 
construction. 

Tkf  Ldxssmg  tmgimf.  planned  by  Mr.  Jarvis,  illustrates  still 
another  design  of  the  -tandem  ""  compound  variety.  In  this 
case  both  steam-chests  are  on  the  same  side,  giving  short 
connection  between  the  two  chests,  and  diminishing  the  sur- 
face exposed  to  steam,  which  exposure  is  detrimental  to 
economy.  It  is  seen  in  Fig.  64. 

The  shaft-governor,  keyed  to  the  shaft,  obviates  danger 
due  to  the  breaking  of  belts  or  gears.  This  governor  is  of  the 
class  in  which  the  eccentric  is  hung  on  an  arm,  which  allows  it 
to  swing  across  the  shaft  by  levers  pivoted  to  the  spider  of  the 
wheel  In  its  details  it  is  the  design  of  Prof.  R.  C  Carpenter. 

To  obtain  the  astatic  or  isochronous  property,  the  gov- 
ernor must  be  so  arranged  that  with  a  slight  variation  in 
speed  it  may  move  through  its  entire  range.  This  end  is 

that  the  weights  with  their  arms  remain  against  the  inner  stops 
until  the  speed  has  nearly  reached  its  governing  range.     A 
slight  additional  increase  would  then  cause  the  weight  and . 
arms  to  move,  if  the  increase  were  not  checked,  through  the 
entire  range  of  action. 

This  action  is  restrained  by  the  air  dash-pot,  seen  in  Fig. 
65.  Inertia  is  made  to  act  usefully  by  so  pivoting  the  arms 
that,  when  the  governor  is  in  operation,  the 


I5O  A   MANUAL    OF   THE   STEAM-ENGINE. 

such  a  position  that  a  line  drawn  through  their  centre  of 
gravity  perpendicular  to  the  radius  will  pass  to  one  side  of  the 
arm-pivot.  The  force  due  to  inertia,  when  the  speed  changes, 
acts  nearly  along  this  line,  and  tends  to  turn  the  arm  about 
the  pivot,  and  thus  move  the  eccentric  in  the  same  manner 


FIG.  65.— CA 


as   the  centrifugal    force,    and   acting  most  quickly,   it  gives 
the  governor  a  greater  sensitiveness. 

36.  The  Single-acting  High-speed  Engine  is  a  peculiar 
but  now  familiar  type.  In  the  "single-acting  engine,"  the 
steam  drives  the  piston  in  but  one  direction,  and  the  return- 
stroke  must  be  made  without  the  production  of  useful  work. 
In  the  "double-acting  engine,"  the  steam  acts  upon  the  piston 
in  both  directions,  and  with  practically  equal  effect.  Thus,  a 
more  regular  action  is  secured  with  a  given  weight  of  balance- 


STRUCTURE  OF  THE  STEAM-EXGIXE.  !$! 

wheel,  or  the  same  regularity  with  a  wheel  of  less  weight  than 
is  required  for  the  other  form  of  engine.  This  smoothness  off 
motion  is  one  of  the  most  essential  features  of  steam-engine 
economy.  At  the  speeds  which  have  been  lately  attained, 
however,  the  inertia  of  moving  parts  becomes  so  great  that 
moderate  variations  in  the  impelling  power  become  com- 
paratively insignificant,  and  have  no  perceptible  effect  upon 
the  smoothness  of  revolution  of  the  crank-shaft. 

The  double-acting  engine  evidently  possessed  greater  power 
than  its  predecessor,  when  of  the  same  size,  and  the  -  efficiency 
of  the  machine"  was  correspondingly  increased. 

But  the  very  conditions  which  have  been  thus  made  to  aid 
in  securing  regularity  have  introduced  a  new  difficulty:  At 
every  revolution  of  the  engine,  the  crank  *•  turns  the  centre "" 
twice ;  and,  at  every  passage  of  the  centre,  the  direction  of 
pressure  upon  the  crank-pin  is  reversed,  thus  producing  a  shock 
which  varies  with  the  difference  of  pressure,  the  suddenness 
with  which  it  is  felt  at  the  pin,  and  the  extent  of  the  "  lost 
motion  "  between  the  pin  and  its  bearings.  Some  lost  motion 
must  always  be  permitted,  to  avoid  danger  of  heating  the 
journal  and  injury  to  the  machine.  The  counteracting  adjust- 
ments are  found  to  be,  usually,  the  utilization  of  the  inertia  of 
the  reciprocating  parts ;  the  adoption  of  heavy  compression, 
and  very  careful  adjustment  of  the  fit  of  the  brasses  on  the 
pin.  With  skilful  use  of  these  expedients,  and  with  the  in- 
troduction of  perfection  of  workmanship,  and  of  qualities  of 
material,  such  as  have  only  been  attained  in  late  years,  the 
"high-speed  engine  "  has  been  made  successful  at  as  high  as 
300  and  even,  in  some  cases,  600  or  more  revolutions  per 
minute. 

But  much  higher  speeds  than  these  are  sometimes  de- 
manded ;  and  engines  must,  in  the  future,  be  buflt  to  run. 
regularly,  steadily,  and  safely,  at,  probably,  very  much  higher 
velocities.  This  may,  ultimately,  lead  to  radical  changes  in 
the  design  of  the  now  standard  forms  of  fast  engines.  Nev- 
ertheless, the  limit  of  speed  has  by  no  means  been  reached, 
even  at  the  higher  of  the  above  speeds,  with  the  common  type 


152 


.A    MANUAL    OF   THE   STEAM-ENGINE. 


of  engine.  The  speed  of  even  450  times  the  cube  root  of  the 
length  of  stroke,  now  a  common  figure,  and  over  three  times 
that  given  by  Watt's  rule,  is  occasionally  greatly  exceeded. 
Ericsson  designed  an  engine,  some  years  ago,  for  electric  light- 
in^,  which  ran,  for  years,  at  1250  revolutions  per  minute, 
without  accident.  The  piston-speed  was  about  twice  that  of 


FIG  66.—  ERICSSON'S  ENGINE.    (Sc 


the  average  "  high-speed  "   engine,  and  nearly  ten  times  that 
adopted  by  Watt. 

The  object  of  the  inventor  was  to  design  a  steam-engine 
for  the  special  work  of  driving  small  dynamo-electric  machines, 
and  hence  to  secure  great  stability  and  strength,  a  minimum 
number  of  parts  requiring  lubrication,  and  absolute  certainty 
that  the  parts  retained  should  be,  at  all  times,  thoroughly 
supplied  with  the  lubricant.  The  engine  is  therefore  made  a 
"  half-trunk  "  engine,  the  trunk,  F,  F,  Fig.  66,  serving  as  an 


STRUCTURE   OF   THE   STEAM-ENGINE.  153 

oil-reservoir.  The  joint  in  the  eccentric-rod  is  provided  with  a 
piston  moving  in  a  cylindrical  guide,  N,  which  is  also  an  oil- 
reservoir.  The  cylinder,  C,  and  base-plate,  B,  are  in  one  cast- 
ing, upon  which  is  set  the  hollow  frame  supporting  the  crank- 
shaft, H  £,  and  balance-wheel.  Every  journal  and  rubbing 
part  has  an  oil-reservoir  and  special  provision  for  effective 
lubrication. 

There  comes  a  time,  in  the  attempt  to  secure  smooth  work- 
ing, and  as  speeds  are  increased,  when  the  weight  of  running 
parts,  as  calculated  for  strength  only,  becomes  as  great  as  is 
desirable  to  effect  this  object  by  their  inertia ;  there  comes  a 
time,  also,  as  compression  is  increased,  when  the  "  cushioned  " 
steam  is  carried  up  to  boiler-pressure,  and  this  would  seem  the 
natural  limit.  The  next  device  adopted  by  the  engineer,  in 
chronological  order,  is  that  of  preventing  the  lift  of  the  brasses 
of  the  crank-pin  and  of  the  cross  head  pin  when  turning 
the  centres,  while  still  leaving  the  freedom  of  fit  required  to 
give  safety  from  heating.  This  last  expedient  is  that  which 
has  led  to  the  construction  of  a  class  of  engines  which  are  as 
peculiar  and  as  typical  as  either  of  the  classes  which  have  been 
already  described. 

Westing/wuse's  Engine  belongs  to  this  class,  and  is  here 
taken  as  its  representative.  The  change  of  construction 
characteristic  of  this  type  of  engine  is  a  return  to  the  original 
"  single-acting "  plan  of  engine.  The  simple  form  of  this 
engine,  Figs.  67,  68,  has  two  cylinders,  A  A,  fitted  with  single- 
acting  pistons,  D  D,  forming  trunks  filling  the  bore  of  the 
cylinder,  giving  a  long  steam-tight  bearing,  and  taking  the  con- 
necting-rod pin,  A  B,  at  a  point  at  which  no  tendency  to  rock 
the  piston  can  be  produced.  The  top  of  the  piston  is  cored 
out  to  prevent  transfer  of  heat  from  the  working  to  the  non- 
working  end.  The  rods,  F  F,  take  hold  of  the  crank-pins 
within  an  inclosed  chamber,  C,  forming  part  of  the  engine- 
frame,  E  C.  This  frame  and  bed-plate  also  acts  as  a  reservoir 
for  oil  lubricating  the  journals  and  pistons,  which  oil  floats  on 
water  and  is  dashed  up  over  the  moving  parts  so  enclosed,  at 
every  revolution  of  the  engine.  No  other  attention  is  required 


154 


A   MANUAL   OF    THE   STEAM-ENGINE. 


than  to  keep  a  supply  of  oil  in  the  chamber,  by  filling  as  loss 
occurs  by  leakage.  In  fact,  the  whole  engine  is  thus  shut  in 
by  its  frame,  and  its  working  parts  are  invisible  while  working 
— an  arrangement  at  once  a  means  of  security  and  convenience. 
The  valve  adopted  in  this  engine  is  a  piston-valve  of  the 
class  already  described,  but  having  some  peculiarities  specially 
adapting  it  to  its  use  in  this  engine.  Its  guide,  /,  Fig.  67,  is  a 


'-7 r-:  •'  '•'/' lISSIl 

FIG.  67.—  WESTTNGHOXTSE  BNOINF.     (Scale  ^.1 

piston  traversing  a  cylinder  separating  the  exhaust  space  from 
the  chamber  below.  This  one  valve,  V,  distributes  steam  to 
both  cylinders,  the  two  cranks  being  set  directly  opposite  each 
other.  This  adjustment  of  the  cranks  also  gives  a  perfect 


STRUCTURE  OF  THE   STEAJf-EXGlXE.  155 

balance  of  reciprocating  parts,  and  secures  smoothness  of  move- 
ment off  the  whole  machine,  whatever  speed  may  be  adopted  ; 
and  exceptional  speeds  of  1000  revolutions,  or  more,  per  min- 
ute are  reached  without  observable  vibration. 

The  governor,  /,  and  its  action,  are  precisely  like  the  same 


parts  in  engines  of  this  class  described  earlier.  It  actuates 
the  eccentric,  and  determines  the  point  of  cut-off  by  varying 
the  throw  of  the  valve,  while  retaining  constant  lead.  The 
governor  is  usually  so  adjusted  that  it  will  not  come  into  play 
until  the  engine  falls  one  per  cent  below,  or  rises  one  per  cent 
above,  the  normal  speed ;  its  full  traverse  is  effected,  also, 


156  A    MANUAL   OF   THE   STEAM-ENGINE. 

within  this  range,  the  intention  being  that  the  speed  shall  never 
vary  more  than  one  per  cent  from  that  fixed  as  its  proper  ve- 
locity. The  range  of  expansion  is  from  o  to  about  f  stroke. 

One  of  the  dangers  to  which  fast-running  engines  are  pe- 
culiarly exposed  is  that  of  injury  by  the  entrapping  of  water  in 
the  cylinder,  and  the  plunging  of  the  piston  against  the  mass 
of  incompressible  fluid  which  then  fills  the  clearance-spaces. 
In  this  engine,  in  addition  to  the  relief-cocks,  or  valves,  which 
are  always  fitted  to  such  engines,  a  safeguard  is  introduced  in 
the  form  of  what  engineers  are  accustomed  to  call  the  "  break- 
ing-piece," a  part  which  is  made  purposely  weaker  than  other 
portions  of  the  machine,  exposed  to  a  common  danger,  so  that 
this  piece  may  go  when  danger  arises.  This  piece  is  always 
one  the  replacement  of  which  will  give  little  trouble,  and  make 
but  little  expense.  Such  a  breaking-piece  is  made  to  form  a 
part  of  the  cylinder-head.  This  may  be  knocked  out  without 
injury  to  any  important,  or  costly,  part  of  the  structure.* 

The  Single-acting  Multicylilider  Engine  is  often  adopted  for 
work  in  which  high  speed  of  rotation  is  an  advantage.  The 
Westinghouse  compound  engine,  illustrated  in  the  engraving, 
is  a  good  typical  representative  of  this  class,  and  is  one  of  the 
simplest  devices  of  its  kind.  A  single  piston-valve,  set  hori- 
zontally above  the  two  cylinders,  distributes  the  steam  and  is 
regulated  by  a  shaft-governor  which  properly  varies  its  throw. 
The  cranks  are  set  opposite  each  other ;  the  motions  of  the 
pistons  are  synchronous  in  opposite  directions,  and  no  receiver 
is  needed.  Both  engines  are  single-acting,  and  high  compres- 
sion does  away,  largely,  with  the  wastes  due  to  considerable 
clearance.  The  cut-off  in  the  high-pressure  cylinder  is  effected 
by  the  lap  of  the  valve.  It  has  been  found  possible  by  this 
arrangement  to  bring  down  the  consumption  of  steam  to  less 
than  20  pounds  (9  kilos)  per  horse  power  per  hour  when  con- 


*The  Author  planned  an  engine,  about  the  year  1860,  in  which  the  whole 
cylinder-head  was  made  a  safety-valve  which  could  lift  and  discharge  the  water 
into  the  chamber  behind  it.  the  cover  of  the  latter  being  bolted  on,  while  the 
cylinder-head  was  only  held  in  place,  against  a  faced  joint,  by  steam-pressure. 


STRUCTURE   OF   THE   STEAM-ENGINE.  157 


densing,  and  below   25   pounds  (i  I   kilos)  when  working  non- 
condensing. 


In  such  single-acting  engines,  it  is  usually  irifehded  that 
the  rod  shall  never  leave  the  crank-pin,  in  order  that  pounding 
may  not  occur.  It  is  therefore  evidently  necessary  that  they 


158 


A    MANUAL   OF   THE  STEAM-ENGINE. 


should  be  so  proportioned  and  speeded  that  the  action  of  the 
inertia  of  their  reciprocating  parts  shall  not  produce  stresses, 
on  turning  the  centre,  in  excess  of  the  sum  of  weights  and 
steam-pressure. 

An  ingenious  modification  of  the  enclosed  single-acting  com- 
pound type  of  engine,  the  "central-valve  engine"  of  Mr.  Wil- 
lans — which  is  also  interesting  as 
having  been  the  subject  of  ex- 
ceptionally complete  scientific  in- 
vestigation— is  seen  in  Fig.  70.* 
It  was  studied  as  a  simple,  a  com- 
pound, and  a  triple-expansion  en- 
gine ;  being  easily  adapted  to 
either  system. 

As  here  shown,  its  three  cylin- 
ders are  placed  in  series  and  "  tan- 
dem." The  valves  are  on  one 
rod,  driven  by  a  single  eccentric 
on  the  crank-pin ;  the  rod  being 
in  the  axis  of  the  engine  and  the 
valves  within  the  hollow  piston- 
rod.  Cut-off  is  effected  by  the 
passage  of  the  ports  into  metallic 
rings  in  the  ends  of  the  cylinders, 
and  is  adjustable  by  hand  or  by 
the  governor.  Compression  is 
effected  in  the  separate  cushion- 
chamber,  f 

These  engines  are  usually 
grouped  in  pairs,  with  cranks  at 
right-angles. 

F,a.7o.-WILI.AKs'ENGINE.    (Scaled)  Ag    the    valve.faces    move  with 

the  pistons,  the  valve-motion  must  here  be  taken  from  the  pins 
to  secure  the  desired  movement  relatively  to  the  pistons. 

*  The    discussion    of   this  paper  is    remarkably  interesting. — Trans.   Brit. 
Inst.  C.  E. ;  March,  1888;  1887-1889;  No.  2306;  vol.  xciii. 
f  Ibid  ,  vol.  Ixxxi.  p.  166. 


STRUCTURE   OF   THE  STEAAf-ENGIXE. 


'59 


The  work  on  the  main  journals  and  pins  is  substantially  all  on 
the  upper  4i  brass  "  of  the  latter  and  the  lower  of  the  former, 


FIG.  71. — TRIUMPH  ENGINE, 

and  the  crank-pin  working-side  is  never  expected  to  leave  the 
pin.      The   eccentric-rod,  like   the  connecting-rod,  is  always 


l6o  A    MANUAL    OF   THE   STEAM-ENGINE. 

in  compression,  and  the  main  bearings  also  are  always  under 
constant  downward  thrust.  Lubrication  is  secured,  by  the 
Westinghouse  method,  by  the  dipping  of  the  crank  into  a  pool 
of  oil  and  water  in  the  crank-case.  The  guide-pistons  are 
arranged  to  produce  the  needed  cushion  by  compressing  the 
air  in  the  compression-chambers  and  this  is  adjustable  as  may 
prove  to  be  advisable.  The  governor  is  of  the  now  familiar 
Hartnell  type. 

Another  recent  and  peculiar  example  of  this  class  of  en- 
closed engines  is  the  so-called  'Triumph"  engine  of  Mr. 
Eickershoff,  a  "  valveless  "  engine,  in  which  the  piston  of  one 
of  its  elements  serves  to  distribute  the  steam  to  the  others.  It 
consists  of  three  engines,  side  by  side,  each  having  the  general 
construction  shown  in  Fig.  71,  coupled  to  cranks  set  at 
angles  of  120°.  Its  simplicity  is  its  striking  feature,  having 
neither  valves,  eccentrics,  piston-  or  valve-rods,  cross-heads  nor 
stuffing-boxes.  The  distribution  is  remarkably  good.  Regu- 
lation is  effected  by  a  throttling-governor  on  the  steam-chest. 

With  the  exception  of  the  cut-off,  each  piston  controls  the 
steam  in  the  cylinder  next  preceding  in  the  order  of  rotation, 
and  when  acting  as  a  valve  is  at  or  near  its  maximum  speed, 
while  at  the  same  moment  the  pistons  in  the  preceding  cylin- 
der are  at  their  slowest  speed.  This  simple  expedient  controls 
the  steam  in  this  engine  in  a  manner  remarkable  for  its  very 
great  efficiency. 

The  indicator-diagram  here  given  was  taken  from  a  7  x  14x8 
inch  engine,  non-condensing.  XX  is  the  atmospheric  line ; 
AB  is  the  admission-line  in  the  high-pressure  cylinder;  BC, 
the  steam-line  ;  C,  the  point  of  cut-off  ;  CD,  expansion-line  for 
high-pressure  cylinder  only;  D,  point  of  release  to  low-pressure 
cylinder;  DEF,  expansion-line,  showing  expansion  in  both 
high-  and  low-pressure  cylinders,  represented  also  by  expansion- 
line  LM  of  the  low-pressure  card  ;  F,  point  of  compression  in 
the  high-pressure  cylinder  connection  with  the  low-pressure 
closing ;  FA  is  the  compression-line. 

In  the  low-pressure  card  KLis  the  admission-line  ;  LM,  the 
expansion-line,  corresponding  to  line  DEFoi  the  high-pressure 


STRUCTURE   OF   THE   STEAM-EXGIXE. 


161 


card ;  M  is  the  point  of  cut-off  of  the  high-pressure  cylinder,  cor- 
responding with  compression-point  F  of  the  high-pressure  card  : 
JAVisthe  expansion-line  for  the  low-pressure  cylinder  only; 
X  is  the  point  of  release  to  the  exhaust ;  NP  is  the  exhaust- 
line ;  PQ,  line  of  back-pressure ;  QK,  compression-line.  It  must 
be  remembered  that  the  piston  in  the  cylinder  from  which  the 
high-pressure  card  is  taken  is  120°  in  advance  of  the  piston  in 
the  cylinder  from  which  the  low-pressure  card  is  taken.  The 


FiG.    72. — bOHCATOB-DIAGKAXS. 


ratio  of  the  clearance  to  the  volume  of  the  high-pressure  cylinder 
is  such  that  the  compression  is  always  brought  to  initial  pres- 
sure, irrespective  of  change  in  load.  By  this  means  the  cylin- 
der-walls are  brought  to  the  temperature  of  the  entering  steam 
and  condensation  prevented,  and  shock  in  passing  the  centres 
is  avoided. 

The  plan  of  enclosing  the  "  running  parts  "  of  the  engine 
to  insure  freedom  from  dust,  flooded  journals,  and  exemption 
from  expense  in  finishing  small  parts,  is  illustrated,  in  a 


162 


A    MANUAL    OF    THE    STEAM-ENGINE. 


special  case,  as  here  shown,  an  upright  single-valve  automatic 
engine  designed  by  Sturtevant.     In  this  case,  a  pair  of  engines 


FIG.  73.-' 

are  set  with  cranks  opposite  to  secure  a  balance,  and  a  single 
valve  answers  for  both.  An  excellent  and  often  practised 
arrangement  of  oil-cups  is  here  shown ;  all  being  of  the 


STRUCTURE  OF   THE   STEAM-ENGINE. 


I63 


•  sight-feed  "  class,  all  set  in  view  and  together,  and  where 
readily  accessible.  This  general  plan  is  adopted  for  engines  of 
10  to  35  horse-power. 

37.  Pumping-engines  are  built,  as  a  rule,  compound,  and 
will  be  considered  as  such  in  the  chapter  relating  to  that  Ha« 
of  constructions.  Their  principal  types  may,  however,  be 
properly  described  here. 

A  simple  form  of  pumping-engine  without  fly-wheel  is  the 
now  common  "  direct-acting  steam-pump."  This  engine  is 
generally  made  use  of  as  a  forcing-  and  fire-pump,  and  wherever 


the  amount  of  water  to  be  moved  is  not  large,  and  where  the 
pressure  is  comparatively  great.  The  steam-cylinder,  ARf  and 
feed-pump.  Fig.  74.  are  in  line,  and  the  two  pistons  have  usually 
one  rod  in  common.  The  two  cylinders  are  connected  by  a 
strong  frame,  and  two  standards  fitted  with  lugs  cany  the  whole, 
and  serve  as  a  means  of  bolting  the  pump  to  the  floor  or  to  its 
foundation. 

The  method  of  working  the  steam-valve  of  the  modern 
steam-pump  is  very  ingenious  and  peculiar.  As  shown,  the 
pistons  are  moving  toward  the  left ;  when  they  reach  the  end 


164  A   MANUAL    OF   THE   STEAM-ENGINE. 

of  their  stroke,  the  face  of  the  piston  strikes  a  pin  or  other 
contrivance,  and  thus  moves  a  small  auxiliary  valve,  /,  which 
opens  a  port,  £,  and  causes  steam  to  be  admitted  behind  a 
piston,  or  permit  steam  to  be  exhausted,  as  in  the  figure,  from 
before  the  auxiliary  piston,  F,  and  the  pressure  within  the 
main  steam-chest  then  forces  that  piston  over,  moving  the 
main  steam-valve,  G,  to  which  it  is  attached,  admitting  steam 
to  the  left-hand  side  of  the  main  piston,  and  exhausting  on  the 
right-hand  side,  A.  Thus  the  motion  of  the  engine  operates 
its  own  valves  in  such  a  manner  that  it  is  never  liable  to  stop 
working  at  the  end  of  the  stroke,  notwithstanding  the  absence 
of  the  crank  and  fly-wheel,  or  of  independent  mechanism,  like 
the  cataract  of  the  Cornish  engine.  There  is  a  very  consider- 
able variety  of  pumps  of  this  class,  all  differing  in  detail,  but 
all  presenting  the  distinguishing  feature  of  auxiliary  valve  and 
piston,  and  a  connection  by  which  it  and  the  main  engine  each 
works  the  valve  of  the  other  combination. 

In  some  cases  these  pumps  are  made  of  considerable  size, 
and  are  applied  to  the  elevation  of  water  in  situations  to  which 
the  Cornish  engine,  described  in  the  preceding  chapter,  was 
formerly  considered  exclusively  applicable.  Fig.  75  illustrates 
such  a  pumping-engine,  as  built  for  supplying  cities  with  water. 
This  is  a  Worthington  "  compound  "  direct-acting  pumping- 
engine.  The  cylinders,  A  B,  are  placed  in  line,  working  one 
pump,  F,  and  operating  their  own  air-pumps,  D  D,  by  a  bell- 
crank  lever,  connected  to  the  pump-buckets  by  links.  Steam 
exhausted  from  the  small  cylinder,  A,  is  further  expanded  in 
the  large  cylinder,  B,  and  thence  goes  to  the  condenser,  C. 
The  valves  are  moved  by  valve-gear  which  is  actuated  by  the 
piston-rod  of  a  similar  pair  of  cylinders  placed  by  the  side  of  the 
first.  These  valves  are  constructed  substantially  on  the  plan 
of  the  Corliss  and  are  thus  very  fairly  balanced,  are  easily  and 
promptly  moved,  and  give  little  clearance.  By  connecting  the 
valves  of  each  engine  with  the  piston-rod  of  the  other,  it  is  seen 
that  the  two  engines  must  work  alternately,  the  one  making  a 
stroke  while  the  other  is  still,  and  then  itself  stopping  a 
moment  while  the  latter  makes  its  stroke. 


STRUCTURE   OF  THE   STEAM-ENGINE.  165 


166  A    MANUAL   OF   THE   STEAM-ENGINE. 

Water  enters  the  pump  through  the  induction-pipe,  E, 
passes  into  the  pump-barrel  through  the  valves,  V  F,  and  issues 
through  the  eduction-valves,  T  T,  and  goes  on  to  the  "  mains  " 
by  the  pipe,  G,  above  which  is  seen  an  air-chamber,  which 
assists  to  preserve  a  uniform  pressure  on  that  side  the  pump. 

The  "  high-duty  attachment,"  U  U,  of  the  later  engines  of 
this  type  performs  an  exceedingly  important  office  in  a  very 
ingenious  yet  simple  manner.  It  consists  of  a  pair  of  plungers 
working  in  oscillating  barrels,  U  U,  attached  to  a  cross-head 
on  each  piston-rod  common  to  engine  and  pump.  Water-pres- 
sure is  introduced  behind  these  plungers  and  retained  as  nearly 
uniform  as  practicable  as  the  engine  makes  its  stroke.  It  is 
at  once  seen  that  this  pressure  resists  the  motion  of  the  engine 
from  the  beginning  to  the  middle  of  its  stroke.  At  mid-stroke, 
the  centre-lines  of  the  plungers  are  perpendicular  to  the  Line 
of  the  rod ;  they  counterbalance  each  other,  and  the  action  of 
the  pair  is  neutral  as  respects  the  engine.  Beyond  half-stroke 
this  pressure  aids  the  steam,  and  the  more  as  the  end  of  stroke 
is  approached.  The  irregular  action  of  the  expanding  steam 
is  thus  met  by  a  correspondingly  variable  opposite  action  of 
"equalizers,"  and  it  is  easy,  with  high  ratios  of  expansion, 
even,  to  thus  secure  a  very  uniform  pressure  in  excess  of  the 
resistance  of  the  water-column,  by  careful  proportioning  of 
parts  and  of  pressures. 

By  this  simple  and  ingenious  device,  due  to  Mr.  C.  C. 
Worthington,  it  is  possible  to  increase  the  ratio  of  expansion 
in  the  direct-acting  engine  very  greatly  with  corresponding 
gain  in  duty;  the  engine  thus  entering  the  class  known  as 
"  high-duty  engines."  This  attachment  thus  does  the  duty  of 
a  fly-wheel,  often,  of  enormous  weight,  and  thus  increases 
effectively  the  efficiency  of  the  engine  as  a  machine.  It  works 
properly,  with  the  same  variations  of  pressures,  at  all  speeds, 
and  is  also,  at  times,  a  safety-attachment,  stopping  the  engine 
in  case  of  a  breakage  in  the  mains. 
In  the  "  equalizer  "  system,  let 

A  =  total  area  of  section  of  plungers; 
p  =  pressure  admitted  upon  them  ; 


STRUCTURE   OF   THE  STEAM-ENGINE.  167 


1 68  A    MANUAL    OF   THE   STEAM-ENGINE. 

L  =  their  full,  joint,  load  ; 

T  =  thrust  in  line  with  piston-rod  ; 

8   =  angle  of  axis  of  equalizer  with  vertical. 

Then  the  total  load  and  the  stress  on  the  t\vo  equalizer-rods 
is 

L  =  Ap  =  r'cot  e  • 

T=  Apsin  0  =  L  sin  Q; 

At  mid-stroke  #0  =  o     and      T  —  o  =  L. 
At  the  extreme  positions,  0,,  0a, 

T=Ap  sin  0lt  =  Ap  sin  02; 

and  these  values  should  be  made  to  approximately  equal  the 
initial  load  on  the  engine-piston,  less  the  resistance  in  the 
pump  at  starting,  and  to  the  latter  quantity,  less  the  terminal 
pressure  of  engine-piston,  at  the  end  of  stroke.  The  alti- 
tude of  the  equalizer-trunnions  above  the  centre-line  of  the 
engine,  and  the  length  of  stroke  thus  fixed,  are  the  elements 
determining  the  quantity  of  work  done  in  the  equalizer-cylin- 
ders and  the  completeness  of  equalization.  The  stroke,  s, 
should  have  such  extent  that  the  work  per  stroke  may  be  equal 
to  the  alternate  excess  and  deficiency  of  the  work  of  the 
engine,  in  the  earlier  and  the  later  half-stroke,  respectively,  above 
and  below  that  demanded,  in  the  same  time,  at  the  pump. 

A  small  sketch  illustrating  this  equalization  will  be  found 
in  the  chapter  on  Engine-trials. 

Beam  pumping-engines  are  now  almost  invariably  built  with 
crank  and  fly-wheel,  and  very  frequently  are  compound  engines. 
The  illustration  on  page  169  represents  an  engine  of  the  latter 
form. 

A  and  B  are  the  two  steam-cylinders,  connected  by  links 
and  parallel  motion,  CD,  to  the  great  cast-iron  beam,  EF.  At 
the  opposite  end  of  the  beam,  the  connecting-rod,  G,  turns  a 
crank,  H,  and  fly-wheel,  LMt  which  regulates  the  motion  of 
the  engine  and  controls  the  length  of  stroke,  averting  all  danger 
of  accident  occurring  in  consequence  of  the  piston  striking 
either  cylinder-head.  The  beam  is  carried  on  handsomely- 


STKl'CT*~RE  OF  TOM  STMAM-JSHGOOL 


169 


shaped  iron  columns,  which,  with  cylinders*  pomp,  and  fly- 
wheeL  are  supported  by  a  substantial  stone  foundation.  The 
pump-rod,  Ir  works  a  double-acting  pump,  /„  and  the  resistance 
to  the  issuing  water  is  rendered  uniform  by  an  air-chamber,  Kr 
within  which  the  water  rises  and  falls  when  pressures  tend  to 
vary  greatly.  A  revolving  shaft.  -V.  driven  from  the  fly-whcd 
abaft,  carries  cams,  OP,  which  move  the  lifting-rods  seen 
directly  over  them  and  the  valves  which  they  actuate.  Be- 
tween the  steam-cylinders  and  the  columns  which  carry  the 
beams  is  a  well,  in  which  are  placed  the  condenser  and  air- 


pump.     Steam  is  carried  at  60  or  80  pounds  pressure,  and  ex- 
panded from  6  to  10  times. 

A  later  form  of  double-cylinder  beam  pmnping-engine  is 
that  invented  and  designed  by  E.  D.  Leavittt.  and  shown  in 
Figs.  78  and  79.  The  two  cylinders  are  placed  one  on  each 
side  the  centre  of  the  beam,  and  are  so  inclined  that  they  may 
be  coupled  to  opposite  ends  of  it,  while  their  lower  ends  are 
placed  dose  together.  At  their  upper  ends  a  valve  is  placed 
at  each  end  of  the  connecting  steam-pipe.  At  their  lower  ends 
a  single  valve  serves  as  exhaust-valve  to  the  high-pressure  and 
as  steam-valve  to  the  low-pressure  cylinder.  The  pistons  move 


I/O 


A  MANUAL    OF    THE    STEAM-ENGINE. 


in  opposite  directions,  and  steam  is  exhausted  from  the  high- 
pressure  cylinder  directly  into  the  nearer  end  of  the  low- 
pressure  cylinder.  The  pump,  of  the  "  Thames-Ditton  "  or 
"  bucket-and-plunger  "  variety,  takes  a  full  supply  of  water  on 


FIG.  78.— THE  LEAVITT  WATER-WORKS  ENGINE. 

the  down-stroke,  and  discharges  half  when  rising  and  half  when 
descending  again.  The  duty  of  this  engine  is  reported  as  ex- 
ceeding 1 10,000,000  foot-pounds  for  every  too  pounds  of  coal 
burned.  The  duty  of  a  moderately  good  engine  is  usually 
considered  to  be  from  60  to  70  millions ;  while  100,000,000  is 
a  high  figure. 


STRUCTURE  OF  THE   STEAM-EXGIXE. 


171 


The  Wolff  and  Receiver  types  are  the  two  most  familiar 
forms  of  pumping-engine.  The  Wolff  engine  is  so  designed 
that  the  motions  of  the  two  pistons  are  coincident  in  time,  as 
when  both  are  attached  to  the  same  end  of  a  working-beam. 
Fig.  79.  It  is  often  found  advantageous  to  add  a  second, 
high-pressure,  cylinder  to  a  low-pressure  engine,  thus  converting 
it  into  a  compound  engine.  This  is  usually  done  by  placing 
the  new  cylinder  beside  the  old  and  connecting  it  to  the  beam 
through  the  old  air-pump  links.  This  compounding  system  is 


FIG.  79.—  THE 


commonly  known  as  "  McXaughting,"  from  the  first  engineer 
to  practise  it.  In  such  cases,  the  steam-passages  lead  from 
either  end  of  the  one  cylinder  to  the  opposite  end  of  the  other, 
and  no  intermediate  receiver  is  needed.  Where,  as  in  the 
Gaskill  engine  of  the  Holly  Mfg.  Co.,  Figs.  80,  81,  and  82,  the 
proportions  of  the  cylinder  are  such,  the  diameter  being  great 
in  proportion  to  the  stroke,  that  it  is  possible  to  introduce  a 
beam  in  the  manner  shown,  and  to  secure  alternation  of  move- 
ment, the  intervening  steam-passages  become  of  minimum 
length,  and  "  dead-space"  is  made  comparatively  small,  with 


\72 


MANUAL    OF   THE    STEAM-ENGINE. 


STRUCTURE  OF   THE  STKAJf-EHGlXE. 


»73 


very  advantageous  economical  results;  while  the  engine  be- 
comes very  compact. 

When,  as  is  sometimes   the   fact,  the   two   cylinders   are 


placed  at  opposite  ends  of  the  beam,  the  latter  being  of  com- 
mon proportions  and  the  engine  of  long  stroke,  the  centre- 
fines  of  the  cylinders  are  separated  by  a  distance  equal  to  from 


174  A   MANUAL    OF   THE   STEAM-ENGINE. 


FIG.  82.— COMPOUND  PUMPING-ENGINE. 


STRUCTURE  OF  THE   STEAM-EXGIXE. 


1/5 


two  to  three  times  the  length  of  stroke,  and  the  steam-passage* 
and  dead-spaces  become  seriously  large.  This  objection  has 
been  met  by  Dr.  Leavftt  by  inclining  the  cylinders,  as  in  Figs. 
78  and  79,  and  throwing  their  lower  ends  in  under  the  main 
beam-centre,  thus  considerably  shortening  the  connecting  pipes. 


A  Corliss  Pmrnpimg-cmguu.  designed  by  that  great  engineer 
for  the  water-works  of  Pawtucket,  IL  I.,  has  been  reported  as 
doing,  continuously,  a  "  duty"  of  over  120^0000000.  This  «*«g"nr, 
Fig.  83,  consists  of  a  pair  of  horizontal  steam-cylinders,  side  by 
side,  driving  a  pair  of  double-acting  pumps,  each  in  line  with 
one  of  the  engine-cylinders  and  the  two  having  a  common 


176 


MANUAL    OF   THE   STEAM-ENGINE. 


piston-rod.  A  bell-crank  lever  and  suitable  links  connect  the 
engines  with  the  single  balance-wheel,  placed  between  and 
above  them.  The  smaller  cylinder  takes  steam  of  about  ten 


FIG.  84. — VERTICAL  TRIPLE-EXPANSION  ENGINES. 

atmospheres  absolute  pressure  (127  pounds  by  gauge),  and  its 
exhaust  passes  across  to  the  larger  cylinder,  whence  it  is  passed 
into  the  condenser,  below  the  engine.  The  ratio  of  expansion 
is  from  15  to  20,  and  the  speed  of  engine  50  revolutions  per 
minute. 


STRUCTURE  OF  THE  STEAJi-EXGlXE.  1/7 

The  pomps  are  fitted  with  a  large  number  of  small  and 
light  valves  and  thus  are  subject  to  very  little  waste  by  leakage 
or  back-flow  of  water  while  they  are  seating,  and  demand 
very  little  power  in  their  operation. 

As  in  all  engines  of  this  kind,  a  receiver  is  attached  between 
the  engine-cylinders,  and  in  this  case  the  steam  is  superheated 
both  before  entering  the  engine  and  while  passing  from  the  one 
cylinder  to  the  other.  The  valve-gear  is  of  the  usual  Corliss 
type,  the  expansion  variable  on  both  cylinders. 

Fig.  84  illustrates  a  type  of  vertical  triple-expanding  pump- 
ing-engines  for  water-works,  such  as  have  been  designed  by 
Mr.  Reynolds  and  the  Allis  Co.  for  a  number  of  large  cities. 
Their  capacity  averages  about  20,000^000  gallons  per  day. 

jj  The  cylinders  are  attached  to  heavy  A-frames  which  are 
secured  to  the  bed-plates.  In  the  A-frames,  the  guides  are 
formed  for  the  cross-heads.  The  plungers  move  with  the 
cranks,  which  are  set  120  degrees  apart  to  insure  a  constant 
and  steady  flow  of  water  in  the  delivery-mains.  The  pumps 
have  outside-packed  plungers  of  the  single-acting  type,  one 
plunger  being  located  under  and  operated  by  each  piston. 
Each  plunger  is  connected  to  its  steam-piston  by  four  rods 
attached  to  the  cross-heads.  The  condenser  and  pumps  are 
placed  in  a  pit  below  the  engine-room  floor.  The  pump-valves 
are  mounted  on  cages,  and  so  arranged  that  any  series  of 
valves  can  be  easily  removed  or  replaced.  All  the  operations 
of  the  engine  are  performed  from  one  central  position  by  the 
engineer. 

The  engraving  following  illustrates  a  pair  of  vertical  triple- 
i  expansion  pumping-enghies  which  were  designed  by  Mr.  Rey- 
nolds for  the  city  of  Allegheny,  Pa.,  to  pump  six  million  gal- 
lons of  water,  each  twenty-four  hours,  against  a  head  of  220 
feet,  and  develop  a  duty  of  ninety-five  million  foot-pounds  for 
each  one  thousand  pounds  of  water  fed  to  the  boilers.  The 
duty  obtained  by  a  twenty-four-hour  run  was  over  107.000.000 
foot-pounds. 

This  type  is  a  favorite  with  many  builders,  as  it  bongs  all 
parts  within  a  small  floor-plan,  yet  gives  accessibility  of  parts, 


FIG.  85. -T 


ISO  -.A    MANUAL   OF   THE   STEAM-ENGINE. 

a  moderate  size  and  cost  of  foundation  for  a  given  capacity, 
and  direct  connection  of  the  cylinders  in  series  and  the  pumps. 
The  section  at  the  left  is  so  made  as  to  give  a  good  idea  of  the 
arrangement  of  steam-passages  and  of  water-connections.  This 
design  is  seen  to  be  a  direct  connected  engine  set  on  end. 

A  design  of  blowing-engine,  of  air-pumping,  for  large  blast- 
furnaces, illustrating  well  the  compactness,  stiffness,  and  neat- 
ness attainable  in  such  designs,  and  also  the  form  of  valve- 
motion  adopted  with  the  poppet-valve,  is  shown  in  the  outline 
engraving  on  page  179.*  This  design  is  by  Messrs.  Gordon, 
Strobel  &  Lawrence.  The  steam-cylinders  are  42  and  the 
blast-cylinder  84  inches  in  diameter,  their  common  stroke  4 
feet.  The  box-form  of  frame  permits  great  stiffness  and  ad- 
mits the  placing  of  the  two  cylinders  in  line,  the  main  (i  5-inch) 
shaft  beneath,  and  a  convenient  general  arrangement  of  valve- 
gearing.  In  the  latter,  as  seen,  a  rock  shaft,  actuated  directly 
by  the  eccentric-rod,  produces  the  vibration  of  the  "wipers" 
raising  the  "  toes,"  which,  in  turn,  raise  and  depress  the  valves. 
A  trip-arrangement  permits  a  variable  cut-off  from  one  to 
three-fourths  stroke,  and  a  constant  lead  is  maintained.  The 
lift  of  the  steam-yalve  varies  from  f-  inch  to  2-J  inches,  as  the  ex- 
pansion decreases.  The  action  of  the  exhaust  is  unaffected  by 
that  of  the  steam-valve.  The  air-valves  are  so  large  in  total 
area  that,  at  the  working-speed,  no  observable  loss  of  pressure 
occurs  at  their  ports.  The  depth  of  piston  is  one  fourth  the 
diameter  in  the  steam-cylinder  and  one  eighth  in  the  blast-cyl- 
inder. This  engine  makes  about  35  revolutions  per  minute, 
with  60  pounds  of  steam  and  cut-off  at  ±. 

38.  Portable  Engines  are  such  as  may  be  conveniently 
moved  from  place  to  place.  They  are  generally  of  small  size, 
moderate  power,  compact  construction,  non-condensing,  em- 
ploying steam  of  high  pressure  in  cylinders  worked  at  high 
piston-speed,  and  produced  in  boilers  of  the  tubular  class  and 
which  commonly  serve,  also,  as  engine-frames.  In  some  cases, 

*  Reproduced  by  permission  from  the  Iron  Age  o* 


STRUCTURE   OF    THE   STEAM-ENGINE.  l8l 

they  consist  of  engine  and  boiler  mounted  on  a  common  bed. 
Often  they  are  mounted  on  wheels,  in  \vhich  case  they  are 
usually  known  as  "  agricultural  engines." 

Road-locomotives,  which  are  self-impelling  portable  engines, 
are  much  used  in  some  parts  of  the  world,  and  the  steam 
"road-roller"  is  a  road-locomotive  which  has  heavy  rollers  in 
place  of  wheels,  and  which  may  be  used  in  rolling  the  surface 


FIG.  87.— SEMI-PORTABLE  ENGINE.    (Scale 


of  macadamized  or  other  roads.  Similarly,  a  "steam  fire-en- 
gine "  is  a  portable  engine  carrying  a  steam-pump  which  may 
be  used  in  extinguishing  fires. 

The  "  semi-portable  "  engine  in  Fig.  87  is  not  fastened  to 
the  boiler,  and  is  therefore  not  .affected  by  expansion,  nor  are 
the  bearings  overheated  by  conduction  or  by  ascending  heat 


1 82 


A    MANUAL    OF   THE   STEAM-ENGINE. 


from  the  boiler.  The  fly-wheel  is  at  the  base,  which  arrange- 
ment secures  steadiness  at  the  high 
speed  which  is  a  requisite  for  econ- 
omy of  fuel.  The  boilers  are  of  the 
upright  tubular  style,  with  internal 
fire-box,  and  are  intended  to  be 
worked  at  150  pounds  pressure  (10 
atmospheres)  per  inch.  These  boil- 
ers are  fitted  with  a  baffle-plate  and 
circulating-pipe,  to  prevent  priming, 
and  also  with  a  fusible  plug,  which 
will  melt  and  prevent  the  crown- 
sheet  of  the  boiler  burning,  if  the 
water  gets  low. 

Another  illustration  of  this  class 
of  engine,  as  built  in  small  sizes,  is 
seen  in  Fig.  88.  The  peculiarity  of 
this  engine  is  that  the  cylinder  is 
placed  in  the  top  of  the  boiler,  which 
is  upright.  By  this  arrangement  the 
engine  is  constantly  drawing  from  the 
boiler  the  dryest  steam,  and  there  is  thus  no  liability  of  serious 
loss  by  condensation,  which  is  rapid,  even  in  a  short  pipe,  when 
the  engine  is  separate  from  the  boiler.  The  engine  illustrated 
is  rated  at  10  horse-power. 

Among  the  earliest  of  American  engineers  to  turn  attention 
to  this  department  of  construction  were  Messrs.  Babcock  & 
Wilcox.  The  style  of  engine  which  was  designed  and  intro- 
duced by  them  has  now  become  almost  as  generally  accepted 
as  standard  among  builders  of  small  engines  as  has  the  Corliss 
engine  among  constructors  of  drop  cut-off  engines.  It  has 
been  copied  in  all  parts  of  Europe,  as  well  as  in  the  United 
States.  It  may  be  taken  as  representative  of  the  best  methods 
of  construction  of  this  class  of  machinery  in  this  country,  and 
as  exhibiting  the  elegance  in  proportions,  and  that  excellence  of 
material  and  workmanship,  which  are  now  becoming  recognized 
as  desirable  in  steam-engines  of  even  the  smallest  size. 


FIG.  88.— SEMI-PORT 
(Scale  A 


STMUTTUSE  Of  THE  STEAM-ENGINE-  183 

Figs.  30  and  31  exhibit  the  form  of  the  engine  here  to 
be  described.  It  is  a  ~  vertical  engine ""  mounted  upon  a  base 
plate  of  neat  and  strong  form,  and  with  the  steam-cylinder 
bolted  by  the  lower  head  to  a  very  strong  and  very  graceful 
frame.  1~Mc  mam  journals  are  earned  m  bearings  JUBSJ  meted 
in  the  frame,  and  consequently  free  from  liability  to  loss  of 
perfect  alignment,  or  to  unequal  wear.  The  valve  is  either  a 
plain  locomotive-slide  or,  preferably,  a  piston-valve.  The 
Latter  is  fitted  in  a  detachable  seat,  which  can  be  easily  removed 
for  renewal  of  seat  and  valve,  should  accident  or  wear  ever 
make  k  necessary. 

The  vertical  position  of  the  engine  pievenb.  wear  within 
fhe  cylinder  becoming  serious  or  unsymmetricaL  The  pistons 
are  hollow,  and  are  packed  with  rings  set  with  *"*%•*•••  spring 
to  keep  them  up  to  a  bearing.  The  cross-head  has  its  gibs 
turned  to  fit  the  guides  in  the  frame,  which  latter  are  part  of 
the  casting  of  the  frame  and  are  bored  out  in  line  with  the 
cylinder,  and  cannot  puiiilillly  g6*  out  °f  fine. 

The  engine  above  referred  to  is  of  small  size — 4  or  5  hone- 
power — and  has  been  iiUMiiaBy  designed  for  electric-fighting 
purposes.  The  governor  regulates  by  adjusting  the  supply  off 
steam  passing  to  the  engine  through  a  throttle-valve— a  method 
which  seems  to  have  been  here  more  successful  than  is  usual 
in  engines  having  to  perform  so  t^rarHng  a.  kind  «f  work.  The 
speed  of  this  engine  is  usually  250  to  300  revolutions  per 
minute. 

Larger  engines  of  this  style  are  often  constructed,  ranging 
up  to  TOO  horse-power.  These  engines,  when  of  15  to  IOO 
horse-power,  are  properly  classed  as  stationary  engines ;  they 
are  given  an  independent  crank-shaft  pillow-block  and  a 
counterbalanced  disk-crank.  In  these  engines,  of  all  sizes,  the 
modern  innovation  of  the  use  of  steel  for  running  parts  is  very 
generally  introduced.  The  rods,  pins,  and  minor  parts  are  of 
this  metal;  the  bearings  are  usually  of  bronze  fined  with 
Babbitt-metal,  and  are  given  large  area.  Crank-shafts  are 
either  of  M^cl  or  of  hammered  iron. 

The  later  work  of  the  best  English  builders  has  given 


184  A   MANUAL   OF   THE  STEAM-ENGINE. 

remarkable  economical  results.  Some  of  these  portable  engines 
have  exhibited,  at  competitive  trials,  an  economical  efficiency 
equal  to  that  of  the  largest  marine  engines.  The  causes  of  this 
remarkable  economy  are  readily  learned  by  an  inspection  of 
the  engines,  and  by  observation  of  the  method  of  managing 
them  at  test-trials.  The  engines  are  very  carefully  designed. 
The  pistons  travel  at  high  speed.  Their  valve-gear  consists 
usually  of  a  plain  slide-valve,  supplemented  by  a  separate  ex- 
pansion-slide, driven  by  an  independent  eccentric,  and  capable 
of  considerable  variation  in  the  point  of  cut-off.  This  form  of 
expansion-gear  is  very  effective  at  the  usual  ratio  of  expansion, 
which  is  not  far  from  four  or  five.  The  governor  is  usually 
attached  to  a  throttle-valve  in  the  steam-pipe,  an  arrangement 
which  is  not  the  best  possible  under  variable  loads,  but  which 
produces  no  serious  loss  of  efficiency  when  the  engine  is 
driven,  as  at  competitive  trials,  under  the  very  uniform  load  of 
a  brake  and  at  very  nearly  maximum  capacity.  The  most 
successful  engines  have  steam-jacketed  cylinders  with  high 
steam  and  considerable  expansion.  The  boilers  are,  as  are 
also  all  other  heated  surfaces,  carefully  clothed  with  non-con- 
ducting material,  and  well  lagged  over  all.  The  details  are 
carefully  proportioned,  the  rods  and  frames  are  strong  and 
well  secured  together,  and  the  bearings  have  large  rubbing- 
surfaces.  The  connecting-rods  are  long  and  easy-working,  and 
every  part  is  capable  of  doing  its  work  without  straining  and 
with  the  least  friction. 

In  handling  the  engines  at  the  competitive  trial,  experienced 
and  skilful  drivers  are  selected.  The  difference  between  the 
performances  of  the  same  engine  in  different  hands  has  been 
found  to  amount  to  from  10  to  15  per  cent,  even  where  the 
competitors  were  both  considered  exceptionally  skilful  men. 
In  manipulating  the  engine,  the  fires  are  attended  to  with  the 
utmost  care ;  coal  is  thrown  upon  them  at  regular  and  fre- 
quent intervals,  and  a  uniform  depth  of  fuel  and  a  perfectly 
clean  fire  are  secured.  The  sides  and  corners  of  the  fire  are 
looked  after,  especially.  The  fire-doors  are  kept  open  the 
least  possible  time ;  not  a  square  inch  of  grate-surface  is  left 


STRUCTURE   OF   THE  STEAM-ENGINE.  185 

unutilized,  and  every  pound  of  coal  gives  out  its  maximum  of 
calorific  power,  and  in  precisely  the  place  where  it  is  needed. 
Feed-water  is  supplied  as  nearly  as  possible  continuously,  and 
with  the  utmost  regularity.  In  some  cases  the  engine-driver 
stands  by  his  engine  constantly,  feeding  the  fire  with  coal  in 
handfuls,  and  supplying  the  water  to  the  heater  by  hand  by 
means  of  a  cup.  Heaters  are  invariably  used  in  such  cases. 
The  exhaust  is  contracted  no  more  than  is  absolutely  necessary 
for  draught.  The  brake  is  watched  carefully,  lest  irregularity 
of  lubrication  should  cause  oscillation  of  speed  with  the  chang- 
ing resistance.  The  load  is  made  the  maximum  which  the 
engine  is  designed  to  drive  with  economy.  Thus  all  conditions 
are  made  as  favorable  as  possible  to  economy,  and  they  are 
preserved  as  invariable  as  the  utmost  care  on  the  part  of  the 
attendant  can  make  them. 

These  trials  are  usually  of  only  three  or  five  hours'  duration, 
and  terminate  before  it  becomes  necessary  to  clean  fires. 

Agricultural  Engines. — The  next  illustration  represents  the 
portable,  "  agricultural,"  steam-engine  as  built  by  one  of  the 
earliest  and  best  manufacturers  of  such  engines  in  the  United 
States.  In  the  boilers  of  these  engines  the  heating-surface  is 
given  less  extent  than  in  the  stationary  engine-boiler,  but  much 
greater  than  in  the  locomotive,  and  varies  from  10  to  20  square 
feet  per  horse-power.  The  boilers  are  made  very  strong,  to 
enable  them  to  withstand  the  strains  due  to  the  attached  en- 
gine, which  are  estimated  as  equivalent  to  from  one  tenth  to 
one  eighth  that  due  to  the  steam-pressure.  The  engine  is 
mounted,  in  this  example,  directly  over  the  boiler,  and  all 
parts  are  in  sight  and  readily  accessible  to  the  engineer. 

Compound  Portable  Engines  have  been  found  to  exhibit 
great  economy  as  compared  with  the  simple  engine,  notwith- 
standing the  fact  that  the  advantages  of  compounding  are  gen- 
erally supposed  to  be  less  on  small  than  on  large  engines.  The 
plan  adopted  is  usually  that  of  placing  the  two  engines  side  by 
side,  connecting  them  to  cranks,  on  a  common  crank-shaft,  set 
at  right-angles,  and  providing  a  receiver  of  moderate  size  to 
take  the  exhaust  of  the  smaller  and  to  supply  steam  to  the 


1 86 


A    MANUAL    OF   THE   STEAM-ENGINE. 


larger  cylinder.  In  some  instances,  the  Wolff  system  of  two 
pistons  having  simultaneous  opposite  motions  and  without 
receiver  is  adopted,  a  plan  admissible  with  small  engines,  but 
less  suitable  for  large  powers.  The  compounding  of  engines 


FIG.  89.— T 


of  this  class,  which  are  usually  of  less  than  25  horse-power,  has 
been  found  to  produce  a  saving  of,  often,  twenty-five  per  cent 
of  the  fuel  and  steam. 

Steam  Fire-engines  have  become  standard  in  general  plan  and 
arrangement  of  details.  These  are  probably  the  best  illustra- 
tions of  extreme  lightness,  combined  with  strength  of  parts  and 
working  power,  which  have  ever  been  produced  in  any  branch 
of  mechanical  engineering.  By  using  a  small  boiler  crowded 
with  heating-surface,  very  carefully  proportioned  and  arranged, 
and  with  small  water-spaces  ;  by  adopting  steel  for  running- 
gear  and  working  parts  wherever  possible  ;  by  working  at  high 


STRUCTURE   OF  THE   STEAM-ENGIXE.  l8/ 

piston-speed  and  with  high  steam-pressure ;  by  selecting  fuel 
with  extreme  care — by  all  these  expedients,  the  steam  fire- 
engine  has  been  brought,  in  this  country,  to  a  state  of  efficiency 
far  superior  to  anything  seen  elsewhere.  Steam  is  raised  with 
wonderful  promptness,  even  from  cold  water,  and  water  is 
thrown  from  the  nozzle  at  the  end  of  long  lines  of  hose  to  great 
distances.  But  this  combination  of  lightness  with  power  is 
only  attained  at  the  expense  of  a  certain  regularity  of  action 
which  can  only  be  secured  by  greater  water  and  steam  capacity 
in  the  boiler. 

The  small  quantity  of  water  contained  within  the  boiler 
makes  it  necessary  to  give  constant  attention  to  the  feed,  and 
the  tendency,  almost  invariably  observed,  to  serious  foaming 
and  priming  not  only  compels  unintermitted  care  while  run- 
ning, but  even  introduces  an  element  of  danger  which  is  not  to 
be  despised,  even  though  the  machine  be  in  charge  of  the  most 
experienced  and  skilful  attendants.  Even  the  greatest  care, 
directed  by  the  utmost  skill,  would  not  avail  to  prevent  frequent 
explosions,  were  it  not  for  the  fact  that  it  rarely,  if  ever, 
happens  that  accidents  to  such  boilers  occur  from  low  water, 
unless  the  boiler  is  actually  completely  emptied  of  water.  In 
driving  them  at  fires,  they  frequently  foam  so  violently  that  it 
is  utterly  impossible  to  obtain  any  clew  to  the  amount  of  water 
present,  and  the  attendant  usually  keeps  his  feed-pump  on  and 
allows  the  foaming  to  go  on.  As  long  as  water  is  passing  into 
the  boiler  it  seems  unlikely  that  any  portion  will  become  over- 
heated and  that  accident  will  occur.  (See  page  191.) 

39.  Road  Locomotives  and  Rollers  are  built,  necessarily, 
with  even  greater  care  and  of  greater  strength  than  the  ordi- 
nary portable  engine ;  since  they  are  exposed  to  rougher  usage 
and  more  serious  strain. 

In  this,  as  in  the  class  of  engines  last  described,  the  draught 
is  obtained  by  the  blast  of  the  exhaust-steam  which  is  led 
into  the  chimney.  The  usual  consumption  of  fuel  is  from  4  to 
6  pounds  pei  hour  and  per  horse-power,  burning  from  1 5  to  20 
pounds  on  each  square  foot  of  grate,  and  each  pound  evaporat- 


1 88 


A    MANUAL    OF    THE  STEAM-ENGINE. 


ing  about  8  pounds  of  water.    A  usual  weight  is,  for  the  larger 
sizes,  500  pounds  per  horse-power. 

Road-engines  are  arranged  to  propel  themselves,  as  in  the 
Mills  road-engine  or  locomotive,  of  which  the  accompanying 
engraving  is  a  representation.  This  engine  is  proportioned  for 
hauling  a  tank  containing  10  barrels,  or  more,  of  water  and  a 
grain-separator  over  all  ordinary  roads,  and  to  drive  a  thrashing- 
machine  or  saw-mill,  developing  20  or  25  horse-power.  This 
example  of  the  road-engine  has  a  boiler  built  to  work  at  250 


FIG.  90. — THRASHER'S  ROAD-ENGINE.     (Scale  fg.) 

pounds  of  steam  ;  the  engine  is  designed  for  a  maximum  power 
of  30  horses.  It  has  a  balanced  valve  and  automatic  cut-off, 
and  is  fitted  with  a  reversing-gear  for  use  on  the  road.  The 
driving-wheels  are  of  wrought-iron,  56  inches  diameter  and 
8  inches  wide,  with  cast-iron  driving-arms.  Both  wheels  are 
drivers  on  curves  as  well  as  on  straight  lines.  The  engine  is 
guided  and  fired  by  one  man,  and  the  total  weight  is  so  small 
that  it  will  pass  safely  over  any  good  country  bridge.  A  brake 
is  attached,  to  insure  safety  when  going  down-hill.  Although 
designed  to  move  at  a  speed  of  about  three  miles  per  hour,  the 


STRUCTURE  OF   THE  STEAJt-EXGIXE. 


189 


Telocity  of  the  piston  may  be  increased  so  that  four  miles  per 
hour  may  be  accomplished  when  necessary. 

This  is  an  excellent  example  of  this  kind  of  engine  as  con- 
structed at  the  present  time.  The  strongly-built  boiler,  with 
its  heater,  the  jacketed  cylinder,  and  light,  strong  frame  of  the 
engine,  the  steel  running-gear,  the  carefully-covered  surfaces  of 
cylinder  and  boiler,  and  excellent  proportions  of  details,  are 
illustrations  of  good  modern  engineering. 

Fig.  91  is  an  engraving  of  a  road-roller  as  built  by  one  of 
the  most  successful  among  the  firms  engaged  in  this  work. 


The  structure  of  such  an  engine,  if  of  the  better  class,  illus- 
trates many  specially  interesting  features  of  modern  construc- 
tion. They  are  often  made  with  single  engines;  but.  as  in 
this  case,  a  pair  coupled  at  right-angles,  as  in  the  locomotive, 
is  preferable ;  and  it  may  often  be  advisable  to  compound  them. 
There  should  be  no  danger  of  the  machine  getting  stalled  by 
reason  of  the  engine  "  catching  on  the  centre."  These  ma- 
chines are  made  of  from  ten  to  fifteen  tons  weight :  the  valve- 


190 


A    MANUAL   OF   THE   STEAM-ENGINE. 


motion  is  usually  the  common  locomotive  gear ;  the  best  have 
steel  running  parts  and  steel  boilers ;  a  brake  is  fitted  to  the 
driving-wheels;  and  special  noiseless  safety-valves  are  used. 
The  gearing  should  be  of  annealed  cast-steel,  and  the  driving- 
wheels  are  best  made  of  a  mixture  of  peculiarly  strong  iron,  as 
"  car-wheel  "  iron  with  new  No.  i  foundry-iron. 

This  class  of  road-locomotive  was  brought  into  use  about 


FIG.  92.— R 


1829  on  French  roads,  and   about   1865  in   England  and  her 
colonies. 

The  Author  has  made  a  trial  of  one  of  these  machines 
constructed  by  very  successful  British  builders  (see  above  fig- 
ure), to  determine  its  power,  speed,  and  convenience  of  work- 
ing and  manoeuvring.  The  following  were  the  principal  di- 
mensions : 

Weight  of  engine,  complete,  5  tons  4  cwt 11,648  pounds. 

Steam-cylinder—diameter 7|  inches. 

Stroke  of  piston IO           <« 

Revolutions  of  crank  to  one  of  driving-wheels 17 

Driving-wheels—diameter 60  inches. 

breadth  of  tire 10           " 

weight,  each 45o  pounds. 


STRUCTURE  OF  THE   STEAM-ENGINE.  igi 

Boiler— length  oreralL...... 8      feet. 

"        diameter  of  shell 30        " 

thickness  of  shell tr  inch. 

fire-box  sheets,  outside,  thickness £      " 

Load  on  driving-wheels,  4  tons  10  cwt 10,080      pounds. 

The  boiler  was  of  the  ordinary  locomotive  type,  and  the 
engine  was  mounted  upon  it,  as  is  usual  with  portable  engines. 
The  steam-cylinder  was  steam-jacketed,  in  accordance  with  the 
most  advanced  practice  here  and  abroad.  The  crank-shaft 
and  other  wrought-iron  parts  subjected  to  heavy  strains  were 
strong  and  plainly  finished.  The  gearing  was  of  malleableized 
cast-iron,  and  all  bearings,  from  crank-shaft  to  driving-wheel, 
on  each  side,  were  carried  by  a  single  sheet  of  half-inch  plate, 
which  also  formed  the  sides  of  the  fire-box  exterior.  Its  per- 
formance was  thoroughly  satisfactory. 

As  the  marine  engine  illustrates  the  highest  result  of  ap- 
plication of  invention  and  engineering  talent  to  production  of 
economy  of  fuel,  and  the  most  elaborate  and  perfect  type  of 
engine,  so  the  steam  fire-engine  exemplifies  the  result  of  the 
same  application  of  genius  to  the  production  of  a  machine  in 
which  everything  is  subordinated  to  quickness  and  power 
in  action.  Thus,  referring  to  Fig.  93,  that  of  an  engine 
designed  by  the  Manchester  Locomotive  Works,  we  find  that, 
in  this  class  of  engine,  the  demand  for  lightness,  strength, 
compactness,  quick  action,  and  large  and  concentrated  power 
is  met,  generally,  by  the  use,  as  here  seen,  of  the  vertical  tubu- 
lar boiler,  with  the  exhaust-blast  of  the  locomotive,  with  tubes 
crowded  in  more  thickly  than  would  be  desirable  or  safe  with 
the  horizontal  form  ;  large  steam  and  water  pipes,  double- 
acting  pumps,  set  vertically,  as  a  rule,  in  the  larger  sizes,  large 
steam-cylinders,  a  large  air-chamber,  and  a  steel  or  wrought- 
iron  frame.  The  whole  is  mounted  on  springs  of  great 
strength  and  flexibility  combined.  Large  fire  engines  of  this 
kind  will  weigh  three  tons,  and  will  .throw  1000  gallons  a  min- 
ute, in  a  2-inch  stream,  to  a  distance  of  300  or  325  feet,  or  to  a 
height  of  200  feet  or  more.  Their  steam-cylinders  are  as  large 
as  9  or  10  inches  diameter,  and  pumps  5f  or  6,  with  a  stroke  of 


STRUCTURE   OF  THE  STEAM-ENGINE.  193 

6  to  9  inches.  Only  the  best  of  materials  can  be  used  in  such 
machinery  as  this. 

The  balance  obtainable  by  the  use  of  three  engines  is 
especially  useful  in  the  case  of  the  steam  fire-engine;  where 
smoothness  and  steadiness  of  action  is  necessary  on  so  unsub- 
stantial a  base.  Here,  also,  the  use  of  three  attached  pumps, 
as  in  Fig.  94,  gives  a  very  valuable  gain  in  smooth-working 
of  the  water-side  of  the  machine.  With  skilful  designing,  the 
added  weight  is  comparatively  unimportant ;  since  it  only 
affects  the  engine  and  is  to  probably  usually  a  sensible  ex- 
tent compensated  by  reduced  size,  or  by  greater  efficiency 
of  the  boiler  and  by  decided  gain  in  reduction  of  friction  and 
greater  "  throw"  of  the  stream  leaving  the  hose-nozzle.  The 
details  of  the  design  by  Mr.  Knaust,  here  shown,  so  far  as  con- 
cerns the  peculiarities  of  this  class  of  engine,  can  be  readily 
seen  and  need  no  special  description. 

The  steam  fire-engine  is  sometimes  constructed  as  a  "  fire- 
boat"  of  enormous  power,  the  whole  steam-power  of  the  main 
boilers  being  there  available.  The  New  Yorker,  designed 
by  Mr.  Cowles,  for  example,  displaces  351  tons,  has  a  speed 
of  15  knots,  has  four  steam-pumps,  each  of  1 6-inch  steam- and 
lo-inch  water-cylinders,  capable  of  discharging  10,000  gallons 
per  minute  to  a  maximum  distance  of  250  feet  in  a  5-inch 
stream,  or  to  less  distances  in  a  number  of  smaller  streams. 

40.  The  Locomotive  Engine  is  the  best  known  example 
of  sustained  power,  with  minimum  weight,  which  has  yet  been 
produced  by  the  mechanical  engineer. 

A  locomotive  has  two  steam-cylinders,  either  side  by  side 
within  the  frame,  and  immediately  beneath  the  forward  end  of 
the  boiler,  or  on  each  side  and  exterior  to  the  frame.  The 
engines  are  non-condensing,  and  of  the  simplest  possible  con- 
struction. The  whole  machine  is  carried  upon  strong  but  flexi- 
ble steel  springs.  The  steam-pressure  is  usually  more  than  loo 
pounds.  The  pulling-power  is  generally  about  one  fifth  the 
weight  under  most  favorable  conditions,  and  becomes  as  low 
as  one  tenth  on  wet  rails.  The  fuel  employed  is  wood  in  new 
countries,  coke  in  bituminous-coal  districts,  and  anthracite  coal 


STRUCTURE   OF  THE   STEAM-EXG1XE.  IQ5 

in  the  eastern  part  of  the  United  States.  The  general  arrange- 
ment and  the  proportions  of  locomotives  differ  somewhat  in 
different  localities.  The  peculiarities  of  the  American  type 
(Fig.  95 )  are  the  truck,  //,  or  bogie,  supporting  the  forward 
part  of  the  engine,  the  system  of  equalizers,  or  beams  which 
distribute  the  weight  of  the  machine  equally  over  the  several 
axles,  and  minor  differences  of  detail.  The  cab  or  house,  r. 
protecting  the  engine-driver  and  fireman,  is  an  American  de- 
vice, which  is  gradually  coming  into  use  abroad  also.  The 
American  locomotive  is  distinguished  by  its  flexibility  and  ease 


of  action  upon  even  roughly-laid  roads.  In  the  sketch,  which 
shows  a  standard  American  engine  in  section,  A  B  is  the  boiler. 
C  one  of  the  steam-cylinders,  D  the  piston,  E  the  cross-head, 
connected  to  the  crank-shaft,  F.  by  the  connecting-rod.  G  H 
the  driving-wheels,  1 J  the  truck-wheels,  carrying  the  truck. 
KL  :  M  N  is  the  fire-box,  O  O  the  tubes,  of  which  but  four  are 
shown.  The  steam-pipe,  R  S,  leads  the  steam  to  the  valw- 
chest,  T,  in  which  is  seen  the  valve,  moved  by  the  valve-gear. 
L~  I "  and  the  link.  If.  The  link  is  raised  or  depressed  by  a 
lever,  JT,  moved  from  the  cab.  The  safety-valve  is  seen  at  the 
top  of  the  dome,  at  Y,  and  the  spring-balance  by  which  the 
load  is  adjusted  is  shown  at  Z.  At  a  is  the  cone-shaped  ex- 
haust-pipe, by  which  a  good  draught  is  secured.  The  attach- 
ments £,  c.  d.  r,  fy  g — whistle,  steam-gauge,  sand-box,  bell, 
head-light,  and  "  cow-catcher  " — are  nearly  all  peculiar,  either 


196  A    MANUAL    OF    THE   STEAM-ENGINE. 

in  construction  or  location,  to  the  American  locomotive.  The 
locomotive  is  furnished  with  a  tender,  which  carries  its  fuel  and 
water.  A  standard  passenger-engine  on  railways  in  the  United 
States  has  four  driving-wheels,  5i  feet  diameter ;  steam-cylin- 
ders, 17  inches  diameter  and  2  feet  stroke  ;  grate-surface  15^ 
square  feet,  and  heating-surface  1058  square  feet.  It  weighs 
63,100  pounds,  of  which  39,000  pounds  are  on  the  drivers  and 
24, 100  on  the  truck.  The  freight-engine  has  six  driving-wheels, 
54f  inches  in  diameter.  The  steam-cylinders  are  18  inches  in 
diameter,  stroke  22  inches,  grate-surface  14.8  square  feet,  heat- 
ing surface  1096  feet.  It  weighs  68,500  pounds,  of  which 


FIG.  96. — THE  AMERICAN  TYPE  OF  PASSENGER-ENGINE. 

48,000  are  on  the  drivers  and  20,500  on  the  truck.  The  former 
takes  a  train  of  five  cars  up  an  average  grade  of  90  feet  to  the 
mile.  The  latter  is  attached  to  a  train  of  1 1  cars.  On  a  grade 
of  50  feet  to  the  mile,  the  former  takes  7  and  the  latter  17 
cars.  Tank-engines  for  very  heavy  work,  such  as  on  grades  of 
320  feet  to  the  mile,  which  are  found  on  some  of  the  mountain 
lines  of  road,  are  made  with  five  pairs  of  driving-wheels,  and 
with  no  truck.  The  steam-cylinders  are  20^-  inches  in  diame- 
ter, 2  feet  stroke;  grate-area,  15!  feet;  heating-surface,  1380 
feet ;  weight  with  tank  full,  and  full  supply  of  wood,  112,000 
pounds  ;  average  weight,  108,000  pounds.  Such  an  engine  has 
hauled  1 10  tons  up  this  grade  at  the  speed  of  5  miles  an  hour, 


STRUCTURE   OF   THE   STEAM-ENGIXE.  197 

the  steam-pressure  being  145  pounds.  The  adhesion  was  Jbout 
23  per  cent  of  the  weight. 

In  checking  a  train  in  motion,  the  inertia  of  the  engine 
itself  absorbs  a  seriously  large  portion  of  the  work  of  the 
brakes.  This  is  sometimes  reduced  by  reversing  the  engine 
and  allowing  the  steam-pressure  to  act  in  aid  of  the  brakes. 
To  avoid  injury  by  abrasion  of  the  surfaces  of  piston,  cylinder, 
and  the  valves  and  valve-seats,  M.  Le  Chatelier  introduced  a 
jet  of  steam  into  the  exhaust-passages  when  reversing,  and 
thus  prevented  the  ingress  of  dust-laden  air  and  the  drying  of 
the  rubbing  surfaces.  This  method  of  checking  a  train  is  rare- 
ly resorted  to  except  in  case  of  danger.  The  introduction  of 
the  "  continuous  "  or  "  air  "  brake,  which  can  be  thrown  into 
action  in  an  instant  on  every  car  of  the  train  by  the  engine- 
driver,  is  so  efficient  that  it  is  now  almost  universally  adopted. 
It  is  one  of  the  most  important  safeguards  which  American 
ingenuity  has  yet  devised.  In  drawing  a  train  weighing  1 50 
tons  at  the  rate  of  60  miles  an  hour,  about  800  effective  horse- 
power is  required.  A  speed  of  80  miles  an  hour  has  been 
sometimes  attained,  and  100  miles  has  probably  been  reached. 

The  standard  locomotive-engine  has  a  maximum  life  which 
may  be  stated  at  an  average  of  about  30  years.  The  annual 
cost  of  repairs  is  from  10  to  15  per  cent  of  its  first  cost.  On 
moderately  level  roads,  the  engine  requires  a  pint  of  oil  to  each 
25  miles,  and  a  ton  of  coal  to  each  40  or  50  miles  run. 

The  compound  locomotive  engine  is  now  coming  to  be 
adopted.  This  involves  considerable  changes  of  proportions, 
increasing  the  volume  and  weight  of  steam-cylinders,  but  en- 
abling the  designer  to  more  than  proportionally  decrease  the 
weight  of  boiler  and  the  quantity  of  fuel  carried.  Xo  serious 
objection  to  their  use  has  been  experienced,  however,  and  no 
difficulty  in  the  construction  of  the  "  double-cylinder "  type 
of  engine  for  the  locomotive.  Many  such  engines  have  been 
constructed.  They  will  be  referred  to  again. 

The  increasing  demands  upon  the  railways  of  the  United 
States  have  recently  brought  about  considerable  changes  in  the 
forms  of  engine  employed.  The  standard  "  American  "  type  cf 


198  A   MANUAL    OF   THE    STEAM-ENGINE. 

locomotive  is  much  less  generally  employed  for  slow  and 
heavy  traffic,  and  its  place  has,  on  the  trunk  lines,  been  taken 
by  8-,  IO-,  and  12-wheeled  engines  of  great  weight.  Even  in  pas- 
senger service,  engines  with  six  and  ten  coupled  wheels  are 
displacing  it  in  many  cases.  For  "switching  "  or  "shunting" 
heavy  trains,  engines  of  40  tons  weight,  with  six  coupled 
wheels  and  17-  to  I  clinch  cylinders  of  24  inches  stroke,  are 
used.  The  weights  on  the  drivers  are  usually  5  to  7  times 
the  adhesion  demanded.  In  Europe,  with  lighter  trains  and 
shorter  runs,  as  a  rule,  but  with  higher  speeds,  the  single  pair 
of  drivers,  the  opposite  extreme  of  practice,  seems  preferred. 
On  both  continents  the  compound  locomotive  is  rapidly  com- 
ing into  use. 

The  modern  developments  of  the  locomotive-engine,  which 
have  been  seen  to  involve  no  change  of  general  construction, 
have  been  mainly  the  refinement  of  details,  the  introduction 


of  a  few  recent  inventions,  as  the  extended  smoke-box,  and 
the  application  of  the  air-brake.  The  engine  is  to-day  the 
locomotive  of  George  and  Robert  Stephenson. 

But  while  the  type  remains  unchanged  in  its  essentials, 
there  are  now  in  use  a  great  number  of  designs  of  engine 
differing  among  each  other  in  proportions  and  often  widely  in 
external  appearance,  designs  which  have  been  produced  in  the 
endeavor  to  adapt  the  machine  to  specific  kinds  of  work  or  to 
special  localities  and  purposes.  Thus  the  fast  passenger  and 


STKCCTCKE  OF   THE  STEAX-EXGIXE. 


-  /.- 


the  slow  freight,  or  "  goods,"  engine  have  very  different  pro- 
portions and  appear  like  quite  different  machines. 

The  common  standard  passenger-engine  is  of  the  type 
illustrated  in  the  accompanying  figure,  as  built  by  the  Rogers 
Works,  in  which  a  comparatively  recent  device,  the  "  extension 
smoke-box,"  is  shown,  acting  as  a  trap  and  temporary  recep- 
tacle for  hot  ashes  and  cinders  carried  through  the  tubes  and  for- 
merly thrown  out  to  set  fire  to  buildings  or  vegetation  or  to 
annoy  the  people  on  the  train. 

Ten- and  twelve-wheeled  engines  are  employed  for  the 
heaviest  kinds  of  work.  These  locomotives  weigh  from  45  to 
75  tons,  and  occasionally  even  more,  of  which  nearly  all  is  car- 
ried on  coupled  driving-wheels  of  not  far  from  4  feet  diameter. 
The  cylinders  are  20  to  22  inches  in  diameter,  and  stroke  of 
piston  usually  about  2  feet.  They  have  25  to  35  square  feet 


of  grate-surface  and  1500  to  2500  feet  of  heating-surface. 
The  alternate  pairs  of  wheels  have  "  blank,"  or  unconed.  tires, 
to  permit  easy  movement  around  curves.  Their  details  are 
similar  to  those  elsewhere  described  as  made  for  standard  pas- 
senger-engines. 

Where  the  fine  is  of  narrow  gauge,  as  often  in  new  coun- 
tries, or  wherever  it  is  found  desirable  to  concentrate  more 
hauling  power  than  the  usual  forms  of  engine  would  give, 
special  designs  have  been  sometimes  adopted.  The  Fairhe 
engine  is  one  of  these.  This  plan  unites  two  engines,  back  to 


200 


A  MANUAL    OF   THE   STEAM-ENGINE. 


back,  in  effect,  giving  a  twin  arrangement  of  engines  and  of 
boiler,  united  at  the  fire-box.  The  plan  is  costly  but  effective. 
A  simpler  system  of  concentration  of  power  is  that  of  Forney, 
which  unites  engine  and  tender  on  one  frame  and  thus  secures 
increased  weight  and  adhesion,  as  seen  in  the  engraving  here 
given  ;  which  gives  a  total  weight  of  60,000  pounds  on  a  nar- 
row and  comparatively  short  wheel-base,  and  makes  an  ex- 
ceptionally handy  and  easily  worked  engine. 

The  "tank-engine,"  of  which  the  last  illustrates  one  form, 
is  sometimes  constructed  on  a  very  large  scale.  Thus,  loco- 
motives built  at  the  Baldwin  Locomotive  Works,  Philadel- 
phia, for  the  Grank  Trunk  Railway,  to  be  used  in  the  St. 
Clair  tunnel,  under  the  bed  of  the  St.  Clair  River,  between 


FIG.  99. — FORNEY  LOCOMOTIVE. 

Port  Huron,  Mich.,  and  Sarnia,  Ont.,  have  five  pairs  of 
50-inch  driving-wheels  on  each  side  of  the  boilers,  the 
cab  in  the  centre  of  the  boiler,  extending  out  over  the 
two  tanks.  The  cylinders  are  22.28  inches,  and  the  boiler 
74  inches  in  diameter,  to  carry  160  pounds  of  steam.  Each 
locomotive  with  tanks  filled  weighs  200,000  pounds,  the  ave- 
rage weight  in  running  order,  with  tanks  half-filled,  being 
180,000  pounds. 

Compound  Locomotives  are  less  common  than  compound 
stationary  engines.  They  are,  however,  gradually  becoming 
used  where  fuel  is  expensive  and  give,  when  well  designed, 
very  marked  economical  advantages.  The  usual  system 


STRUCTURE  OF  THE  STEAM-EXGIXE. 


2:: 


places  a  high-pressure  cylinder  on  one  side  and  a  low-pressure 
cylinder  on  the  other,  the  latter  being  commonly  arranged  to 
take  steam  direct  from  the  boiler  when  starting  or  whenever,  for 
any  reason,  it  is  desirable. 

Some  of  the  more  interesting  and  successful  designs  of 
compound  locomotive-engine  are  those  of  which  outline 
illustrations  follow,  selected  from  Professor  Woods'  mono- 
graph.* That  of  Von  Borries  is  exemplified  by  Figs.  I oo and  101  : 
the  one  exhibiting  the  arrangement  adopted  in  a  heavy  en- 
gine on  the  Prussian  State  Railways^  the  other  a  Spanish 
engine  of  less  power. 


.-     :      ::.:    — .' •      -•    • 


The  former  has  cylinders  18.1  and  25.6  inches  diameter.  24.8 
inches  stroke,  weighs  88,250  pounds,  and  has  1420  square  feet  of 
heating-surface  and  16  feet  grate-surface.  The  driving-wheels 
are  52.4  inches  diameter,  and  the  steam-pressure  175  pounds 


s;  A.  T.  Woods.  M.M.E.  :  X.  Y.,  Van  Aisdafe.  1891. 


;  Feb.  i.  1=59. 


2O2 


A    MANUAL   OF   THE   STEAM-ENGINE. 


The  second  engine  is  of  86,200  pounds  weight,  with  16-  and 
23-inch  cylinders,  24  inches  stroke  of  pistons,  tfa  feet  diameter 
of  drivers,  the  pressure  I/O  pounds. 


FIG.  101. — SPANISH  ENGINE. 


The  arrangement  of  both  engines  involves  the  peculiar 
form  of  starting-valve  devised  by  Von  Borries,  which  is  seen 
in  the  next  figure.  In  the  sketch,  a  is  the  receiver-pipe  to  the 


FIG.  ioia.— VON  BORRIES  VALVE. 


high-pressure,  b  that  to  the  low-pressure  cylinder.     The  valve, 
v,  is  seen  as  in  ordinary  working  when  "  under  way,"  and  the 


STRUCTURE   OF   THE  STEEAM-ENGINE. 


203 


arrows  show  the  course  of  the  steam.  Attached  to  the  back 
of  this  valve  are  two  plungers,  c  c,  constituting  the  starting- 
valve.  When  the  throttle-valve  is  opened,  steam  enters  the  pipe 
d,  passing  back  of  the  plungers,  forcing  the  valve  to  its  seat, 
f,  at  the  same  time  opening  the  ports  h  //,  through  which,  and 
the  passage  b,  it  goes  on  to  the  large  cylinder. 

When  the  engine  starts,  the  exhaust  occurs  from  the  small 
cylinder  and  the  receiver-pressure  rises,  this  valve  becomes 
equilibrated,  returns  to  the  position  shown,  and,  once  thus 
started,  the  engine  acts  as  compound,  and  so  continues  until, 
after  shutting  off  steam,  this  equilibrium  is  lost  and  the 
engine  starts  again,  later,  as  a  simple  machine.  This  device 
is  in  extensive  use. 

In  the  Worsdell  form  of 
engine,  Fig.  102,  the  construc- 
tion is  as  seen  in  the  sketch.* 
A  is  the  steam-pipe,  B  the 
starting-valve  connection,  C  the 
receiver,  D  the  exhaust-pipe,  and 
v  and  Fare  the  starting  and  the 
intercepting  valves.  The  engine 
here  taken  for  illustration  is  an 
English  passenger-locomotive, 
having  16-  and  2O-inch  cylinders, 
24  inches  stroke,  drivers  8of 
inches  in  diameter.  The  steam- 
pressure  the  same  as  the  pre- 
ceding, and  the  weight  of  engine 
97,000  pounds,  of  which  68,000 
rests  on  the  driving-wheels. 
The  areas  of  heating  and  grate 
surface  are,  respectively,  1323^ 
and  17^  square  feet.  Joy's 
valve-gear  is  employed. 

The  construction  of  the  valves  is  seen  in  the  next  figure. 
The  flap-valve   is    the   intercepting-valve,  seen  as  in  regular 
*  Engineering;  March  30^  1888. 


•„— THE  WORSDELL  EXCIXE. 


204 


A   MANUAL    OF   THE    STEAM-ENGINE. 


working.  Its  spindle  is  connected  with  the  small  piston  at 
a,  as  shown.  The  starting-valve  is  set  in  a  pipe  or  casing 
connected  with  the  former,  as  seen  in  the  sketch.  A  valve 
held  in  place  by  a  spring  connects  the  pipe  b  with  the  piston  a. 
The  starting-valve  is  worked  by  the  engine-driver,  the  same 
motion  closing  the  intercepting-valve,  and  the  locomotive 
starts  as  a  simple  engine.  The  rise  of  pressure  in  the  receiver 


Valve  C 

fit 

FIG.  103.— PLAN  AND  SECTION,  WORSDELL'S  VALVE. 

presently  restores  the  valves  to  the  position  shown  and  the 
engine  at  once  becomes  compound. 

The  plan,  more  usual  in  marine  engineering,  of  employing 
one  high-pressure  and  two  low-pressure  cylinders  is  illustrated 
in  the  next  sketch,  that  adopted  on  the  Northern  Railway  of 
France.*  In  the  figure,  A  is  the  main  steam-pipe,  B  the  valve- 

*  Engineering;  Dec.  6,  1889. 


STRUCTURE  OF   THE   STEAM-ENGINE.  2O$ 

chest,  C  C  the  receiver,  all  attached  to  the  small  cylinder,  and 
D  D  are  the  two  low-pressure  exhaust-pipes.  The  cylinders, 
h  and  /  /,  are  high-  and  low-pressure,  respectively,  and  the 
whole  plan  is  readily  traced  out.  The  cranks  of  the  latter  are 
set  at  right  angles,  and  the  high-pressure  crank  at  135  degrees 
with  each.  All  are  on  one  shaft,  the  middle  one  of  three 
driving-axles. 

The  high-pressure  valve-gear  is  the  Rider  modification  of  the 
Meyer  system,  permitting  any  desired  expansion  in  the  high- 
pressure  cylinder.  When  thrown  completely  over,  the  cut-off 


FIG.  104.— DIVIDED  L.  P.  CYUXDER. 

valve  permits  the  steam  to  blow  through  the  small  cylinder, 
and  thus  the  engine  is  converted  into  the  common  form, 
the  two  low-pressure  becoming  the  driving-engines. 

This  engine  has  cylinders  of  17  and  19.7  inches  diameter 
and  27.6  inches  stroke,  driving-wheels  (six)  64.9  inches  diame- 
ter. 1225  square  feet  of  heating-surface,  13  feet  grate-surface, 
weighs  106,176  pounds,  of  which  91,000  rests  on  the  drivers, 
and  the  steam-pressure  by  gauge  is  199  pounds. 


206 


A   MANUAL   OF  THE   STEAM-ENGINE. 


The  Mallet  system,  now  much  employed  and  well  known, 
is  exhibited  in  the  next  figure. 


FIG.  105.— THE  MALLET  SYSTEM. 

Here  A  and  B  are  the  steam-pipe*  and  receiver,  and  C  the 
exhaust-pipe.  D  is  a  starting-valve,  taking  steam  through  E, 
and  F  is  the  "  intercepting-valve."  The  pipe  G  serves  to  con- 
vey the  exhaust  from  the  small  cylinder  when  working  non- 
compound.  A  pressure-reducing  valve  is  placed  between 
starting-valve  and  receiver.  When  in  ordinary  operation  as  a 
compound  engine,  the  pressure  of  boiler-steam  keeps  the  in- 
tercepting-valve closed  against  receiver-pressure.  On  starting 
from  rest,  however,  this  valve  is  relieved  and  steam  passes 
over  into  the  low-pressure  cylinder,  the  pair  then  working  as 
simple  engines.  The  engine  can  thus  start  any  load  that  the 
standard  machine  can  take.  Once  started,  this  and  other 
compounds  have  less  hauling  power  than  the  simple  type  ; 
but  no  such  reduction  occurs  as  to  interfere  with  any  ordinary 
work. 


STRUCTURE  OF   THE   STEAM-ENGINE. 


207 


In  all  these  engines,  automatic  relief-valves  are  desirable, 
on  the  large  cylinder  especially,  since  they  must  be  expected 
to  add  to  the  priming  the  water  of  cylinder-condensation  in 
larger  proportion  than  in  cases  of  restricted  ratios  of  expansion. 

The  Webb  system,  as  introduced  on  the  London  and 
Northwestern  Railway  of  Great  Britain  for  both  passenger 
and  heavy  traffic,  is  exhibited  in  the  accompanying  illustra- 
tion. It  precisely  reverses  the  arrangement  last  described, 
there  being  two  high-pressure  and  one  low-pressure  cylinder, 
their  relative  position  being  the  reverse  of  the  preceding. 


FIG.  106. — THE  WEBB  COMPOUND. 

The  pipes  A  A  and  B  B  take  steam  to  the  small  cylinders, 
and  C  and  D  D  convey  the  rejected  steam  to  the  large  cylin- 
der. The  former  are  placed  ahead  of  the  latter  and  are  con- 
nected to  an  independent  axle,  no  coupling  or  parallel  rods 
being  used,  and  the  two  axles  "  keeping  time  "  only  through 
the  automatic  adjustment  produced  by  their  o\vn  operation. 


208  A    MANUAL    OF   THE    STEAM-ENGINE. 

Where  more  than  two  pairs  of  coupled  drivers  are  employed, 
the  added  axles  are  coupled  to  the  small  engines  and  their 
axles  by  means  of  parallel  rods. 

This  engine  has  the  following  dimensions :  diameter  of 
cylinders,  14,  14,  30  in.;  stroke,  24  in.;  wheels,  diameter,  75  in.; 
steam-pressure,  175  Ibs.;  weight,  99,350  Ibs.;  heating-surface, 
1457  sq.  ft.;  grate,  20.55  scl-  ft-  Two  thirds  the  total  weight 
is  on  the  drivers.  The  valve-motion  is  that  of  Joy.  An  en- 
gine of  this  type,  experimentally  tried  between  New  York  and 
Philadelphia,  making  regularly  87  miles  in  2  hours,  with  7  stops, 
and  200  or  225  tons  weight  of  train,  excelled  the  simple  engine 
by  25  per  cent  in  economy  of  fuel-consumption.  The  parallel 
rod  is  always  felt  to  be  a  source  of  danger  and  of  waste  of 
power  in  the  locomotive,  and  this  plan  is  considered  decidedly 
advantageous  in  this  respect.  On  the  other  hand,  the  low- 
pressure  cylinder  produces  a  comparatively  irregular  "  torque  " 
on  the  axle  to  which  it  is  coupled. 

The  Pitkin  system,  as  introduced  by  Mr.  A.  J.  Pitkin  of 
the  Schenectady  Works,  is  seen  in  Fig.  107,  below. 


FIG.  107.— THE  PITKIN  COMPOUND. 


It  includes  one  high- and  one  low-pressure  cylinder,  with  an 
ingenious  intercepting-valve,  seen  in  the  next  illustration. 
The  receiver  has  a  volume  fifty  per  cent  greater  than  that  of 


STRUCTURE   OF   THE   STEAM-ENGINE. 


209 


the  small  cylinder,  and  the  clearance  in  the  latter  is  about  ten 
per  cent,  a  proportion  shown  by  the  indicator  to  be  desirable 
with  the  proportions  of  valves  employed.  The  valves  are  ar- 
ranged and  the  general  disposition  of  parts  is  as  in  the  standard 
engine  of  the  old  form. 

The  intercepting-valve,  as  here  seen  in  section,  is  as  at  the 


FlG.    toS- Pmtix's   IvnERCKFTDCC-VALVK. 


instant  of  starting  and  before  compound  working  begins,  the 
ports  c  and  d  closed  and  no  connection  existing  between  the 
receiver  and  the  large  cylinder ;  while  the  latter  receives  steam 
through  a  reducing- valve  and  the  port  a  and  the  passage  b. 

On  starting,  the  exhaust  from  the  small  cylinder  fills  the 
receiver,  and  the  back-pressure  taking  effect,  through  e,  on 
the  intercepting-valve  and  destroying  its  equilibrium,  it  at 
once  moves  over  and  the  large  cylinder  takes  its  steam  prop- 
erly for  compound  working. 

The  dash-pot,  A,  prevents  too  sudden  movement. 

This  engine  has  the  following  dimensions :  cylinders,  diam- 
eter, 20  and  29  in.;  stroke  of  piston,  24  in.;  ratio  of  cylinders, 
2.1  :  diameter  drivers  (6),  68  in.;  weight  of  engine,  126,800 
Ibs.:  heating-surface,  1677  sq.  ft.;  grate-surface,  28.57  ^ 
About  80  per  cent  of  the  total  weight  is  on  the  drivers. 


2IO 


A  MANUAL    OF   THE   STEAM-ENGINE, 


Mr.  Von  Borries  estimates  a  saving  of  15  per  cent  and 
upward  as  an  offset  to  an  increase  of  first  cost  amounting  to  2 
or  3  per  cent.  He  also  finds  his  engines  to  exceed  the  common 
type  in  hauling  power  by  from  5  per  cent  on  heavy  engines  to 
10  per  cent,  or  more,  in  fast  passenger-service  ;  a  conclusion 
sustained  by  Mr.  Lapage.  The  increased  weight  of  cylinders 
and  accessories,  for  a  given  power,  is  more  than  compensated 
by  the  decreased  weight  of  boiler  required. 

The  compound  locomotive  engine  has  been  sometimes 
found  to  use  as  little  as  22  pounds  (10  kilos)  of  steam  per  hour 
and  per  horse-power ;  which  is  about  two  thirds  or  three  fourths 
the  quantity  demanded  by  similar  engines  uncompounded. 

M.  Mallet  communicated  to  the  French  Society  of  Engi- 
neers (1883)  a  note  from  M.  Borodin,  giving  the  results  of  ex- 
periments to  determine  the  relative  economy  of  the  simple 


FIG   109.— BRITISH  EXPRESS  ENGINE. 

and  the  compound  system  of  engine  for  locomotives.  The  en- 
gines experimented  with  were  those  designed  for  the  railway 
from  Bayonne  to  Biarritz  by  M.  Mallet.  The  trials  extended 
over  a  considerable  period  of  time,  and  the  comparisons  were 
made  fairly  complete.  The  result  showed  the  compound  sys- 
tem to  have  an  economy  of  from  10  to  20  per  cent,  according 
to  the  conditions  under  which  they  are  carried  out.  The  prac- 
ticable variation  in  the  ratio  of  expansion  is  often  very  greatly 
restricted  in  the  compound  engine.  The  use  of  the  steam- 
jackets  with  which  the  engines  were  provided  did  not  prove  to 
be  of  advantage.  The  expenditure  of  steam  was  greater  when 
they  were  in  use  than  when  they  were  shut  off. 


STRUCTURE   OF   THE   STEAM-ENGINE.  211 

Fig.  109  represents  the  type  of  engine  often  adopted  on 
English  roads  for  very  high  speeds  and  with  comparatively 
light  loads.  This  engine  has  regularly  made  200  miles  in  four 
hours,  and  somewhat  similar  engines  have  made  250  miles  in 
five  hours,  and  even  400  miles  in  eight  hours.  The  diameter 
of  the  drivers,  in  this  example,  is  8  feet,  the  steam-cylinder 
1 8  inches,  and  the  stroke  of  piston  28  inches.  This  type  was 
in  use  even  earlier  than  1880;  at  which  date  the  performance 
just  stated  had  been  attained. 

British  engines  of  this  last-described  type  have  done  ex- 
traordinary work.  Such  locomotives  on  the  longer  main  lines, 
between  London  and  Glasgow,  make  an  average  of  50  miles 
an  hour  for  400  miles.  The  Midland  Railway  employs  engines 
with  cylinders  18x26,  a  single  pair  of  drivers  7  feet  4  inches 
diameter;  with  1240  feet  of  heating-surface  and  20  feet  of 
grate,  to  haul  trains  of  225  to  250  tons  weight,  at  nearly  50 
miles  an  hour,  and  with  a  fuel-expenditure  of  26  pounds  per 
mile.  Compound  engines  of  recent  construction  have  wheels 
7f  feet  in  diameter,  and  have  made  nearly  ninety  miles  an  hour. 
One  of  Mr.  Worsdell's  engines  has,  for  illustration,  20  and  28 
by  24  inch  cylinders,  7  feet  7^  inch  drivers  (single  pair),  1 140 
feet  of  heating  and  20  feet  of  grate,  and  has  attained  an  aver- 
age of  over  50  miles  an  hour  on  26.4  pounds  of  coal  per  mile  ; 
the  train,  engine  included,  weighing  something  over  300  tons. 
The  steam-pressure  carried  is  175  pounds. 

41.  The  Marine  Engine,  on  the  rivers  of  the  United 
States,  remains  largely  as  it  was  left  by  the  earlier  engines.  It 
is  a  beam-engine,  of  moderate  steam-pressure,  driving  the 
radial  paddle-wheel :  the  details  are  little,  if  at  all,  altered. 
The  pressure  of  steam  is  now  sometimes  as  high  as  60  pounds 
per  square  inch  or  even  more.  The  valves  are  of  the  disk  or 
poppet  variety,  rising  and  falling  vertically.  They  are  four  in 
number,  two  steam  and  two  exhaust  valves  being  placed  at 
each  end  of  the  steam-cylinder.  The  beam-engine  is  a  pecu- 
liarly American  type,  seldom  if  ever  seen  abroad. 

Fig.  1 10  is  an  outline  sketch  of  this  engine  as  built  for  a 
steamer  plying  on  the  Hudson  River.  This  class  of  engine  is 


212 


A  MANUAL   OF   THE   STEAM-ENGINE. 


usually  adopted  in  vessels  of  great  length,  light  draught,  and 
high  speed.  But  one  steam-cylinder  is  commonly  used.  The 
cross-head  is  coupled  to  one  end  of  the  beam  by  means  of  a 
pair  of  links,  and  the  motion  of  the  opposite  end  of  the  beam 
is  transmitted  to  the  crank  by  a  connecting-rod  of  moderate 


1J. 


-irrvr 


Via 


ill 


FIG.  no.  — 


EAM-ENGINE. 


length.  The  beam  has  a  cast-iron  centre  surrounded  by  a 
wrought-iron  strap  of  lozenge  shape,  in  which  are  forged  the 
bosses  for  the  end-centres,  or  for  the  pins  to  which  the  con- 
necting-rod and  the  links  are  attached.  The  main  centre  of 
the  beam  is  supported  by  a  "  gallows-frame"  of  timbers  so  ar- 
ranged as  to  receive  all  stresses  longitudinally.  The  crank  and 
shaft  are  of  wrought  iron.  The  valve-gear  is  very  usually  of 


STRUCTURE  OF   THE   STEAM-EXCISE.  21$ 

the  form  known  as  the  Stevens  valve-gear,  the  invention  of 
Robert  L.  and  Francis  B.  Stevens.  The  condenser  is  placed 
immediately  beneath  the  steam-cylinder.  The  air-pump  is 
placed  close  beside  it,  and  worked  by  a  rod  attached  to  the 
beam.  Steam-vessels  on  the  Hudson  River  have  been  driven 
by  such  engines  at  the  rate  of  20  miles  an  hour.  This  form  of 
engine  is  remarkable  for  its  smoothness  of  operation,  its 
economy  and  durability,  its  compactness,  and  the  latitude 
which  it  permits  in  the  change  of  shape  of  the  long,  flexible 
vessels  in  which  it  is  generally  used,  without  injury  by  "  getting 
out  of  line." 

For  paddle-engines  of  large  vessels,  the  favorite  type,  which 
has  been  the  side-lever  engine,  is  now  rarely  built.  For  smaller 
vessels,  the  oscillating  engine  with  feathering  paddle-wheels  is 
still  largely  employed  in  Europe.  It  is  very  compact,  light,  and 
moderately  economical,  and  excels  in  simplicity.  The  usual  ar- 
rangement is  such  that  the  feathering-wheel  has  the  same 
action  upon  the  water  as  a  radial  wheel  of  double  diameter. 
This  reduction  of  the  diameter  of  the  wheel,  while  retaining 
maximum  effectiveness,  permits  a  high  speed  of  engine,  and 
therefore  less  weight,  volume,  and  cost.  The  smaller  wheel- 
boxes,  by  offering  less  resistance  to  the  wind,  retard  the  prog- 
ress of  the  vessel  less  than  those  of  radial  wheels.  Inclined  en- 
gines are  sometimes  used  for  driving  paddle-wheels.  In  these 
the  steam-cylinder  lies  in  an  inclined  position,  and  its  connect- 
ing-rod directly  connects  the  crank  with  the  cross-head.  The 
condenser  and  air-pump  usually  lie  beneath  the  cross-head 
guides,  and  are  worked  by  a  bell-crank  driven  by  links  on  each 
side  the  connecting-rod,  attached  to  the  cross-head.  Such  en- 
gines are  used  to  some  extent  in  Europe,  and  they  have  been 
adopted  in  the  United  States  navy  for  side-wheel  gunboats. 
They  have  also  been  used  on  ferry-boats  plying  between  New 
York  and  Brooklyn. 

The  non-condensing  direct-acting  engine  is  used  principally 
on  the  Western  rivers  of  the  United  States,  is  driven  by  steam 
of  from  100  to  150  pounds  pressure,  and  exhausts  into  the  at- 
mosphere. It  is  the  simplest  possible  form  of  direct-acting  en- 


214 


A  MANUAL    OF   THE   STEAM-ENGINE. 


gine.  The  valves  are  usually  of  the  "  poppet  "  variety,  and  are 
operated  by  cams  which  act  at  the  ends  of  long  levers  having 
their  fulcra  on  the  opposite  side  of  the  valve,  the  stem  of  which 
latter  is  attached  at  an  intermediate  point.  The  engine  is  hori- 


FIG.  ni.-S 


zontal,  and  the  connecting-rod  directly  attached  to  cross-head 
and  crank-pin  without  intermediate  mechanism.  The  paddle- 
wheel  is  used,  sometimes  as  a  stern-wheel,  as  in  the  plan  of 
Jonathan  Hulls  of  1737,  sometimes  as  a  side-wheel,  as  is  most 
usual  elsewhere. 


STRUCTURE   OF   THE   STEAM-ENGINE.  21$ 

Special  designs  of  marine  engine  are  sometimes  found  de- 
sirable for  small  powers.  That  here  illustrated,  for  example, 
as  designed  by  Shipman,  is  very  similar  in  general  arrangement 
to  some  forms  of  semi-portable  engine,  the  engine  and  boiler 
having  a  common  base.  Larger  sizes,  however,  are  separated. 
The  boiler  is  water-tubular,  of  the  general  form  of  that  first 
used  by  Stevens.  The  engine,  either  simple  or  compound,  is 
vertical  and  of  the  usual  standard  type,  with  link-motion,  when 
used  as  a  yacht-engine,  and  having  a  reverse-lever. 

The  essential  feature  of  this  motor  is  that  it  is  an  auto- 
matic petroleum-burning  engine,  designed  for  use  where  a 
moderate  amount  of  power  is  required.  When  steam  has  been 
generated,  no  further  attention  is  required  beyond  that  of  open- 
ing and  shutting  the  steam-valve  whenever  the  engine  is  started 
or  stopped,  the  fire,  speed,  and  water-feed  being  arranged  as  to 
adjust  themselves  automatically. 

Two  small  aspirators  or  atomizers,  taking  steam  from  the 
boiler,  take  up  the  petroleum  fuel,  from  a  chamber  below,  and 
drive  it  into  the  furnaces  in  fine  spray.  Torches  ignite  this 
spray  as  it  passes  inward.  The  steam  and  petroleum  supply 
of  the  atomizers  is  regulated  by  a  diaphragm  connected  to  a 
valve  in  the  steam-pipe. 

This  diaphragm  is  exposed  to  steam-pressure  on  the  one 
side,  and  is  held  down  by  a  spring,  loaded  to  a  certain  pressure, 
on  the  other.  Its  movement  is  conveyed  to  the  valve  by  a  rod, 
and  it  thus  regulates  the  amount  of  steam  passing  to  the  atom- 
izers. 

The  water  in  the  boiler  is  kept  at  a  constant  level  by  means 
of  a  float,  connected  to  a  tap  in  the  suction-pipe  of  the  pump. 
This  float  is  placed  in  a  chamber  which  is  joined  to  the  top  and 
bottom  of  the  boiler,  and  rises  or  falls  with  the  level  of  the 
water.  The  movement  is  conveyed,  by  means  of  levers,  to  the 
tap  in  the  suction-pipe,  which  it  opens  or  closes  as  the  water- 
level  changes. 

The  speed  of  the  engine  is  regulated  by  means  of  a  gov- 
ernor. When  once  steam  is  up,  the  fires,  the  water-supply,  the 
oiling,  and  the  speed  of  the  engine  require  no  further  attention. 


216 


A  MANUAL    OF    THE   STEAM-ENGINE. 


When  first  starting,  a  sufficient  pressure  is  required  in  the  boiler 
to  work  the  atomizers,  and  for  this  a  hand  air-pump  is  pro- 
vided. 

In  vessels,  in  nearly  all  cases,  the  ordinary  screw-engine  is 
adopted,  and  is  direct-acting.  Two  engines  are  placed  side  by 
side,  with  cranks  on  the  shaft  at  an  angle  of  90°  with  each 
other.  In  merchant-steamers,  the  steam-cylinders  are  usually 


FIG.  i  ia. — COMPOUND  MARINE  ENGINE. 

vertical  and  directly  over  the  crank-pins,  to  which  the  cross- 
heads  are  coupled.  The  condenser  is  placed  behind  the  engine- 
frame,  or,  where  a  jet-condenser  is  used,  the  frame  itself  is 
sometimes  made  hollow,  and  serves  as  a  condenser.  The  air- 
pump  is  worked  by  a  beam  connected  by  links  with  the  cross- 
head.  The  general  arrangement  is  like  that  shown  in  Fig.  112. 
For  naval  purposes  such  a  form  is  objectionable,  since  its  height 
is  so  great  that  it  would  be  exposed  to  injury  by  shot.  In  naval 
engineering  the  cylinder  is  placed  horizontally. 


STRUCTURE  OF   THE   STEAM-ENGINE.  21 7 

The  trunk-engine,  in  which  the  connecting-rod  is  attached 
directly  to  the  piston  and  vibrates  within  a  trunk  or  cylinder 
secured  to  the  piston,  moving  with  it,  and  extending  outside 
the  cylinder,  like  an  immense  hollow  piston-rod,  has  been  fre- 
quently used  in  the  British  navy.  It  has  rarely  been  adopted 
in  the  United  States. 

42.  Standard  Forms  of  marine  engines,  in  nearly  all 
steam-vessels  built  for  the  merchant-service,  and  in  some  naval 
vessels,  have  come  to  be  some  modification  of  the  compound 
engine.  Figs.  112  and  113  represent  the  usual  form  of  the 
two-cyHnder  compound  engine.  Here  A  A,  B  B  are  the  small 
and  the  large,  or  the  high-pressure  and  the  low-pressure, 
cylinders  respectively.  C  C  are  the  valve-chests.  G  G  is  the 


^!I_. 


FIG.  nj.— COWPOCXB  MARTVI  Fxcrv*  (SECTTOK). 

condenser,  which  is  invariably  a  surface-condenser.  The  con- 
densing water  is  sometimes  directed  around  the  tubes  con- 
tained within  the  casing,  G  G,  while  the  steam  is  exhausted 
around  them  and  among  them,  and  sometimes  the  steam  is 
condensed  within  the  tubes,  while  the  injection-water  which  is 
sent  into  the  condenser  to  produce  condensation  passes  around 


2l8  A   MANUAL   OF    THE   STEAM-ENGINE. 

the  exterior  of  the  tubes.  In  either  case,  the  tubes  are  usually 
of  small  diameter,  varying  from  five  eighths  to  half  an  inch, 
and  in  length  from  four  to  seven  feet.  The  extent  of  heating- 
surface  is  usually  from  one  half  to  three  fourths  that  of  the 
heating-surface  of  the  boilers. 

The  air  and  circulating  pumps  are  placed  on  the  lower  part 
of  the  condenser-casting,  and  are  operated  by  a  crank  on  the 
main  shaft  at  N\  or  they  are  sometimes  placed  as  in  the  style 
of  engine  last  described,  and  driven  by  a  beam  worked  by  the 
cross-head.  The  piston-rods,  T  S,  are  guided  by  the  cross- 
heads,  V  V,  working  in  slipper-guides,  and  to  these  cross-heads 
are  attached  the  connecting-rods,  XX,  driving  the  cranks,  M 
M.  The  cranks  are  now  usually  set  at  right-angles  ;  in  some 
engines  this  angle  is  increased  to  120°,  or  even  180°.  Where 
it  is  arranged  as  here  shown,  an  intermediate  reservoir,  P  O,  is 
placed  between  the  two  cylinders  to  prevent  the  excessive 
variations  of  pressure  that  would  otherwise  accompany  the 
varying  relative  motions  of  the  pistons,  as  the  steam  passes 
from  the  high-pressure  to  the  low-pressure  cylinder.  Steam 
from  the  boilers  enters  the  high-pressure  steam-chest,  X,  and 
is  admitted  by  the  steam-valve  alternately  above  and  below 
the  piston  as  usual.  The  exhaust  steam  is  conducted  through 
the  exhaust  passage  around  into  the  reservoir,  P,  whence  it  is 
taken  by  the  low-pressure  cylinder,  precisely  as  the  smaller 
cylinder  drew  its  steam  from  the  boiler.  From  the  large  or 
low-pressure  cylinder  the  steam  is  exhausted  into  the  con- 
denser. The  valve-gear  is  usually  a  Stephenson  link,  ge,  the 
position  of  which  is  determined,  and  the  reversal  of  which  is 
accomplished,  by  a  hand-wheel,  o,  and  screw,  m  np,  which,  by 
the  bell-crank,  k  i,  are  attached  to  the  link,  ^v.  The  "box- 
framing"  forms  also  the  hot-well.  The  surface-condenser  is 
cleared  by  a  single-acting  air-pump,  inside  the  frame,  at  T. 
The  feed-pump  and  the  bilge-pumps  are  driven  from  the  cross- 
head  of  the  air-pump. 

The  "tandem  compound"  marine  engine,  Fig.  114,  is  a 
simpler  and  less  expensive  construction,  but  it  is  so  subject  to 
uncertainty  in  starting  and  so  liable  to  become  fixed  "on  the 


STRUCTURE   OF   THE   STEAM-EXGINE. 


2I9 


centre,"  that  if  adopted  at  all  for  marine  work,  it  is  very  gener- 
ally duplicated,  the  two  engines  having  cranks  at  right  angles, 
and  thus  its  special  advantage  sacrificed.  Such  a  combination 
is,  however,  excellent  as  a  "  quadruple-expansion  "  engine,  the 
second  set  of  steam-cylinders  taking  steam  from  the  first,  and 


FK_  TT« — TAXOTEW  Cowocsro  ETQME.    (Scale  £.) 

a  pair  of  two-cylinder  compound  engines  of  different  size  being 
thus  grouped  to  give  four  cylinders  "  in  series." 

The  latest  types  of  Marine  Engine  are  those  compounded 
engines  in  which  the  number  of  engines  in  series  is  three,  or 
even  more,  usually  driving  three  equidistant  cranks,  and  those 
which  are  designed  to  drive  two,  or  even  three,  screws  inde- 
pendently. In  the  extension  of  the  principle  of  compounding 


220 


A    MANUAL    OF    THE    STEAM-ENGINE. 


in  multiple-cylinder  engines,  it  is  probably  desirable  to  restrict 
the  number  of  cranks  to  three,  even  with  a  pair  of  low-pressure 
cylinders,  or  in  the  quadruple-expansion  engine  ;  both  as  a  mat- 
ter of  economy  and  to  secure  smooth-working  with  minimum 


FIG.  115. — TRIPLE-EXPANSION  ENGINE. 

friction.     The  balance   is  usually  practically  perfect  and  the 
full  advantage  of  compounding  is  attained. 

In  these  cases  the  construction  of  all  the  engines  which 
constitute  an  element  of  the  compounded  machine  is  commonly 
substantially  the  same  in  general,  the  differences  being  prin- 


STRUCTURE   OF    THE   STEAM-ENGINE. 


221 


cipally  in  the  proportions  of  the  steam-cylinder  and  its  acces- 
sories. The  triple-expansion  engine  thus  usually  consists,  as  a 
whole,  of  three  similar  simple  engines,  side  by  side,  so  ar- 


ranged, as  to  size  of  cylinder  and  disposition  of  pipes  and 
valves,  that  they  work  as  a  series  in  taking  and  exhausting 
steam.  There  are,  however,  a  number  of  successful  arrange- 


222  A    MANUAL   OF   THE   STEAM-ENGINE. 

ments  of  three-  and  of  four-cylinder  engines  driving  but  two 
cranks  and  in  which  the  "  tandem  "  disposition  of  cylinders  is 
adopted  with  good  results. 

The  engraving  represents  one  set  of  the  triple-expansion 
engines  of  the  twin-screw  sister-ships,  the  City  of  Paris  and  the 
City  of  New  York.  Their  general  arrangement  is  well  shown. 
Each  set  drives  one  screw.  The  magnitude  of  these  great 
engines  is  indicated  by  the  altitude  of  the  working  platforms 
and  the  reversing  wheel.  This  may  be  taken  to  represent  a 
standard  and  very  satisfactory  disposition  of  parts  and  general 
proportion  of  engines. 

A  good  sample  set  of  figures  for  the  proportions  and  per- 
formance of  these  engines  are  : 

Steam-cylinders,  diameter,  inches  .........  45,  71,  113 

Stroke  of  pistons,  feet  ...........................  5 

Ratios  of  volumes.  .  .  I  ;  2.489;  6.304  01-0.402  ;  i  ;  2.53 
Steam-pressure,  per  gauge,  Ibs  ..................  148 

Rev.  per  min  ...................  .  ...............  87 

Vacuum,  inches  .........................    .......  26 

Mean  pressures,  Ibs  .....................  64  ;  32  ;   14 

Indicated  power,  H.  P  .......................  1  9,  1  75 

Temp,  feed-water,  Fahr  .........  .  .............  1  19° 

"        sea-water  ........................  54° 

Area  H.  S.,  sq.  ft  ...........................  50,250 

"     G.  S.,    "    "  ...........................  i  ,294 

"     cond.  surf  .............................  33,ooo 

I.  H.  P.  per  sq.   ft.  G.  S  .......................  14.8 


H-s 


"      "      "   condens.  surface.  .  .  .  --  =  0.58 

Ratio  H.  S.  to  G.  S  ...........................  38.8 

"      "    C.S  ...........................  1.52 

These  figures  are  given  by  the  engineer  officers  of  the  ship 
for  a  passage  across  the  Atlantic  made  in  5  days,  19  hours,  34 


STRUCTURE  OF  THE  STEAM-ENGlffE.  22$ 

minutes,  at  its  date  the  quickest    on  record.     One  day's  run 
was  311  sea-miles,* 

The  arrangement  of  these  engines  in  twin-screw  steamers  is 
seen  in  the  next  figure,  which  exhibits  the  machinery  of  the 
steamer  Columbia  of  the  Hamburg-American  Line,  a  ship 


?K»  07.— TOTUB-I  1 1 1  mmm 

of  12,000  tons  displacement  and  about  15,000  horse-power: 
each  set  of  triple-expansion  engines,  as  shown,  having  half  that 
power.  The  cylinders  are  40.  66.  and  101  inches  diameter, 
and  the  stroke  of  piston  66  inches.  The  shafts  are  of  steel.  2oi 
inches  diameter,  driving  screws  of  manganese  bronze  18  feet 
diameter  and  of  32  feet  pitch.  These  engines  have  driven  the 

*  Am.  Machinist;  Feb.  12,  iSgi. 


224 


A    MANUAL    OF   THE    STEAM-ENGINE. 


Columbia  3045  knots — New  York  to  Southampton — in  6  days, 
15  hours,  or  19.15  knots  per  hour. 


FlG.     Il8.  —  QUADRUPLH-EXI'ANSION     ENGINE.  —  FlG. 


An  illustration  of  a  standard  type  of  quadruple-expansion 
marine  engine  is  seen  in  the  section  herewith  given.     This  is  a 


STRUCTURE  OF   Tff£  STEAM-E&GIA'E.  22$ 

Scotch  engine  of  550  horse-power,  cylinders  loj.  14,  and  20 
inches  diameter,  and  20  inches  stroke  off  piston.  Only  the 
low-pressure  cylinder  is  jacketed.  The  cranks  being  set  at 
right  angles,  the  two  pairs  off  pistons  have  not  synchronous  mo- 
tion, and  a  receiver  or  large  connecting  pipes  most  be  adopted 
in  this  arrangement  to  insure  good  pressure-changes  between 
tile  second  and  third  cylinders. 

The  most  extraordinary  concentration  off  steam-power  is 
illustrated  in  the  more  recent  constructions  off  torpedo-boats. 
These  little  craft  are  given  the  lightest  possible  hulk,  fine  lines, 
unencumbered  decks,  and  maximum  power,  everything  being 
made  subordinate  to  speed.  That  here  figured,  the  Aviete 
(page  226),  a  Thoraeycroft  boat  built  for  the  Spanish  Govern- 
ment, has  made  26  knots  an  hour  (over  30  statute  miles). 
The  hull  is  but  147^  feet  long,  off  14^  feet  beam,  and  5  feet 
draught,  or  but  a  trifle  longer  than  Fulton's  dermont.  Speeds 
exceeding  20  knots  are  common  with  this  dass  of  boat. 
This  type  of  boat  has  been  given  as  much  as  1600  indicated 
horse-power,  steam  being  worked  at  150  pounds  pressure  in 
water-tubular  boilers,  driving  a  hull  displacing  100  tons,,  at 
speeds  off  from  25  to  26  knots.  The  coal  consumed  at  stand- 
ard half-speed— 10  knots— is  about  ft  tons  as  a  minimmp. 
Twin-screws  are  used.  On  long  runs  these,  the  M  measured- 
mile  trial,'*  results  are  not  usually  approached  very  doseh/- 
In  this  work,  the  water-tube  boiler  is.  in  many  cases,  substi- 
tuted for  the  ordinary  ~  shell "  fire-tube  form  with  good  re- 
salts.  The  coal-consumption  ranges  not  far  from  2  pounds 
per  I.  H.  P.  per  hour  in  good  work. 

The  naval  engine  of  recent  times  is  distinguished  by  a 
combination  of  strength,  lightness,  compactness,  and  power, 
which  makes  it  the  most  remarkable  of  all  the  achievements  of 
modern  engineers  and  mechanics.  This  is  exemplified  by  the 
later  engines  built  for  boats  of  the  class  here  illustrated.  The 
triple-compound  engine  has  cylinders  14.  20,  and  31^  inches 
diameter,  16  inches  stroke,  and  taking  steam,  at  200  pounds 
pressure,  from  water-tube  boilers  rated  at  1300  horse-power, 
and  sometimes  actually  exceeding  that  figure.  ~  White  metal "" 


226 


A   MANUAL   OF    THE   STEAM-ENGINE. 


STRUCTURE   OF   THE   STEAM-ENGINE.  227 

is  used  in  all  bearings,  and  both  oil  and  water  are  supplied  to  all 
especially  important  journals.  The  low-pressure  valve  is  bal- 
anced by  an  adjustable  arrangement,  and  the  piston-rings  are 
made  of  an  alloy  requiring  no  lubrication,  thus  securing, 
among  other  advantages,  a  better  action  of  the  condenser. 
The  frames  and  all  parts  not  necessarily  cast  are  of  forged  steel. 

General  experience,  in  brief,  indicates  the  compound  engine 
as  customarily  employed  to  exhibit  an  increase  in  economy 
over  the  simple  engine  which  it  displaced  amounting  to  about 
30  per  cent,  and  a  superiority  of  20  or  25  per  cent  of  the  triple- 
expansion  engine,  with  steam  at  140-160  pounds,  over  the 
compound  at  90-100 ;  while  the  latter  has  not  been  found  to 
show  much  advantage  with  increasing  pressures.  The  reasons 
for  the  facts  are  readily  seen  on  studying,  as  elsewhere,  the 
theory  of  the  engine.  Similarly  the  quadruple-expansion  en- 
gine exhibits  superiority,  in  less  degree,  at  200  pounds,  over 
the  triple-expansion. 

The  three-crank  engine  also  is  found  to  possess  advantages 
over  the  two-crank,  in  efficiency  of  mechanism  and  smoothness 
of  operation,  and  to  demand,  often,  even  less  repair.  With 
similar  size  of  low-pressure  cylinder,  this  form  of  triple-expan- 
sion engine  may  give  considerably  greater  power  than  the  com- 
pound, with  less  serious  stresses  on  the  working  parts ;  and 
this  difference,  again,  makes  it  practicable  to  build  the  former 
at  as  small  cost  as  the  latter,  when  of  equal  power. 

The  latest  type  of  river  and  sound  steamers  is  illustrated 
by  the  Plymouth  of  the  Fall  River  Line  between  New  York 
and  New  England,  traversing  Long  Island  Sound. 

The  dimensions  of  the  Plymouth  are  as  follows : 

Feet.  Inches. 

Length  overall..... 366 

Length  on  water-line , 351       S 

Breadth  over  guards 87 

Breadth  of  boll 50 

Depth  at  lowest  point  of  sheer 21 

Draught  of  water,  light II 

Distance  from  keel  to  topmast-head  119 

Distance  from  keel  to  dome-deck 55       3 

Distance  from  keel  to  top  of  boose  on  dome 59       3 


228  A    MANUAL    OF   THE    STEAM-ENGINE, 


STKUCTUKE  OF   THE  STEAlf-EXGIXE.  22O, 

The  ship  is  constructed  on  the  double  hull,  bracket  plate 
and  longitudinal  system,  securing  safety  for  the  ship  as  regards 
either  sinking  or  destruction  by  fire.  The  designers  and  con- 
structors were  the  same  as  of  the  Puritan,  previously  described. 

The  Plymouth  is  fitted  with  a  four-cylinder,  double-in- 
clined, triple-expansion,  direct-acting  engine  of  5500  indicated 
horse-power.  The  high-pressure  cylinder.  47  inches  diameter, 
takes  steam  at  a  pressure  of  160  pounds  per  square  inch.  The 
intermediate  cylinder  is  75  inches  in  diameter.  The  high- 
pressure  and  intermediate  cylinders  are  placed  forward  of  the 
centre  of  the  shaft,  and  are  connected  to  crank-pins,  placed  at 
right-angles.  Abaft  the  shaft  are  two  low-pressure  cylinders, 
each  8i£  inches  in  diameter.  One  low-pressure  is  connected 
to  the  same  crank-pin  as  the  high-pressure  cylinder,  and  the 
other  to  the  same  crank-pin  as  the  intermediate  cylinder.  All 
pistons  have  a  stroke  of  &  feet  3  inches.  Each  of  the  two  low- 
pressure  cylinders  is  supplied  with  its  own  air-pump  and  sur- 
face-condenser, with  independent  centrifugal  circulating  pump. 
The  high-pressure  cylinder  alone  has  an  adjustable  drop  cut- 
off. On  all  the  other  cylinders  the  cut-off  is  fixed. 

The  engine  keelsons  and  frames  are  made  of  steel,  strength- 
ened in  the  usual  manner  with  angles  and  intercostals.  The 
wheels  are  of  the  feathering  type,  30  feet  diameter  outside  the 
buckets.  Each  wheel  has  12  curved  steel  buckets,  each  being 
4  feet  wide  and  13  feet  3  inches  long. 

43.  Adaptation  of  Structure  to  economical  requirements 
is  evidently  one  of  the  essential  elements  of  successful  appli- 
cation of  the  steam-engine  to  best  advantage.  As  will  be 
shown  elsewhere,  for  every  pressure  and  every  engine  there  is 
always  a  certain  best  ratio  of  expansion,  all  things  considered; 
and  the  proper  number  of  steam-cylinders  in  series  in  the 
multiple-cylinder  engine  is  fixed  by  the  steam-pressure  adopted. 
It  thus  happens  that,  as  pressures  have  risen,  the  compound 
engine  has  displaced  the  simple  engine,  at  sea,  and  the  **  triple- 
expansion"  engine  has,  at  pressures  exceeding  about  ten  atmos- 
pheres (135  Ibs.  by  gauge)  begun  to  displace  the  older  double- 
cyiinder  compound  engine ;  and  even  the  "*  quadruple-expan- 


230 


A    MANUAL    OF   THE    STEAM-ENGINE. 


sion"  engine,  with  its  four  cylinders  in  series,  has  been  adopted 
for  pressures  considerably  exceeding  the  latter. 

The  structure  of  these  engines  is  essentially  similar  to  that 


FIG.  122.— BAILEY-FKIEDRICH  MOTOR. 


of  the  older  compound,  the  high-pressure  cylinder  of  the 
latter  becoming,  in  turn,  an  intermediate  cylinder.  These 
forms  will  be  described  more  fully  later. 


STRUCTURE   OF   THE   STEAM-ENGINE.  231 

In  illustration  of  the  above :  The  "  domestic"  or  other 
small  motors  are  often  given  peculiar  and  ingenious  forms  to 
secure  automatic  operat-on  and  relief  from  cost  of  attendance. 

The  Friedrich  Motor  is  a  combined  engine  and  boiler 
The  engine  is  a  high-expansion  engine,  fitted  with  a  governor 
determining  the  amount  of  expansion  automatically,  accord- 
ing  to  the  work. 

A  surface-condenser  condenses  the  exhaust  steam,  and  a 
feed-pump  returns  it  to  the  boiler.  Thus  the  water  is  used 
over  and  over  again,  and  no  incrustation  takes  place  in  the 
boiler. 

It  is  stated  that  a  four-horse  engine  of  this  kind  requires 
about  135  pounds  of  coke  in  six  hours. 

The  boiler  generates  its  steam  mainly  in  tubes  suspended 
in  a  furnace  extending  the  full  width  and  length  of  the  boiler. 
The  boiler-top  consists  partly  of  the  lower  part  of  the  engine- 
frame,  which  there  forms  a  steam-dome,  with  the  steam-cylin- 
der suspended  in  it,  and  the  remainder  is  a  plate  which  is 
readily  removed  for  access  to  the  interior  for  inspection  and 
cleaning. 

The  furnace  is  fitted  with  a  fuel-hopper  or  magazine,  and 
above  this  is  an  air-valve  acted  upon  automatically  by  the 
steam,  in  such  a  manner  as  to  lift  it  and  pass  air  over  the  fire 
whenever  the  generation  of  steam  is  too  rapid  and  the  pressure 
too  high,  thus  regulating  the  consumption  of  the  fuel  according 
to  the  demand.  The  whole  is  mounted  upon  a  base-plate, 
fitted  below  the  fireplace  with  an  ash-pan,  as  seen,  charged  with 
water  to  keep  the  floor  cool  and  preserve  the  grate-bars. 

44.  Special  Types  of  steam-engine  are  occasionally  used 
experimentally  and  temporarily,  or  are  permanently  employed 
where  found  to  be  specially  adapted  to  some  peculiar  purpose. 
Thus  the  single-acting  engine  has  been  found  to  have  its 
own  special  field  ;  the  Cornish  engine  was  long  used  exclu- 
sively for  a  mine-pump ;  the  rotary  engine  finds  its  place,  and 
even  a  steam-turbine  is  successfully  applied  to  driving  machin- 
ery in  which  an  enormous  speed  of  rotation  is  demanded. 
The  superiority  of  a  rotary  motion  for  a  steam-engine  is  ap- 


232  A  MANUAL   OF   THE   STEAM-ENGINE. 

patently  so  evident  that  many  attempts  have  been  made  to 
overcome  the  practical  difficulties  to  which  it  is  subject.  One 
of  these  difficulties,  and  the  principal  one,  has  been  the  pack- 
ing of  the  part  which  performs  the  office  of  the  piston  in  the 
straight  cylinder.  The  often  claimed  advantages  of  the 
rotary  engine  are  the  reduction  in  the  size  of  the  engine, 
claimed  to  result  from  the  great  velocity  of  rotation ;  the 
avoidance  of  great  accidental  strains,  especially  noticed  in 
propelling  ships  ;  and  a  great  saving  of  the  power  which  is, 
erroneously,  asserted  to  be  expended  in  the  reciprocating 
engine  in  overcoming  the  inertia  while  changing  the  direction 
of  the  motions.  These  advantages,  so  far  as  they  exist,  adapt 
the  rotary  engine,  in  an  especial  manner,  to  the  purposes  of 
steam  fire-engines. 

In  the  Holly  steam  fire-engine,  seen  in  Fig.  125,  eccentrics 
and  sliding-cams,  which  are  frequently  used  in  rotary  engines, 
are  avoided.  Corrugated  pistons,  or  irregular  cams,  are 
adopted,  forming  chambers  within  the  cases.  In  the  engine 
the  steam  enters  at  the  bottom  of  the  case,  and  presses  the 
cams  apart.  The  only  packing  used  is  in  the  ends  of  the  long 
metal  cogs,  which  are  ground  to  fit  the  case  and  are  kept 
out  by  the  momentum  of  the  cams,  assisted  by  a  slight 
spring  back  of  the  packing-pieces.  The  friction  on  the  pump, 
Fig.  124,  is  said  to  be  less  than  in  the  engine.  This  is  the 
reason  given  in  support  of  the  claim  that  the  rotary  engine 
forces  water  to  a  given  distance  with  less  steam-pressure 
than  is  necessary  to  drive  reciprocating  engines.  The  smaller 
amount  of  power  necessary  to  do  the  work,  the  less  strain  and 
consequent  wear  and  tear  upon  the  whole  machine,  are  said  to 
make  it  durable  and  reliable.  The  pump  being  chambered, 
its  liability  to  injury  by  the  use  of  dirty  or  gritty  water  is 
lessened  ;  and  it  is  stated  that  it  will  last  for  years,  pumping 
gritty  water  that  would  soon  cut  out  a  piston-pump. 

This  engine  contains  two  rotating  cams,  each  of  which  is 
also  a  gear  having  eight  short  teeth,  arranged  in  pairs,  with 
one  long  tooth  and  one  deep  space  between.  The  short  teeth 
are  for  the  purpose  of  insuring  that  the  two  cams  rotate 


STRUCTURE   OF   THE   STEAM-EXGIXE. 


233 


exactly   together.      The   long   teeth   are   abutments   for  the 
steam,  forming,  as  they  do,  steam-tight  joints  with  the  walls 


FIG.  rrj. — ROTARY  E.VCT.VB. 

of  the  case  in  which  they  rotate,  and  with  the  deep  spaces  in 
which  they  engage.  The  steam  entering  at  the  bottom  of  the 
case  tends  to  press  the  abutments  apart  and  thus  cause 
rotation  of  the  pistons  in  opposite  directions.  The  tightness 
of  the  joints  of  the  teeth  with  the  case  is  insured  by  packing- 
pieces  set  out  by  springs.  The  steam  is  discharged  at  the 


FTC.   \*4.—  ROTA«T  PCMF. 

top  of  the  case.  The  heads  of  the  cams  are  turned  to  fit  the 
flat  ends  of  the  case,  which  are  provided  with  recesses  for 
lubricant. 


234 


A   MANUAL   OF   THE   STEAM-ENGINE. 


STRUCTURE   OF   THE   STEAM-ENGI\E, 


235 


In  the  construction  of  the  pump  three  long  teeth  are 
introduced  to  each  cam,  and  fewer  guide-teeth.  The  water 
enters  at  the  bottom  of  the  case,  and  is  discharged  at  the  top. 


The  revolution  of  the  pump-pistons  in  opposite  directions 
causes  a  vacuum  in  the  case,  and  the  water  is  caught  by  the 
abutments  and  swept  out  of  the  case.  The  greater  number 
of  teeth  is  given  in  order  to  insure  greater  steadiness  of 
stream  than  would  be  given  by  only  two  long  teeth  upon  each 
piston. 


236  A    MANUAL    OF    THE   STEAM-ENGINE. 

The  motion  being  continuous  and  the  connections  tight, 
the  stream  is  unintermittent.  The  journals  of  the  engine  and 
pump  run  in  long  bearings.  There  are  suitable  stuffing-boxes 
to  insure  steam  and  water-tight  joints  for  the  shafts.  The 
certainty  of  rotation  of  the  cams  is  further  insured  by  well- 
cut  gear-wheels  on  the  shafts  outside  the  steam  and  water 
cases. 

The  steam-cams  are  given  greater  diameter  than  those  for 
the  water,  to  permit  a  greater  water-pressure  to  be  maintained  ; 
the  steadiness  of  this  water-pressure  is  further  insured  by  an 
air-chamber.  Engines  of  this  class  have  now  been  in  use 
many  years. 

A  singular  device,  but  one  found  effective  for  very  low 
lifts,  is  illustrated  in  Fig.  126,  as  built  by  Allis  for  the  city  of 
Chicago,  111.  A  vertical  engine  of  economical  type,  and 
designed  for  a  somewhat  high  speed  of  rotation,  is  connected 
to  the  shaft  of  a  screw-propeller  of  suitable  dimensions  and 
proportions,  but  differing  from  the  marine  screw  in  the  greater 
area  of  its  blades.  This  raises  water  from  a  low  level  on 
the  one  side  to  a  higher  level  on  the  other  with  satisfactory 
economy. 


FIG.  127.— THE  "  AUTOMATIC 

An  interesting  modification  of  the  Corliss  principle  in  the 
adaptation  of  the  "  automatic"  system  of  shaft-governor  regu- 
lation is  illustrated  in  the  accompanying  engraving.  In  this 
arrangement,  the  Payne  engine,  the  advantages  of  the  pecul- 
iar kinematic  movement  of  Corliss  and  of  his  form  of  valve, 


STXUCTUZM  OF  THE  STEAM-ENGINE.  2tf 

are  combined  in  the  positive-motion  system  of  gearing  essen- 
tial to  the  *•  high-speed  *"  engine.  As  in  some  other  engines, 
the  steam-  and  exhaust-valves  are  here  in  the  same  shell, 
and  the  small  clearance  of  this  form  of  engine,  the  peculiar 
movement  of  the  valves,  and  the  exact  regulation  of  the 
shaft-governor,  and  the  high-speed  system,  are  combined  in  a 
very  compact  machine. 

The  illustration  herewith  given  represents  a  compound  en- 
gine with  automatic  expansion-gear  as  designed  by  Fowler 
&  Co.  of  Leeds,  G.  R,  for  stationary  purposes.  The  use  of 
rope-transmission,  now  in  extensive  use,  is  here  exhibited,  the 
fly-wheel  being  suitably  grooved  to  carry  it.  The  cut-off 
mechanism  is  adjusted  by  the  governor  seen  on  the  horizontal 
shaft  above  the  high-pressure  steam-chest.  The  cut  shows 


» 


weH,  also,  the  various  important  accessories  of  the  engine :  its 
pass-over  steam-pipe,  relief-valves,  indicator-motion,  and  sys- 
tem of  lubrication,  as  well  as  the  general  features  of  a  carefully 
considered  design. 

The  Slfam-htrbiMf  constitutes  a  class  of  steam-engine 
which,  although  the  first  invented  and  familiar,  as  a  type,  to 
all  engineers  from  the  days  of  Hero  the  Younger,  and  known 
to  have  a  high  theoretical  and  moderately  high  actual  effi- 


238  A    MANUAL   OF   THE   STEAM-ENGINE. 

ciency,  has  been  only  experimentally  used  until  a  very  recent 
date.  That  of  Hero  has  been  illustrated  in  Fig.  I.  The 
Atwater  engine  of  about  1840  was  of  this  type,  and  was  said 
to  be  as  economical  as  the  engines  of  the  time  of  equal  power. 
Steam-turbines  of  the  inward-flow  type  have  been  used  by 
Gorman  and  others.* 

The  later  "  compound "  steam-turbine  has  recently  been 
somewhat  extensively  employed  in  the  operation  of  dynamo- 
electric  machinery.  It  consists  of  two  sets  of  parallel-flow  tur- 
bines set,  in  twin  series,  on  one  shaft  on  either  side  the  induc- 
tion-pipe, thus  balancing.  The  passages  are  gradually  enlarged 
as  the  volume  of  the  steam  increases  with  its  progressive  ex- 
pansion. 

The  turbines  thus  alternate  with  their  guide-blades,  and 
both  the  vanes  and  the  blades  are  carefully  proportioned  and 
set  to  secure  maximum  attainable  efficiency  at  the  proposed 
speed  of  rotation,  their  pitches  and  depths  being  suitably 
varied. 

The  computed  efficiency,  without  allowances  for  wastes, 
is  about  87  per  cent.  The  actual  consumption  of  steam  is 
found  to  be  35  to  40  pounds  per  electrical  horse-power  pro- 
duced, and  per  hour  as  steam-pressures  rise  from  60  to  90 
pounds  by  gauge.  The  speed  of  rotation  ranges  from  5000  or 
10,000  revolutions  per  minute  upward,  according  to  size  and 
steam-pressure;  1 8,000  and  20,000  being  common  speeds  for 
the  smaller  sizes. 

Dow's  turbine  is  an  inward-flow  wheel  with  concentric  sets 
of  guides  and  vanes  in  series,  and  is  said  to  have  attained 
35,000  revolutions  per  minute,  working  regularly  at  25,000, 
consuming  55  pounds  of  steam  per  horse-power  per  hour. 
Only  the  most  perfect  construction  is  here  admissible. 

The  theory  of  this  type  of  machine  is  that  familiar  to  the 
hydraulic  engineer,  and  the  speeds  of  orifice  for  maximum  effi- 
ciency are  well  known  to  be  infinite  in  the  Hero  class  of  tur- 
bine and  approximately  one  half  the  final  velocity  of  flow  in 


*  Rankine,  p.  538. 


STRUCTURE   OF   THE   STEAM-EXCISE.  239 

the  guide-blade  turbine.  Since  these  speeds  are  impracticable 
in  their  use,  a  certain  loss  of  energy  is  thus  inevitable.  In 
compensation  for  this  loss,  in  the  steam-turbine,  is  the  fact  that 
it  is*  not  subject  to  that  fluctuation  of  temperature  of  parts 
exposed  to  contact  with  the  steam  which  results  in  large 
wastes  by  cylinder-condensation  in  the  common  forms  of 
steam-engine.  A  gain  of  from  25  to  50  per  cent,  as  compared 
with  the  latter,  in  this  way,  is  to  be  counted  upon. 

The  Dow  turbine,  as  built  for  work,  in  connection  with  the 
Howell  torpedo,  gives  an  average  of  about  1 1  horse-power  in 
coming  up  to  speed  in  regular  working,  at  60  pounds  steam- 
pressure,  and  weighs  from  loo  to  1 50  pounds,  or  not  far  from 
13  pounds  per  horse-power.*  Its  fly-wheel  rim  attains  a  speed 
of  nearly  7  miles  an  hour  at  10,000  revolutions  per  minute. 
The  designer  estimates  its  power  at  150  pounds  steam-pres- 
sure and  the  same  speed  at  40  horse-power,  or  one  horse-power 
to  3.75  pounds  weight,  and  states  that  this  may  be  still  further 
reduced  to  the  extraordinary  minimum  of  2\  pounds  weight 
per  horse-power,  a  figure  well  within  the  estimated  allowable 
maximum  for  use  in  aeronautic  work. 

The  steam-turbine  of  Parsons,  Fig.  129,  is  an  engine  con- 
sisting of  a  series  of  turbines,  the  different  pairs  of  guides  and 
wheels  being  so  placed  that  the  fluid  passes  successively  from 
one  pair  to  the  next.  Of  the  two  forms,  radial  and  axial  flow, 
only  the  latter  have  been  used  here.  Two  series  of  cylindrical 
turbines  are  used,  arranged  symmetrically  to  the  right  and  left 
of  the  central  steam-inlet,  the  exhaust  taking  place  from  the 
two  ends.  In  this  manner  a  balance  is  obtained,  and  the  bear- 
ings are  relieved  of  end-pressure.  Oil  is  forced  through  the 
bearings  by  a  pump.  The  bearings  are  thus  forcibly  deluged 
with  oil,  which  returns  to  a  reservoir.  The  governor  is  a  suc- 
tion fan  mounted  upon  the  spindle  and  connected  with  a  dia- 
phragm, which  operates  the  throttle-valve  against  the  power  of 
a  spring.  Its  action  is  found  to  be  rapid  and  certain. 

Such  engines  have  been  successfully  employed  in  driving 

•Electrical  World;   April  18,  1891. 


240 


A   MANUAL    OF   THE  STEAM-ENGINE. 


electric  machinery  and  in  "spinning"  the  "fly"  of  the  Howell 
torpedo.     For  alternating  electric  currents,  this  system  pos- 


sesses the  peculiar  advantage  of  permitting  a  "  dynamo"  to  be 
employed  having  but  two  poles.  It.  may  be  readily  driven 
continuously  at  speeds  exceeding  10,000  revolutions  per  minute, 


STRUCTURE  OF  THE  STEAM-EXGISCE.  2.±: 

and,  like  the  Dow  turbine,  elsewhere  icfeiied  to,  has  been 
driven  at  20^000  and  upward.  With  the  lower  speeds  of  revo- 
lution usual  with  ordinary  engines,  the  number  off  poles  required 
generally  approximates  the  quotient  IZJOQO  divided  by  tine 
speed  off  engine,  if  directly  connected. 

The  best  off  these  machines  have  demanded  from  35  pounds 
of  steam  per  horse-power  per  hour,,  upward,  according  to  pres- 
sure  employed.  It  may  be  assumed  that  they  wiH  require  not 
for  from  the  weight 


where/,  Iks  between  50  and  aoo  pounds  per  square  inch  by 
gauge,  and  the  appaiatus  is  operated  under  favorable  condi- 
tions  ;  the  value  of  *  tying  between  350  and  400  with  dry  steam. 

In  the  United  States,  the  substitution  of  the  Dow  turbine 
for  the  sy  interns  previously  in  use,  for  torpedoes,  has  brought 
down  die  weight  and  volume  of  marliinMy  from  the  earlier 
mhmnnm  of  560  pounds  and  three  cubic  feet  per  «"^*"«*»  to 
75  pounds  and  one  cubic  foot. 

^Exfcwimtfrntal  Emgimts™  or  steam-engines  designed  es- 
pecialy  for  purposes  of  instruction  and  research,  are  now  fre- 
quently UHisli  lifted,  and  especially  in  equipping  European 
schools.  Such  engines  arc  illustrated  in  the  frontispiece  of 
this  volume,  as  buffi:  for  Owens  College,  Manchester,  G.  B.  :* 
while  other  forms  designed  by  American  engineers  and  as  con- 
structed for  Sibfiey  College,  Cornell  University,  and  for  the 
Massachusetts  Institute  of  Technology,  will  be  represented  in 
a  later  chapter  (VoL  II.)  on  Engine  Trials. 

In  the  design  of  such  engines,  the  problem  is  ordinarily  to 
make  aH  adjustments  cover  a  wide  range  ;  in  order  that  the 
laws  affecting  variation  of  pressures,  temperatures,  speeds, 
steam-distribution,  as  determinimig  efficiency,  may  be  SUims- 
trated  ;  as  wefl  as  to  secure  a  means  of  investigating  problems 
still  unsolved  and  of  checking  results  previously  obtained  but 


7--.;     -.-.?:     r-  -:•---  .    :=     --:!-:  .    J    I 


242  A    MANUAL   OF   THE   STEAM-ENGINE. 

requiring  confirmation.  The  engine  illustrated  consists  of  a 
triple-expansion  combination  so  arranged  that  each  element 
may  be  worked  and  tested  independently,  if  desired,  as  well  as 
either  compounded  or  triple-expansion.  The  type  adopted  is 
that  familiar  in  marine  engineering,  with  inverted  cylinders, 
jacketed  on  sides  and  ends,  and  each  jacket  separately  piped 
to  permit  its  action  to  be  ascertained. 

The  working-pressure  is  200  pounds  as  a  maximum ;  the 
piston-speed  may  attain  1000  feet  per  minute;  the  Meyer  ex- 
pansion-valves give  a  range  of  expansion  from  r  =  1.5  to 
r  =  oo.  The  cylinders  are  5,  8,  and  12  inches  diameter,  10, 
10,  and  15  inches  stroke.  The  engine  can  be  worked  either 
condensing  or  non-condensing.  This  engine  was  designed 
under  the  supervision  of  Professor  Reynolds  and  built  by 
Messrs.  Mather  &  Platt. 

A  surface-condenser  is  used  containing  160  square  feet  sur- 
face, and  is  served  by  an  air-pump,  driven  by  the  largest  engine, 
9  inches  diameter  and  4^  inches  stroke.  Hydraulic  brakes  are 
employed,  which  are  simply  adaptations  of  the  centrifugal 
pump. 

On  trial  the  engine  worked  admirably  and  economically, 
demanding  but  1.33  pounds  of  fuel  per  horse-power  per  hour; 
the  efficiency  being  0.20  at  200  pounds  pressure.  The  efficiency 
of  machine  was  about  0.80.  The  performance  of  the  engine, 
in  all  respects,  is  reported  to  be  eminently  satisfactory.  (See 
§  128,  Chap.  V.) 


CHAPTER  IIL 
THE  .PHILOSOPHY  OF  THE  STEAM-ENGINE. 

45.  The  Scope  of  the  Philosophy  of  the  Ste^  m -engine, 
and  a  complete  history  of  the  development  of  the  Theory  of 
the   Steam-engine,  would    include,  first,  the  history  of  the 
Mechanical  Theory  of  Heat;    secondly,  the    history  of  the 
Science  of  Thermodynamics,  which  has  been  the  outgrowth  of 
that  theory ;  third,  the  history  of  the  application  of  the  Science 
of  Heat-transformation  to  the  case  of  the  Steam-engine ;  and, 
fourthly,  an  account  of  the  completion  of  the  Theory  of  the 
Steam-  and  other  Heat-engines  by  the   introduction  of  the 
theory  of  losses  by  the  more  or  less  avoidable  forms  of  waste, 
as  distinguished  from  those  necessary  and  unavoidable  wastes 
indicated  by  the  pure  theory  of  thermodynamics.     The  first 
and  second  of  these  divisions  are  treated  of  in  works  on  thermo- 
dynamics and  in  treatises  on  physics.    The  third  division  is 
briefly  considered,  and  usually  very  incompletely,  in  treatises 
on  the  steam-engine ;  while  the  last  is  of  too  recent  develop- 
ment to  be  the  subject  of  complete  treatment,  as  yet,  in  any 
existing  works.    Our  principal  object  is,  here,  simply  to  collect 
into  a  condensed  form,  and  in  proper  relations,  these  several 
branches  of  the  subject,  leaving  for  an  appropriate  time  and 
place  that  more  full  and  complete  account  which  might  now. 
for  the  first  time  in  history,  be  prepared. 

46.  The  Nature  of  the  Processes  observed  in  the  opera- 
tion of  the  steam-engine  are  such  as  wfll  illustrate  many  of  the 
most  important  principles  and  facts  which  constitute  the  physi- 
cal sciences,     The  steam-engine  is  an  exceedingly  ingenious 
hot  very  imperfect  machine  for  transforming  the  heat-energy 


244  A    MANUAL    OF   THE   STEAM-ENGINE. 

obtained  by  the  chemical  combination  of  a  combustible  with 
the  supporter  of  combustion  into  mechanical  energy.  The 
original  source  of  this  energy  is  found  far  back  of  its  first  ap- 
pearance in  the  steam-boiler.  It  had  its  origin  at  the  begin- 
ning. When  the  solar  system  had  been  formed  from  the  nebu- 
lous chaos  of  creation,  the  glowing  mass  which  is  now  called 
the  sun  was  the  depository  of  a  vast  store  of  heat-energy,  which 
was  thence  radiated  into  space  and  showered  upon  the  attend- 
ant worlds  in  inconceivable  quantity  and  with  unmeasured  in- 
tensity. During  the  past  life  of  the  globe,  the  heat-energy 
received  from  the  sun  was  partly  expended  in  the  production 
of  forests  and  the  storage  of  an  immense  quantity  of  carbon, 
which  had  previously  existed  in  the  atmosphere,  combined 
with  oxygen,  as  carbonic  acid.  The  geological  changes  which 
buried  these  forests  resulted  in  the  formation  of  coal-beds  and 
the  storage  of  a  vast  amount  of  carbon,  of  which  the  affinity 
for  oxygen  remained  unsatisfied  until  finally  uncovered  by  man. 
Thus  we  owe  to  the  heat  and  light  of  the  sun,  as  was  pointed 
out  by  George  Stephenson,  the  incalculable  store  of  energy 
upon  which  the  human  race  is  dependent  for  life. 

This  coal,  thrown  upon  the  grate  in  the  steam-boiler,  takes 
fire,  and,  uniting  again  with  the  oxygen,  sets  free  heat  in  pre- 
cisely the  same  quantity  that  it  was  received  from  the  sun  and 
appropriated  during  the  growth  of  the  tree.  The  actual  energy 
thus  rendered  available  is  transferred,  by  conduction  and  radi- 
ation, to  the  water  in  the  steam-boiler,  converts  that  water  into 
steam;  and  its  mechanical  effect  is  seen  in  the  expansion  of  the 
liquid  into  vapor  against  superincumbent  pressure.  Trans- 
ferred from  the  boiler  to  the  engine,  the  steam  is  there  per- 
mitted to  expand,  doing  work,  and  the  heat-energy  with  which 
it  is  charged  becomes  partly  converted  into  mechanical  energy, 
and  is  applied  to  useful  work. 

Thus  we  may  trace  the  store  of  energy  received  from  the 
sun  and  contained  in  our  coal  through  its  several  changes  until 
it  is  finally  set  at  work;  and  we  might  go  still  farther  and  ob- 
serve how,  in  each  case,  it  is  again  usually  re-transformed  and 
again  set  free  as  heat-energy. 


THE  PHILOSOPHY  OF   THE   STEAAI-EXGIXE.  24$ 

47.  The  Nature,  Sources,  and  Transformations  of  En- 
ergy in  these  several  processes  are  thus  easily  traced.     The 
transformation  which  takes  place  in  the  furnace  is  a  chemical 
change ;  the  transfer  of  heat  to  the  water  and  the  subsequent 
phenomena  accompanying  its  passage  through  the  engine  are 
physical  changes,  some  of  which  require  for  their  investigation 
abstruse  mathematical  operations.    A  thorough  comprehension 
of  the  principles  governing  the  operation  of  the  steam-engine, 
therefore,  can  only  be  attained  after  studying  the  phenomena 
of   physical  science  with  sufficient   minuteness  and  accuracy 
to   be   able   to   express    with    precision   the    laws    of   which 
those  sciences  are  constituted.     The  study  of  the  philosophy 
of  the   steam-engine  involves  the   study   of   Chemistry  and 
Physics,  and  of  the  science  of  Energetics,  of  which  the  science 
of  Thermodynamics  is  a  branch.     This  sketch  may,  therefore, 
include  an  outline  of  the  growth  of  the  several  sciences  which 
together  make  up  its  philosophy,  and  especially  of  the  science 
of  thermodynamics,  which   is   peculiarly  the   science   of  the 
heat-engines.* 

48.  The  Chemical  Principles  involved   in  the  action   of 
all  the  steam-engines  are  those  illustrated  in  the  combustion 
of  the  fuels.     All  essential  elements  of  this  part  of  the  philos- 
ophy of  heat-engines  are  now  at  least  approximately  knowrn, 
and   it   is  perfectly  possible   for  the  engineer,   knowing  the 
composition  and  physical  structure  of  his  fuel,  to  compute  very 
exactly  the  quantity  of  heat-energy  stored  in  its  mass  and  the 
amount  probably  to  be  realized  in  the  furnace  in  which  it  is 
consumed  and  stored  in  the  working-fluid  to  be  sent  forward 
into  his  engine. 

In  all  cases,  he  is  supplied,  as  fuel,  with  a  certain  known 
composition  of  carbon,  hydrogen,  and  their  compounds,  unim- 
portant proportions  of  other  combustible  elements,  as  sulphur, 
and  a  quantity  of  incombustible  mineral  matter,  forming, 
finally,  ash  and  clinker,  or  cinders.  The  union  of  these  com- 

*  For  a  somewhat  detailed  account  of  the  early  and  mediaeval  progress  of 
the  sciences,  see  the  "  History  of  ihe  Steam-engine,"  by  the  Author,  chapter 
vii :  International  Series  ;  New  York,  D.  Appleton  &  Co. 


246  A   MANUAL   OF   THE   STEAM-ENGINE. 

bustible  elements  and  compounds  with  the  oxygen  of  the  air 
produces  a  definite  and  easily  calculable  amount  of  heat-energy, 
of  which  a  part,  equally  easy  of  computation  when  the  extent, 
nature,  location,  and  arrangement  of  the  absorbing,  or  "  heat- 
ing," surfaces  are  known,  is  taken  up  for  useful  purposes ;  while 
the  rest  is  sent  up-chimney  or  otherwise  wasted.  The  physical, 
as  well  as  the  chemical,  character  of  the  fuels  and  the  greater 
or  less  completeness  of  their  combustion  and  the  consequent 
character  of  the  discharged  furnace-gases  aids  in  determining 
the  final  result  and  the  total  efficiency  of  the  system. 

49.  The  Physical  Principles  involved  in  the  storage, 
transfer,  and  utilization  of  heat  in  the  steam-engine  are  those 
which  relate  to  the  transfer,  storage,  and  re-transfer  of  heat- 
energy  in  the  passage  of  that  energy  from  the  furnace-gases 
to  the  boiler,  its  storage  in  the  water  and  steam,  and  its  transfer 
to  the  engine,  with  continuous  loss  and  waste,  until  finally,  a 
part  being  transformed  into  mechanical  energy  and  more  or 
less  usefully  applied,  the  remainder  is  finally  discharged 
from  the  engine  and  entirely  lost  and  wasted,  as  a  source  of 
power.  Conduction,  radiation,  convection  of  heat,  and  heat 
conversion  into  other  kinds  of  energy,  are  the  physical  phe- 
nomena involved  in  these  operations. 

In  some  cases  these  processes  are  somewhat  obscure  and 
remained  for  many  years  but  little  understood.  This  is 
especially  the  fact  with  respect  to  those  operations  which  go 
on  within  the  engine  cylinder  in  the  course  of  the  cycle  there 
performed  and  which  involve  the  introduction  of  the  steam 
and  its  temporary  storage  into  a  cooler  space  in  which  it  is 
partly  condensed  by  surrender  of  heat  to  the  enclosing  walls  ; 
the  gradual  reduction  of  temperature  and  pressure  of  the 
steam  with  increasing  expansion  of  volume,  and  with  restora- 
tion of  that  heat,  in  part,  to  the  fluid,  and  finally  the  discharge 
of  the  steam  from  the  cylinder  at  a  still  further  reduced  tem- 
perature, with  complete  restoration  of  the  heat  previously 
stored  in  the  walls  of  that  vessel.  The  application  of  the 
principles  of  physics  to  this  series  of  changes  is  quite  as 
essemial  to  a  complete  theory  of  the  real  heat-engine  as  is  that 


THE  PHILOSOPHY  OF   THE  STEAM-EXGINE.  247 

of  the  principles  of  thermodynamics  to  the  processes  of  trans- 
formation of  energy. 

50.  The  Mechanical  Principles  which  are  included  in  a 
complete  theory  of  the  action  of  the  heat-engines  will  be 
illustrated  in  the  chapters  on  the  design  of  the  various  parts  of 
the  engine.  It  is  sufficient  here  to  present  a  general  outline  of 
the  modern  science. 

The  science  of  mechanics  is  of  comparatively  recent  date, 
and  with  the  publication  of  Newton's  Principia  became  thor- 
oughly consistent  and  logically  complete,  so  far  as  was  possible 
without  a  knowledge  of  the  modern  principles  of  energetics, 
Newton's  enunciations  of  the  laws  of  motion  were  the  basis  of 
the  whole  science  of  dynamics,  as  applied  to  bodies  moving 
freely  under  the  action  of  applied  forces,  either  constant  or 
variable.  They  are  as  perfect  a  basis  for  that  science  as  are 
the  primary  principles  of  geometry  for  the  whole  beautiful 
structure  which  is  built  up  on  them. 

The  three  perfect  qualitative  expressions  of  dynamical 
law  are : 

1.  Every  free  body  continues  in  the  state  in  which  it  may 
be,  whether  of  rest  or  of  rectilinear  uniform  motion,  until  com- 
pelled to  deviate  from  that  state  by  impressed  forces. 

2.  Change  of  motion  is  proportional  to  the  force  impressed, 
and  in  the  direction  of  the  right  line  in  which  that  force  acts. 

3.  Action  is  always  opposed  by  reaction ;  action  and  reac- 
tion are  equal,  and  in  directly  contrary  directions. 

We  may  add  to  these  principles  a  definition  of  a  force, 
which  is  equally  and  absolutely  complete : 

Force  is  that  which  produces,  or  tends  to  produce,  motion, 
or  change  of  motion,  in  bodies.  It  is  measured  statically  by 
the  weight  that  will  counterpoise  it,  or  by  the  pressure  which 
it  will  produce,  and  dynamically  by  the  velocity  which  it  wiP 
produce,  acting  in  the  unit  of  time  on  the  unit  of  mass. 

The  quantitative  determinations  of  dynamic  effects  o 
forces  are  always  readily  made  when  it  is  remembered  that 
the  effect  of  a  force  equal  to  its  own  weight,  when  the  body 
is  free  to  move,  is  to  produce  in  one  second  a  velocity  of  32.2 


248  A    MANUAL    OF    THE    STEAM-ENGINE. 

feet  per  second,  which  quantity  is  the  unit  of  dynamic  meas- 
urement. 

Work  is  the  product  of  the  resistance  met  in  any  instance 
of  the  exertion  of  a  force,  into  the  distance  through  which 
that  force  overcomes  the  resistance. 

Energy  is  the  work  which  a  body  is  capable  of  doing,  by  its 
weight  or  inertia,  under  given  conditions.  The  energy  of  a 
falling  body,  or  of  a  flying  shot,  is  about  ^  its  weight  mul- 
tiplied by  the  square  of  its  velocity,  or.  which  is  the  same 
thing,  the  product  of  its  weight  into  the  height  of  fall  or 
height  due  its  velocity.  These  principles  and  definitions,  with 
the  long-settled  definitions  of  the  primary  ideas  of  space  and 
time,  were  all  that  were  needed  to  lead  the  way  to  that  grand- 
est of  all  physical  generalizations,  the  doctrine  of  the  persist- 
ence or  conservation  of  all  energy,  and  to  its  corollary  declar- 
ing the  equivalence  of  all  forms  of  energy,  and  also  to  the 
experimental  demonstration  of  the  transformability  of  energy 
from  one  mode  of  existence  to  another,  and  its  universal  ex- 
istence in  the  various  modes  of  motion  of  bodies  and  of  their 
molecules. 

Experimental  physical  science  had  hardly  become  acknowl- 
edged as  the  only  and  the  proper  method  of  acquiring  knowl- 
edge of  natural  phenomena  at  the  time  of  Newton  ;  but  this 
soon  became  a  generally  accepted  principle.  In  physics,  Gil- 
bert had  made  valuable  investigations  before  Newton,  and 
Galileo's  experiments  at  Pisa  had  been  examples  of  similarly 
useful  research.  In  chemistry,  it  was  only  when,  a  century 
later,  Lavoisier  showed  by  his  splendid  example  what  could  be 
done  by  the  skilful  and  intelligent  use  of  quantitative  meas- 
urements, and  made  the  balance  the  chemist's  most  important 
tool,  that  a  science  was  formed  comprehending  all  the  facts 
and  laws  of  chemical  change  and  molecular  combination.  We 
can  now  see  how,  in  all  the  physical  sciences,  four  primitive 
ideas  are  comprehended :  matter,  force,  motion,  and  space— 
which  latter  two  terms  include  all  relations  of  position.  These 
are  the  fundamental  ideas  of  mechanics. 

Based  on  these  notions,  the  science  of  mechanics  compre- 


THE  PHILOSOPHY  OF   THE   STEAM-ENGINE.  249 

bends  four  sections,  which  are  of  general  application  in  the 
study  of  all  physical  phenomena.  These  are  : 

Statics,  which  treats  of  the  action  and  effect  of  forces  only. 

Kinematics,  which  treats  of  relations  of  motion  simply. 

Dynamics,  or  kinetics,  which  treats  of  simple  motion  as  an 
effect  of  the  action  of  forces. 

Energetics,  which  treats  of  modifications  of  energy  under 
the  action  of  forces,  and  of  its  transformation  from  one  mode 
of  manifestation  to  another,  and  from  one  body  to  another. 

51.  Energetics  and  Thermodynamics  are  the  broader 
and  the  narrower  codes  of  similar  law.  Under  the  latter  of 
the  four  divisions  of  mechanical  philosophy  is  comprehended 
that  latest  of  the  minor  sciences,  of  which  the  heat-engines, 
and  especially  the  steam-engine,  illustrate  the  most  important 
applications — Thermodynamics.  This  science  is  simply  a  wider 
generalization  of  principles  which  have  been  established  one 
at  a  time,  and  by  philosophers  widely  separated  both  geo- 
graphically and  historically,  by  both  space  and  time,  and 
which  have  been  slowly  aggregated  to  form  one  after  another 
of  the  sciences,  and  out  of  which  we  are  gradually  evolving 
wider  generalizations,  and  thus  tending  toward  a  condition  of 
scientific  knowledge  which  renders  more  and  more  probable 
the  truth  of  Cicero's  declaration  :  "  One  eternal  and  immu- 
table law  embraces  all  things  and  all  times."  At  the  basis  of 
the  whole  science  of  Energetics  lies  a  principle  which  was 
enunciated  before  Science  had  a  birthplace  or  a  name  : 

All  that  exists,  whether  matter  or  force,  and  in  whatever 
form,  is  indestructible,  except  by  the  Infinite  Power  which  has 
reated  it. 

That  matter  is  indestructible  by  finite  power  became  ad- 
nitted  -as  soon  as  the  chemists,  led  by  their  great  teacher 
Lavoisier,  began  to  apply  the  balance,  and  were  thus  able  to 
show  that  in  all  chemical  change  there  occurs  only  a  modifica- 
tion of  form  or  of  combination  of  elements,  and  no  loss  of 
matter  ever  takes  place.  The  "  persistence  "  of  energy  was  a 
later  discovery,  consequent  largely  upon  the  experimental  de- 
termination of  the  convertibility  of  heat-energy  into  other 


25O  A    MANUAL    OF    THE    STEAM-ENGINE, 

forms  and  into  mechanical  work,  for  which  we  are  indebted  to 
Rumford  and  Davy,  and  to  the  determination  of  the  quantiva- 
lence  anticipated  by  Newton,  shown  and  calculated  approxi- 
mately by  Colding  and  Mayer,  and  measured  with  great  prob- 
able accuracy  by  Joule  and  Rowland. 

52.  The  Ideal  and  the  Real  Engine  must  be  clearly  dis- 
tinguished in  all  that  follows.  The  ideal  engine  of  the  earlier 
method  is  one  in  which  only  thermodynamic  processes  occur. 
Only  transfer  of  heat  from  point  to  point  in  its  cycle  of  opera- 
tions, and  the  conversion  of  thermal  into  mechanical  energy  or 
the  reverse,  are  assumed  as  possible  ;  and  the  problem  studied 
is  that  of  determining  what,  under  certain  specified  conditions, 
is  the  efficiency  of  the  engine,  the  proportion  o'  net  work  per- 
formed to  gross  energy  demanded  for  its  accomplishment. 
Such  an  engine  must  be  constructed  of  materials  without  per- 
meability to  heat,  without  conducting  or  heat-storing  capacity, 
absolutely  free  from  friction,  and  incapable  of  yielding  to  im- 
pressed forces.  It  is  a  purely  ideal  case. 

The  real  engine,  on  the  other  hand,  must  be  composed  of 
such  materials  as  are  available  to  the  engineer.  They  must 
have  strength,  stiffness,  toughness,  and  endurance  under  load 
and  wear,  and  must  be  capable  of  being  given  the  desired  shape 
and  proportions  at  the  least  possible  expense.  Only  iron  and 
steel,  copper  and  the  familiar  alloys  meet  these  requirements ; 
and,  practically,  all  engines  are  composed  of  these  substances, 
and  all  have  their  working  cylinders  made  of  cast-iron,  a  sub- 
stance of  high  conducting  and  storing  power  for  heat.  These 
facts  make  an  enormous  difference  in  the  behavior  of  the  en- 
gine both  as  respects  its  utilization  of  heat  and  its  useful 
application  of  the  energy  produced  within  its  working  cylinder 
by  heat-transformation.  Large  quantities  of  heat  are  neces- 
sarily wasted,  in  the  manner  already  indicated  above,  when 
discussing  the  physical  principles  involved  in  the  action  of  the 
engine ;  and  a  considerable  fraction  of  the  power  exerted  by 
the  steam  on  the  piston  of  the  engine  is,  in  the  actual  case, 
lost  in  the  friction  of  its  own  journals. 

Thus  the  real  case  must  be  carefully  distinguished  from  the 


THE  PHILOSOPHY  OF  THE  STEAJI-EXGIXE.  2$l 

ideal,  and  the  pure  thermodynamic  theory  of  the  latter  consti- 
tutes bat  one  element  of  the  theory  of  the  former. 

53.  The  Scientific  Problem  which  confronts  the  student 
of  the  theory  of  the  steam-engine,  as  a  practical  case,  is  thus 
seen  to  be  the  determination  of  the  quantity  of  heat-energy 
stored  in  a  given  fuel ;  the  proportion  which  may  be  reasonably 
expected  to  be  developed  by  its  combustion;    the  amount 
which  should  be  taken  up  and  stored  for  useful  application  in 
a  steam-generator,  and  the  balance  wasted  at  the  chimney  and 
elsewhere ;  of  that  which  may  be  taken  to  the  engine  through 
a  steam-pipe  of  known  size  and  condition,  of  that  which  will  be 
probably  wasted  by  conduction  and  radiation,  en  route,  or  at 
the  engine  and  within  its  cylinder;  and  finally,  the  quantity 
which  will  be  converted  into  work  and,  of  this,  the  proportion 
that  will  be  capable  of  useful  application. 

The  determination  of  the  latter  quantity  is  the  measure- 
ment of  a  balance  after  all  wastes  are  deducted  ;  and  the  effi- 
ciency sought  is  the  ratio  of  this  quantity  to  the  mechanical 
equivalent  of  all  heat-energy  supplied  to  the  engine,  or  to  that 
produced  at  the  furnace,  as  the  case  may  demand. 

In  detail,  therefore,  the  problem  to  be  solved  includes  the 
application  of  known  chemical,  physical,  and  mechanical  princi- 
ples to  the  determination,  one  by  one,  of  all  these  quantities 
of  energy,  step  by  step,  from  the  furnace  to  the  driving-shaft 
of  the  engine,  and  the  summation,  at  each  step,  of  such  quanti- 
ties received  or  paid  out  in  such  manner  that  a  final  balance- 
sheet  may  be  constructed  exhibiting  every  item  on  both  sides 
the  account,  and  permitting  the  answering  of  any  question  that 
may  arise  respecting  the  receipt  and  expenditure  of  energy  and 
mechanical  power. 

54.  An  Outline  of  the  Progress  of  Science  in  the  develop- 
ment of  the  philosophy  of  the  steam-engine  may  be  appropri- 
ately here  briefly  given.     It  properly  begins  with  the  history 
of  the  older  philosophies ;  but  its  useful  elements,  and  its  actual 
applications,  only  date  back  to  a  very  recent  period.     As  will 
be  seen,  the  physical  sciences  have  all  had  an  exceedingly  slow 
growth  until  within  the  last  two  or  three  centuries.     The  abso- 


252  A    MANUAL   OF   THE   STEAM-ENGINE. 

lute  impossibility  of  their  promotion  except  through  continu- 
ous experimentation,  and  the  inability  of  mankind  to  construct 
the  apparatus  of  research  until  modern  times,  would  have  caused 
this  late  development  of  sciences  of  this  class,  even  had  the 
true  scientific  spirit  existed  and  the  scientific  method  been 
known  earlier. 

The  physical  sciences  have,  since  the  beginning  of  the  seven- 
teenth century,  had  independent  and  uninterrupted  growth  ; 
but  it  has  been  irregular,  spasmodic,  and  unsymmetrical.  The 
science  of  applied  mechanics,  as  distinguished  from  its  purely 
mathematical  branches,  had  its  origin  with  Galileo  in  the  first 
and  Newton  in  the  second  half  of  that  century ;  chemistry  may 
be  said  to  have  become  a  science  under  the  hand  of  Lavoisier 
at  the  close  of  the  eighteenth  century ;  physics  had  a  longer 
period  of  incubation,  from  the  days  of  Gilbert,  and  energetics 
and  its  minor  branch,  thermodynamics,  have  only  been  con- 
ceived and  organized  into  sciences  in  the  nineteenth  century. 

Throughout  this  whole  period  of  modern  scientific  work, 
the  patient  student  and  careful  observer  will  see  that  these 
various  sciences,  now  seemingly  independent,  are  becoming 
established  in  closer  and  closer  relations,  and  are  gradually 
coming  to  illustrate  continually  more  and  more  clearly  their 
unquestionable  mutual  interdependence.  All  phenomena  of 
motion  and  change  of  molecular  relation,  whether  in  physics, 
chemistry,  or  mechanical  action,  are  subject  to  the  laws  of 
mechanics  and  of  energetics,  and  a  common  science  must 
probably  sooner  or  later  come  to  comprehend  all. 

In  what  follows  the  development  of  the  science  of  thermo- 
dynamics and  the  gradual  construction  of  the  philosophy  of  the 
heat-engines  only  will  be  considered.*  The  student  is,  how 
ever,  advised  to  study  carefully  and  in  a  philosophical  manner 
the  development  of  all,  and  especially  in  their  mutual  relations, 
and  in  their  bearing  upon  the  science  of  energy,  as  mechanical 
and  as  molecular,  and  as  a  science  of  energy-transformations. 

*  For  a  more  detailed  account  see  the  encyclopaedias,  or  consult  the  Author's 
"  History  of  the  Steam-engine,"  chapters  vii,  vui. 


THE  PHILOSOPHY  OF   THE   STEAM-ENGINE.  253 

55.  The  Origin  of  the  "Mechanical  Theory  of  Heat,"  as 
is  now  well  understood,  dates,  as  a  speculation,  from  the  days 
of  the  earliest  philosophies.  The  contest  which  raged  with 
such  intensity,  and  sometimes  acrimony,  among  speculative 
men  of  science,  during  the  last  century,  was  merely  a  repetition 
of  struggles  of  which  we  find  evidences,  at  intervals,  through- 
out the  whole  period  of  recorded  history.*  The  closing  period 
of  this,  which  proved  to  be  an  important  revolution  in  science, 
marked  the  beginning  of  the  nineteenth  century.  It  was  in- 
augurated by  the  introduction  of  experimental  investigation 
directed  toward  the  crucial  point  of  the  question  at  issue.  It 
terminated,  about  the  middle  of  the  century,  with  the  accept- 
ance of  the  general  results  of  such  experiment  by  every  scien- 
tific man  of  acknowledged  standing,  on  either  side  the  Atlantic. 
The  doctrine  that  heat  was  material,  and  its  transfer  a  real 
movement  of  substance  from  the  source  to  the  receiver  of  heat, 
was  thus  finally  completely  superseded  by  the  theory,  now  be- 
come an  ascertained  truth,  that  heat  is  a  form  of  energy,  and 
its  transformation  a  change  in  the  location  and  method  of 
molecular  vibration.  The  Dynamical  Theory  of  Heat  was  first 
given  a  solid  basis  by  the  experiments  of  Count  Rumford 
(Benjamin  Thompson),  in  1/96-7 — of  which  an  account  was 
given  in  a  paper  read  by  Rumford  before  the  Royal  Society  of 
Great  Britain  in  1798, — by  the  experiments  of  Sir  Humphry 
Davy  in  1798-9,  and  by  the  later  and  more  precise  determina- 
tions of  the  value  of  the  mechanical  equivalent  of  heat  by 
Joule  and  others. 

James  Prescott  Joule,  as  early  as  1843,  obtained  a  series  of 
results  varying  in  quantity  from  587  to  1026,  from  which  he 
deduced  an  equivalent  of  770  foot-pounds  by  the  friction  of 
water  in  small  pipes.  In  the  following  year  Mr.  Joule  gave  a 
'mean  value  of  802  foot-pounds.  In  1845  he  found  890  as  the 

*  The  main  portion  of  what  follows  relating  to  this  subject  is  abstracted  from 
a  paper  read  by  the  Author  before  the  British  Association  for  Advancement  of 
Science.  Montreal  meeting,  1884.  For  the  full  paper  see  Trans.  B.  A.  A.  S., 
1884—"  On  the  Theory  of  the  Steam-engine;"  also  "The  Development  of  the 
Philosophy  of  the  Steam-engine;"  R.  H.  Thurston;  N.  Y.,  1889. 


254  A    MANUAL   OF    THE   STEAM-ENGINE 

value  of  the  equivalent.  Two  years  later  he  obtained  781.5 
and  782.1  respectively;  the  mean  of  which  is  781.8.  He,  in 
1849,  undertook  a  final  determination  of  the  equivalent,  and 
carried  out  a  series  of  forty  experiments  on  the  friction  of 
water,  fifty  on  the  friction  of  mercury,  and  twenty  on  the  fric- 
tion of  cast-iron  plates,  from  which  he  deduced  the  value,  772 
foot-pounds,  which  was  accepted  for  a  generation.  His  later 
determination,  made  for  the  British  Association,  1876,  was 
774.1,  with  a  possible  error  of  small  amount.  Still  later  deter- 
minations indicate  a  higher  value. 

Julius  Robert  Mayer  was  engaged,  at  the  same  time,  upon 
investigations  of  equal  importance,  carried  on  in  an  entirely 
different  manner.  In  1840,  a  physician  on  the  island  of  Java, 
he  noticed  that  the  venous  blood  of  his  patients  was  unusually 
red.  He  concluded  that  it  was  owing  to  the  fact  that  a  less 
amount  of  oxidation  of  the  tissues  of  the  body  would  keep  up 
the  bodily  heat  in  a  hot  country  than  would  be  required  in  a 
colder  one.  Following  up  this  thought,  he  came  to  the  con- 
clusion that  a  fixed  relation  must  exist  between  heat  and  work. 
In  1842  he  made  the  attempt  to  determine  this  relation  numeri- 
cally. Professor  Tyndall  thus  describes  his  reasoning  :  "  It  was 
known  that  a  definite  amount  of  air,  in  rising  one  degree  in 
temperature,  can  take  up  two  different  amounts  of  heat.  If  its 
volume  be  kept  constant,  it  takes  up  one  amount ;  if  its  pres- 
sure be  kept  constant,  it  takes  up  a  different  amount.  These 
two  amounts  are  called  the  specific  heats  under  constant  vol- 
ume and  under  constant  pressure.  The  ratio  of  the  first  to  the 
second  is  as  I  :  1.421."  Dr.  Mayer  "first  saw  that  the  excess 
.421  was  not,  as  then  universally  supposed,  heat  actually  lodged 
in  the  gas,  but  heat  which  had  been  actually  consumed  by  the 
gas  in  expanding  against  pressure.  The  amount  of  work  here 
performed  was  accurately  known  ;  the  amount  of  heat  con- 
sumed was  also  accurately  known ;  and  from  these  data  Mayer 
determined  the  mechanical  equivalent  of  heat.  Even  in  this 
first  paper  he  is  able  to  direct  attention  to  the  enormous  dis- 
crepancy between  the  theoretic  power  of  the  fuel  consumed  in 
steam-engines  and  their  useful  effect."  "As  regards  the  mechani- 


THE  PHILOSOPHY  OF   THE   STEAM-EXG1XE.  2$$ 

cal  theory  of  heat,  this  obscure  Heilbronn  physician,  in  the  year 
1842,  was  in  advance  of  all  the  scientific  men  of  the  time." 

In  a  paper  read  before  the  Royal  Society  in  1878,  Joule 
stated  that,  taking  the  unit  of  heat  as  that  which  can  raise  a 
pound  of  water  (weighed  in  a  vacuum)  from  60°  to  61°  F.  on  the 
mercurial  thermometer,  its  mechanical  equivalent,  reduced  to 
the  sea-level  and  to  the  latitude  of  Greenwich,  is  7/2.55  foot- 
pounds. Favre  deduced  753  from  the  friction  of  steel  on  steel, 
and  807  from  the  heat  absorbed  by  an  electromagnetic  engine 
for  the  production  of  work.  Him  deduced  787  from  the  fric- 
tion of  liquids,  and  775  from  the  compression  of  lead.  Quintus 
Icilius  deduced  714^  from  the  heat  developed  in  an  electric  cir- 
cuit. By  comparing  the  work  expended  in  revolving  the  plate 
of  a  Holtz  electrical  machine  with  the  heat  produced  by  the 
resulting  current,  Rosetti  deduced  776.1  foot-pounds.  Le 
Roux,  from  the  heat  produced  by  rotating  a  tube  full  of  water 
in  a  magnetic  field,  found  835.  Violle,  by  similar  experiments 
on  disks  of  metal  in  the  place  of  water,  found  793.2  with  copper, 
794.3  with  tin,  797.3  wjth  lead,  and  792.7  with  aluminium. 
Bartoli  deduced  771.12  from  the  friction  of  mercury  in  small 
tubes.  By  a  careful  study  of  the  velocity  of  sound  in  gases, 
Regnault  re-determined  the  ratio  of  the  two  specific  heats  of 
gases  used  by  Mayer  in  his  first  calculation.  Regnault's  result 
was  1.3945,  instead  of  1.421  ;  and  from  this  and  other  data 
Mayer's  calculation,  repeated,  gave  794.8. 

Prof.  Henry  A.  Rowland  finally  made  a  determination  of 
the  equivalent,  and  his  investigations  involved  many  difficult 
problems  in  thermometry.  He  found  that  the  specific  heat  of 
water  is  greater  near  the  freezing-point  than  at  and  near  8oc. 
Rowland's  result  gives  the  mechanical  equivalent  of  heat  as 
778  foot-pounds  at  39.2°  F.,  the  temperature  being  measured 
by  a  mercurial  thermometer,  and  783  foot  pounds  if  by  an  air- 
thermometer. 

The  value  of  the  mechanical  equivalent  of  heat  is  thus,  very 
possibly, 

778  ft.-lbs.  per  B.  T.  U. ; 

426.8  kilogrammetres  per  calorie ; 


256  A  MANUAL    OF    THE   STEAM-ENGINE. 

and  is  considered  probably  correct  to  within  0.003  of  its  own 
value  ;  i.e.,  it  may  be  as  low  as  776  or  as  high  as  780. 

56.  The  Science  of  Thermodynamics  has  for  its  essential 
basis  the  established  fact  of  the  dynamical  nature  of  heat,  and 
the  fact  of  the  quantivalence  of  two  forms  of  energy — heat  and 
mechanical  motion,  molecular  energy  and  mass  energy.  Rest- 
ing, as  it  does,  on  fundamental,  experimentally  determined, 
principles,  it  could  have  no  existence  until,  during  the  early 
part  of  the  present  century,  these  phenomena  and  these  truths 
were  well  investigated  and  firmly  established. 

The  first  period  of  the  development  of  the  science  was 
occupied  almost  exclusively  by  the  exposition  of  the  dynamical 
theory  of  heat,  which  lies  at  the  bottom  of  the  whole.  Mohr, 
in  1837;  Seguin,  in  1839;  Mayer,  of  Heilbronn,  in  1842;  and 
Colding,  in  1843,  each  took  a  step  into  a  field,  the  limits  of 
which  and  the  importance  of  which  they  could  at  that  time 
hardly  have  imagined.  Mayer  had  a  very  clear  conception  of 
the  bearing  of  the  new  theory  of  heat  upon  dynamics,  and  ex- 
hibited remarkable  insight  into  the  far-reaching  principles  of 
the  new  science.  He  collated  the  facts  more  exactly  deter- 
mined later  by  Joule  and  others  with  the  principle  of  the  con- 
servation 01  energy,  and  applied  the  rudiments  of  a  science 
thus  constructed  to  the  calculation  of  the  quantity  of  carbon 
and  expenditure  of  heat  which  are  unavoidably  needed  by  a 
mountain-climber,  doing  a  given  quantity  of  work,  in  the  ele- 
vation of  his  own  body  to  a  specified  height.  The  work  of 
Mayer  may  be  taken  as  representing  the  first  step  in  the  pro- 
duction of  a  Science  of  Thermodynamics,  and  in  the  deduction 
of  consequences  of  the  fact  which  had,  until  his  time,  so  seldom 
engaged  the  attention  of  men  of  science.  It  was  only  at  about 
the  middle  of  the  nineteenth  century  that  it  began  to  be  plainly 
seen  that  there  existed  such  a  science,  and  that  the  dynamic 
equivalence  of  heat,  and  energy  in  the  mechanical  form,  was 
but  a  single  fact,  which  must  be  taken  in  connection  with  the 
general  principles  of  the  persistence  of  energy,  and  applied  in 
all  cases  of  performance  of  work  by  expenditure  of  heat  through 
the  action  of  elastic  bodies. 


TOE  PHILOSOPHY  OF  THE  STEAJf-EXCIA'E.  257 

In  1850,  Qausius*  adapted  Garnet's  anvesttigatloims  as  the 
correct  theory  of  thermodynamics,  to  accord  with  the  laws  off 
Modern  thermodynamics.  Qausius*  then  stated  Caroot's 
principle  as  follows :  * 

Whenever  heat  is  converted  Into  work,  amathfr  qmamtilj  of 
heat  must,  during  the  working  cycle,  be  transferred  from  a 
hotter  body  to  a  colder  body  ;  the  amount  transferred  depends 
only  on  the  temperatures  between  which  the  transfer  Is 
effected,  and  not  on  the  nature  of  the  body  acting  as  Its  ve- 


This  is  Carnot's  principle,  and  a  direct  consequence  of  the 
second  law  of  thermodynamics. 

57.  The  Theory  of  the  Steam-engine,  like  every  other 
scientific  system,  rests  upon  a  foundation  of  facts  ascertained 
by  experiment,  and  of  principles  determined  by  the  careful 
study  of  the  laws  relating  to  those  facts,  and  controlling  phe- 
'  •mm  in  properly  classed  together  by  that  science.  Like  every 
other  element  entering  into  the  composition  of  a  scientific 
system,  this  theory  has  been  developed  subsequently  to  the 
establishment  of  its  fundamental  facts,  and  the  history  of 
progress  in  the  art  to  which  it  relates  shows  that  the  art  has 
led  the  science  from  the  first.  The  theory  of  the  steam-engine 
includes  all  the  phenomena  and  all  the  principles  involved  in 
the  production  of  power,  by  means  of  the  steam-engine,  from 
the  heat-energy  derived  from  the  chemical  combination  of  a 
combustible  with  the  oxygen  of  the  air  acting  as  a  supporter  of 
the  combustion.  The  remaining  portion  of  this  chapter  will 
be  devoted  to  the  tracing  of  the  growth  of  the  theory  of 
the  steam-engine,  simply  as  a  mechanical  instrument  for 
transformation  of  the  one  form  of  energy  into  the  other — 
of  the  molecular  energy  of  heat-motion,  as  stored  In  the  vapor 
of  water,  into  mass-energy,  or  mechanical  energy,  as  applied  to 
the  driving  of  mechanism.  The  theory  thus  limited  Includes 
a  study  of  the  thermodynamic  phenomena,  as  the  principal 


2$8  A    MANUAL   OF   THE   STEAM-ENGINE. 

and  essential  operations  involved  in  the  performance  of  work 
by  the  engine ;  it  further  includes  the  consideration  of  the 
other  physical  processes  which  attend  this  main  function  of 
the  engine,  and  which,  inevitably  and  unavoidably,  so  far  as  is 
to-day  known,  concur  in  the  production  of  a  waste  of  energy. 

Of  all  the  heat  sent  forward  by  the  steam-boiler  to  the 
engine,  a  certain  part,  definite  in  amount  and  easily  computed 
when  the  power  developed  is  known,  is  expended  by  transfor- 
mation into  mechanical  energy;  another  part,  equally  definite 
and  easily  calculated,  also,  is  expended  as  the  necessarily  occur- 
ring waste  which  must  take  place  in  all  such  transformations, 
at  usual  temperatures  of  reception  and  rejection  of  heat ;  still 
another  portion  is  lost  by  conduction  and  radiation  to  surround- 
ing bodies ;  and,  finally,  a  part,  often  very  large  in  comparison 
with  even  the  first  and  principal  of  these  quantities,  is  wasted 
by  transfer,  within  the  engine,  from  the  induction  to  the  educ- 
tion side,  "  from  steam  to  exhaust,"  by  a  singular  and  interest- 
ing process,  without  conversion  into  useful  effect,  and  by  the 
familiar  processes  of  transfer.  The  science  of  thermodynamics 
only  takes  cognizance  of  the  first  and  second,  which  are  some- 
times among  the  smallest,  of  these  expenditures.  The  science 
of  the  general  physics  of  heat  takes  cognizance  of  the  others 
and  enables  us  to  approximately  compute  their  magnitude. 

The  Science  of  the  Steam-engine  must,  like  every  other 
branch  of  applied  science,  be  considered  as  the  result  of 
two  distinct  processes  of  development :  the  one  is  what  may 
be  called  the  experimental  development  of  the  subject ;  the 
other  is  the  purely  theoretical  progress  of  the  science.  So  far 
as  the  useful  application  of  correct  principles  to  the  improve- 
ment of  the  machine  is  concerned,  the  latter  has  always,  as  is 
usually  the  case  elsewhere,  been  in  advance  of  the  former  in  its 
deduction  of  general  principles  ;  while,  as  invariably,  the  former 
has  kept  far  in  advance,  in  the  working  out  of  practically  use- 
ful results,  and  in  the  determination  of  the  exact  facts  where 
questions  of  economic  importance  have  arisen. 

58.  Carnot's  Work  lies  at  the  foundation  of  the  science  of 
the  steam-engine,  and  its  exposition  may  be  found  in  his 


THE  PHILOSOPHY  OF   THE   STEAM-ENGIXE.  259 

"Reflexions  sur  la  Puissanct  Metric*  du  Feu"*  He  assumed 
the  truth  of  the  theory  of  substantial  caloric ;  nevertheless,  in 
his  development  of  the  theory  of  heat-engines,  he  enunciated 
some  essential  principles,  and  thus  laid  the  foundation  for  a 
theory  of  the  steam-engine  which  was  given  correct  form,  in  all 
its  details,  as  soon  as  the  dynamical  theory  was  taken  for  its 
foundation-principle.  Carnot  asserts  that  "  the  motive  power 
of  heat  is  independent  of  the  means  taken  to  develop  it ;  its 
amount  is  determined,  simply,  by  the  temperature  of  the  bodies 
between  which  the  heat  is  transferred.  Wherever  there  exists  a 
difference  of  temperature,  there  may  be  a  development  of  power. 
The  maximum  amount  of  power  obtainable  by  the  use  of  steam 
is  the  maximum  obtainable  by  any  means  whatever.  High-pres- 
sure engines  derive  their  advantage  over  low-pressure  engines 
simply  from  their  power  of  making  useful  a  greater  range  of 
temperature."  He  made  use  of  the  device  known  as  the 
"  Carnot  Cycle,"  exhibiting  the  successive  expansions  and  com- 
pressions of  the  working  fluid  in  heat-engines,  in  the  process  of 
change  of  volume  and  temperature,  while  following  the  series 
of  changes  which  gives  the  means  of  transformation  of  heat 
into  power  with  final  restoration  of  the  fluid  to  its  initial  con- 
dition, showing  that  such  a  complete  cycle  must  be  traversed 
in  order  to  determine  what  proportion  of  the  heat-energy  avail- 
able can  be  utilized  by  conversion  into  mechanical  energy. 
This  is  one  of  the  most  essential  of  all  the  principles  compre- 
hended in  the  modern  science.  This  "  Carnot  Cycle "  was, 
afterward,  represented  graphically  by  Clapeyron. 

Carnot  shows  that  the  maximum  possible  efficiency  of  fluid 
is  attained,  in  heat-engines,  by  expanding  the  working  fluid 
from  the  maximum  attainable  temperature  and  pressure  down 
to  the  minimum  temperature  and  pressure  that  can  be  per- 
manently maintained  on  the  side  of  condensation  or  rejection, 
i.e.,  if  we  assume  expansion  according  to  the  hyperbolic  law, 

*  Reflexions  sur  la  Puissance  Motrice  da  Feu;  Paris,  1824;  repnbiisbed  by 
Gamhier-Villars:  Paris,  1878.  See,  also,  the  Author's  edition:  "  Reflections  on 
the  Motive  Power  of  Heat,  bj  N.-L-Sadi  Carno*;"  with  notes;  X.  Y.,  J.  Wiley 
A:  Sons. 


260  A    MANUAL   OF   THE   STEAM-ENGINE. 

by  adopting,  as  the  ratio  of  expansion,  the  quotient  of  maxi- 
mum pressure  divided  by  back  pressure.  He  further  shows 
that  the  expansion,  to  give  maximum  efficiency,  should  be  per- 
fectly "  adiabatic."  *  He  even  suggests  that  the  adiabatic  ex- 
pansion of  steam  may  result  in  its  own  condensation,  a  fact  a 
generation  later  discovered  and  proven  by  Rankine  and  Clau- 
sius.  These  principles  have  been  recognized  as  correct  by  all 
authorities,  from  the  time  of  Carnot  to  the  present  day,  and 
have  been,  not  infrequently,  brought  forward  as  new  by  minor 
later  writers  unfamiliar  with  the  literature  of  the  subject.  In- 
troducing into  the  work  of  Carnot  the  dynamical  relation  of 
heat  and  work,  a  relation,  as  shown  by  other  writings,  well 
understood,  if  not  advocated  publicly  by  him,  the  theory  of  the 
steam-engine  becomes  well  defined  and  substantially  accurate. 
The  Count  de  Pambour,  writing  in  1835,  and  later,  takes  up 
the  problem  of  maximum  efficiency  of  the  steam-engine,  shows 
the  distinction  to  be  drawn  between  the  efficiency  of  fluid  and 
efficiency  of  machine,  and  determines  the  value  of  the  ratio  of 
expansion  for  maximum  efficiency  of  engine.  He  makes  this 
ratio  equal  to  the  quotient  of  maximum  initial  pressure  divided 
by  the  sum  of  the  useless  internal  resistances  of  the  engine, 
including  back  pressure  and  friction,  and  reduced  to  equivalent 
pressure  per  unit  of  area  of  piston.  This  result  has  been  gen- 
erally accepted,  although  sometimes  questioned,  and  has  been 
demonstrated  anew,  in  apparent  ignorance  of  the  fact  of  its 
prior  publication  by  De  Pambour,  by  more  than  one  later 
writer.  De  Pambour,  applying  his  methods  to  the  locomotive, 
particularly,  solved  the  problem,  since  distinctively  known  by 
his  name :  Given  the  quantity  of  steam  furnished  by  the  boiler 
in  the  unit  of  time,  and  the  measure  of  resistance  to  the  mo- 
tion of  the  engine ;  to  determine  the  speed  attainable.  Pro- 
fessor Thomas  Tate,  writing  his  "  Mechanical  Philosophy,"  in 
'853'  gives  the  principle  stated  above  a  broader  enunciation, 
thus :  "  The  pressure  of  the  steam,  at  the  end  of  the  stroke,  is 
equal  to  the  sum  of  the  resistances  of  the  unloaded  engine, 

*  For  definition  of    this  and  related  terms,  see   chapter  on  the  Thermody- 
namics of  the  -    Jam-engine. 


THE  PHILOSOPHY  OF  T3E  STEAM-EA"GI.\E.  26l 

whatever  may  be  the  law  expressing  the  relation  of  volume 
and  pressure  of  steam." 

The  development  of  the  Science  of  Thermodynamics  into 
available  and  satisfactory  form  was  effected  mainly  by  Pro- 
fessors Rankine  and  Clausius,  working  independently  but  con- 
temporaneously  from  1849. 

Combes,  in  papers  presented  to  and  published  by  the  Aca- 
demic des  Sciences,  was  probably  the  first  to  introduce  into  the 
theory  of  the  steam-engine  the  consideration  of  that  phenome- 
non, discovered  by  Watt,  to  check  the  wasteful  effects  of 
which  the  latter  invented  the  steam-jacket.*  That  author 
gradually  gave  shape  to  his  ideas,  as  time  went  on.  publishing 
them  in  1845.+  *°d.  later,  in  1863-67.*  He  even  anticipates 
Rankine  and  Clausius  in  one  of  their  most  famous  discoveries, 
saying:  "  La  rapatr  d'fan.  a  Fetal  dt  saturation  ft  entffremenl 
secke,  st  dilatait  sans  addition  mi  soustraction  de  chaltmr ;  ft 
nous  anms  montrf  qne  F expansion  cst  alors  Offompagn/e  tfitmf 
Halt/faction  part  if  Ik  de  rapettr.  Ccst  a  pat  pres  ainsi  qmf  Us 
choses  doirmt  Sf  passer  dans  /fs  machines  a  vapcmr  ordinahres." 
He  goes  on  to  describe  very  clearly  the  phenomenon  of  «  cyl- 
inder-condensation  ;"*  but  in  his  later  works  he  seems  to  have 
paid  less  attention  to  this  action,  and  may  not  have  fully  real- 
ized its  importance:  but  his  conception  of  the  processes  in- 
volved in  such  wastes,  and  in  the  preventive  action  of  the 
jacket,  was  exact  and  well  expressed. 

59.  Clausius'  Work  began  at  some  time  preceding  1850. 
He  applied  the  modern  theory  of  the  steam-engine  to  the 
solution  of  the  various  problems  which  arise  in  the  practice  of 
the  engineer,  so  far  as  they  can  be  solved  by  the  principles  of 
thermodynamics.  His  papers  on  this  subject  were  printed  in 
1850.$  The  Count  de  Pambour  had  taken  a  purely  mechani- 
cal mode  of  treatment,  basing  his  calculations  of  the  work 


:•-} 


|  Principes  de  la  Tbterie  Ufrmnqpr  de  la  Chalew. 

§  PoggendocTs  Annalca,  iSsoet  srq. 

of  Heat;'  translated  br  W.  R.  Browne;  London.  1879. 


262  A   MANUAL    OF   THE   STEAM-ENGINE. 

done  in  the  cylinder  of  the  steam-engine  upon  the  hypothesis 
of  Watt,  that  the  weight  of  steam  acting  in  the  engine  re- 
mained constant  during  expansion,  and  that  the  same  assump- 
tion was  applicable  to  the  expanding  mass  contained  in  engine 
and  boiler  during  the  period  of  admission.  He  had  con- 
structed empirical  formulas,  published  in  his  work  on  the  theory 
of  the  steam-engine,  in  1844,  for  the  relation  of  volume  and 
pressure,  during  expansion,  and  had  based  his  determinations 
of  the  quantity  of  work  done,  and  of  expenditure  of  steam  in 
the  engine,  upon  this  set  of  assumptions  and  formulas,  consid- 
ering the  steam  to  remain  in  its  initial  condition  of  dry  and 
saturated  vapor,  or  of  moist  vapor,  as  the  case  may  be,  from 
the  beginning  to  the  end  of  the  stroke.  Errors  were  thus  in- 
troduced, which,  although  not  important  in  comparison  with 
those  often  occurring  when  the  results  of  purely  thermo- 
dynamic,  and  in  so  far  correct,vtreatmenl  was  compared  with 
the  actual  case,  were,  nevertheless,  sufficiently  great  to  become 
noticeable  when  the  true  theory  of  heat-engines  became 
known,  and  correctly  applied.  Clausius  proved  that,  in  the 
expansion  of  dry  and  saturated  steam,  doing  work  in  the 
engine,  condensation  must  take  place  to  a  certain  extent,  and 
that,  consequently,  the  weight  of  steam  in  the  cylinder  must 
be  somewhat  reduced  by  the  process  of  expansion  beyond  the 
point  of  "  cut-off."  During  the  period  of  compression,  also, 
the  reverse  effect  must  occur,  and  the  compressed  mass  must 
become  superheated,  if  initially  dry.  He  showed  that  the 
amount  of  work  actually  done  in  a  non-conducting  working 
cylinder  must  be  sensibly  different  from  that  estimated  by  the 
method  of  De  Pambour.  Taking  advantage  of  the  re-deter- 
mination of  the  constants  in  Regnault's  equations  effected  by 
Moritz,  Clausius  obtains  numerical  results  in  the  application 
of  the  true  theory,  and  deduces  the  amount  of  work  done  in 
the  steam-engine  under  various  conditions  such  as  are  met 
with  in  practice.  He  shows  how  the  action  of  the  engine  may 
be  made  that  of  the  Carnot  Cycle,  and  determines  the  effect 
of  variation  of  the  temperature  of  the  "  prime"  steam.  The 
investigation  is,  in  the  main,  purely  theoretical ;  no  application 


THE  PHILOSOPHY  OF   THE   STEAM-ENGIXE.  263 

is  made  to  the  cases  met  with  in  real  work,  and  the  compari- 
son of  the  results  of  the  application  of  the  new  theory  to 
practice  in  steam-engineering  is  left  to  others. 

The  work  of  Clausius  is,  throughout,  perfectly  logical,  and 
beautifully  simple  and  concise,  and  his  application  of  the 
theory  to  the  steam-engine  amounts  to  a  complete  reconstruc- 
tion of  the  work  of  Carnot,  and  his  followers,  upon  a  correct 
basis.  He  develops  with  mathematical  exactness  of  method 
and  work  the  fundamental  principles  of  the  science  of  thermo- 
dynamics, constructs  the  .«*  fundamental  equations,"  the  so- 
called  "  General  Equations  of  Thermodynamics,"  and,  in  the 
course  of  his  work,  proves  the  fact  of  the  partial  condensation 
of  saturated  steam,  when  permitted  to  expand  doing  work 
against  resistance. 

60.  Rankine  began  his  work  upon  the  theory  of  the  trans- 
formation of  heat  into  mechanical  energy  at  about  the  same 
time  with  Clausius  (1849),  an<^  published  his  first  important 
deduction,  the  form  of  the  General  Equation  of  Thermo- 
dynamics, nearly  simultaneously,  but  a  little  earlier.*  He 
gave  much  attention  to  the  then  incomplete  work  of  develop- 
ment of  applied  thermodynamics,  and  produced  not  only  the 
whole  theory  of  the  science,  but  very  extended  papers,  includ- 
ing solutions  of  practical  problems  in  the  application  of  the 
science  to  heat-engines.  Stating  with  singular  brevity  and 
clearness  the  main  principles,  and  developing  the  general 
equations  in  substantially  the  same  form,  but  by  less  easily 
followed  processes,  than  his  contemporary,  he  proceeded  at 
once  to  their  application.  He  determines  the  thermodynamic 
functions  for  air  and  other  gases,  exhibits  the  theory  of  the 
hot-air  engine,  as  applied  to  the  more  important  and  typical 
forms,  deduces  expressions  for  their  efficiency,  and  estimates 
the  amount  of  heat  demanded,  and  of  fuel  consumed,  in  their 
operation,  assuming  no  other  expenditure  of  heat  than  that 
required  in  an  engine  free  from  losses  by  conduction  and  radia- 
tion. He  next,  in  a  similar  manner,  applies  the  theory  to  the 

*  Trans.  Royal  Soc.  of  Edinburgh.  1850  et  seq.  Sec,  also,  Rankine's  "  Mis- 
cellaneous Papers"  and  his  "  Manual  of  the  Steam-engine." 


264  A   MANUAL   OF   THE   STEAM-ENGINE. 

steam-engine,  proves  the  fact  of  the  condensation  of  steam 
during  the  period  of  expansion,  estimates  the  amount  of  heat, 
fuel,  and  steam  expended,  and  the  quantity  of  work  done,  and 
determines  thus  the  efficiency  of  the  engine.  He  makes  a 
special  case  of  the  engine  using  superheated  steam,  as  well  as 
that  of  the  "jacketed"  engine,  considers  the  superheated 
steam-engine,  and  the  binary-vapor  engine,  and  reconstructs 
De  Pambour's  problem ;  applying  the  theory  in  the  applica- 
tion of  mechanics  to  general  engineering.  Several  important 
text-books,  a  large  volume  on  shipbuilding,  and  other  works, 
with  an  unknown  number  of  papers,  published  and  unpublished, 
form  a  monument  to  the  power  and  industry  of  this  wonderful 
man  and  remarkable  genius,  that  may  be  looked  upon  as  per- 
haps the  greatest  wonder  of  the  intellectual  world.  Thus, 
Rankine,  producing,  in  part,  the  same  results  as  Clausius,  by 
his  wonderfully  condensed  method  of  treatment,  turned  his 
attention  more  closely  to  the  application  of  the  theory  to  the 
case  of  the  steam-  and  other  heat-engines,  giving,  finally,  in  his 
"Prime  Movers"  (1859),  a  concise  yet  full  exposition  of  the 
correct  theory  of  those  motors,  so  far  as  it  is  possible  to  do  so 
by  purely  thermodynamic  treatment.  He  was  unaware,  ap- 
parently, as  were  all  the  scientific  men  of  his  time,  of  the  ex- 
tent to  which  the  conclusions  reached  by  such  treatment  of 
the  case  are  modified,  in  real  engines,  by  the  interference  of 
other  physical  principles  than  those  taken  cognizance  of  by  his 
science. 

Sir  William  Thomson,  partly  independently,  and  partly 
working  with  Joule,  has  added  much  valuable  work  to  that 
done  by  Clausius  and  Rankine.*  In  the  hands  of  these  great 
men  the  science  took  form,  and  has  now  assumed  its  place 
among  the  most  important  of  all  branches  of  physical  science. 

It  was  Sir  William  Thomson  who  discovered  and  revealed 
to  English  readers  the  remarkable  work  of  Carnot  and  thus 
effectively  aided  in  the  construction  of  the  science.  As  stated 
by  Rankine  :f 

*Edio.  Trans.,  1850  etseq.;  Phil.  Mag.;  and  Mathematical  and  Physical 
Papers. 

t  Steam-engine;  Introduction,  p.  xxxi. 


THE  PHILOSOPHY  OF  THE  STEAM-EXGIXE.  265 

-  Professor  \\THiam  Thomson,  adopting  the  true  theory  of 
beat,  in  1850,,  not  only  solved  some  new  problems  in  thermo- 
dynamics; and  devised  and  carried  out.  jointly  with  Mr.  Joule, 
some  most  important  experiments ;  but  be  extended  analogous 
principles  to  electricity  and  magnetism,  and  thereby  created 
what  may  justly  be  styled  a  new  science.  His  papers  have 
appeared  in  the  Transactions  of  the  Royal  Society  of  Edin- 
burgh for  1851,  and  subsequently  in  the  Philosophical  Maga- 
zine since  185 1.  and  the  Philosophical  Transactions  since  1854. 
Numerical  data,  without  which  the  theoretical  researches  before 
referred  to  would  have  been  fruitless,  were  furnished  by  the  ex- 
periments of  Dulong.  and  MM.  Bravais,  Martins,  Moll,  Van 
Beck,  and  others,  on  the  velocity  of  sound :  by  those  of  M.  Rnd- 
berg.  on  the  expansion  of  gases;  by  the  experiments,  almost 
unparalleled  for  extent  and  precision,  of  M.  Regnaulton.  the 
properties  of  gases  and  vapors,  made  at  the  expense  of  the 
French  Government,  and  published  in  the  Proceedings  and 
Memoirs  of  the  Academy  of  Sciences,  from  1847  to  1854: 
and  by  the  joint  experiments  of  Messrs.  Joule  and  Thomson, 
on  the  thermic  effects  of  currents  of  elastic  fluids,  made  at 
the  expense  of  the  Royal  Society,  and  published  in  the  Philo- 
sophical Transactions  for  1854.** 

Rankine  concludes:  ""Although  the  mechanical  hypothesis 
just  mentioned  may  be  useful  and  interesting  as  a  means  of 
anticipating  laws,  and  connecting  the  science  of  thermodyna- 
mics with  that  of  ordinary  mechanics,  still  it  is  to  be  remem- 
bered that  the  science  of  thermodynamics  is  by  no  means 
dependent  for  its  certainty  upon  that  or  any  other  hypothe- 
sis, having  been  now  reduced  to  a  system  of  principles. 
or  general  facts,  expressing  strictly  the  results  of  experi- 
ment as  to  the  relations  between  heat  and  motive  power. 
In  this  point  of  view  the  laws  of  thermodynamics  may 
be  regarded  as  particular  cases  of  more  general  laws,  ap- 
plicable to  all  such  states  of  matter  as  constitute  Energy,  or 
the  capacity  to  perform  work,  which  more  general  laws  form 
the  basis  of  the  sdnue  of  cmrrgrtics. — a  science  comprehend- 


266  A   MANUAL    OF   THE   STEAM-ENGINE. 

ing,  as  special  branches,  the  theories  of  motion,  heat,  light, 
electricity,  and  all  other  physical  phenomena." 

The  physicist,  as  well  as  the  engineer,  is  still  seeking  to  as- 
certain more  definitely  what  is  the  mechanism  of  heat-energy 
transmission.  It  is  now  well  ascertained  that  both  heat  and 
light  are  originally,  in  space,  methods  of  vibration,  of  oscilla- 
tion, or  of  translation  of  particles  of  a  fluid  known  as  the  "  lumi- 
niferous  sether ;"  but  the  physical  characteristics  of  that  fluid 
are  not  yet  defined  with  certainty.  The  researches  of  Hertz 
and  others  seem  to  indicate  the  probability  that  Clerk  Max- 
well's suggestion  that  this  method  of  transfer  of  energy  may 
be  electromagnetic  in  character.  Professor  D.  V.  Wood,  tak- 
ing up  the  mathematical  physics  of  the  subject,  deduces  by  a 
simple  process,  based  on  probably  substantially  accurate  data,* 
as  follows: 

(1)  This  medium  transmits  energy  at  the  rate  of  186,300 
miles  per  second. 

(2)  Heat-energy  is  transferred  from  the  sun  to  the  earth  at 
the  rate  of  133  foot-pounds  per  square  foot  of  section  of  the 
transmitted  beam. 

(3)  The  medium  may  be  taken  as  possessing  the  character- 
istics of  the  sensibly  perfect  gas. 

His  process  gives  at  once  the  essential  physical  character- 
istics of  a  fluid  capable  of  transmitting  this  known  quantity  of 
energy  at  this  observed  velocity.  It  must  be  a  medium  of 
which  one  pound  would  occupy  about  twenty  times  the  volume 
of  the  earth  ;  its  tension  would  be  one  pound,  nearly,  per 
square  mile  of  section  ;  and  its  specific  heat  must  be  about 
4,600,000,000,000,  that  of  water  being  taken  as  unity.  It 
would  weigh  one  pound  to  every  72  X  IO21  cubic  feet ;  the  heat- 
vibrations  are  about  6x  IO14  per  second  ;  and  it  is  "  everywhere 
practically  non-resisting,  uniform  in  temperature,  density,  and 
elasticity,"  whether  in  the  depths  of  space  and  at  its  own  boun- 
dary, if  it  has  one,  or  at  the  surface  of  the  sun  or  of  the  largest 


*  Philosophical   Magazine,    Nov.    1885;     Van    Nostrand's    Science    Series, 
No.  85. 


THE  PHILOSOPHY  OF   THE   STEAM-EXGINE.  267 

star  in  the  universe.  It  would  not  destroj-  the  motion  of  the 
average  comet  in  a  million  of  millions  of  years. 

6z.  The  Thermodynamic  Theory  of  the  Steam-engine 
stands,  to-day,  substantially  as  it  was  left  by  Clausius  and  Ran- 
lane  and  Thomson,  at  the  close  of  their  work  in  this  field,  in 
the  decade  1850  to  1860.  Many  treatises  have  been  published. 
some  of  them  by  men  of  exceptional  ability  ;  but  all  have  fol- 
lowed the  general  line  first  drawn  by  these  masters,  and  have 
only  now  and  then  found  some  minor  point  to  develop. 

Combes,  Zeuner,  and  other  writers  have  developed  the  sub- 
ject in  detail,  the  latter,  especially,  studying  the  theory  of 
various  working  fluids,  as  of  superheated  steam,  and  the  phe- 
nomena of  heat-transformation  in  relation  to  their  effect  upon 
the  working  substance.  The  pure  theory  of  thermodynamics 
was  substantially  complete,  however,  long  ago.  and  no  impor- 
tant developments  are  to  be  now  anticipated,  except  as  ele- 
ments in  the  expansion  of  similar  principles  into  the  broader 
field  of  energetics. 

02.  The  Limitations  of  thermodynamic  theory  and  of  iis 
application  in  the  design  and  operation  of  heat-engines  were 
first  discovered  by  James  Watt.  They  were  systematically 
and  experimentally  investigated  by  Clark,  in  1852  and  earlier, 
were  observed  and  correctly  interpreted  by  Him  (1855-71,  an<d 
were  revealed  again  by  the  experiments  of  Isherwood  (18601. 
and  by  those  of  Emery  and  many  other  recent  investigators 
on  both  sides  of  the  Atlantic.  These  limitations  are  due  to 
the  fact  that  losses  occur  in  the  operation  of  such  engines 
which  are  not  taken  into  account  by  the  hitherto  accepted 
theory  of  the  engine,  and  have  no  place  in  the  thermodynamic 
treatment  of  the  case. 

It  is  assumed,  in  the  purely  thermodynamic  theory  of  the 
engine,  that  the  expansion  of  the  working  fluid  takes  place  in 
a  cylinder  having  walls  impermeable  to  heat,  and  in  which  no 
losses  by  conduction  or  radiation,  or  by  leakage,  can  occur. 
Of  those  losses  which  actually  take  place  in  the  real  engine, 
that  due  to  leakage  may  be  prevented,  or,  if  occurring,  can  be 
checked ;  but  it  is  impossible,  so  far  as  is  now  known,  to  secure 


268  A    MANUAL    OF   THE   STEAM-ENGINE.  J 

a  working  cylinder  of  perfectly  non-conducting  material.  The 
consequence  is  that,  since  the  steam  or  other  working  fluid 
enters  at  a  high  temperature  and  is  discharged  at  a  compara- 
tively low  temperature,  the  surfaces  of  cylinder,  cylinder-heads, 
and  piston  are,  at  one  instant,  charged  with  heat  of  high  tem- 
perature, and  at  the  next  moment,  exposed  to  lower  tempera- 
tures, are  drained  of  their  surplus  heat,  which  heat  is  then 
rejected  from  the  cylinder  and  wasted.  Thus,  at  each  stroke, 
the  metal  surfaces,  exposed  to  the  action  of  the  expanding 
substance,  alternately  absorb  heat  from  it,  and  surrender  that 
heat  to  the  "  exhaust."  As  the  range  of  temperature  worked 
through  in  the  engine  increases,  as  the  quantity  of  steam 
worked  per  stroke  diminishes,  and  as  the  time  allowed  for 
transfer  of  heat  to  and  from  the  sides  and  ends  of  the  cylinder 
and  the  piston  is  increased,  the  magnitude  of  this  loss  increases. 
These  physical  phenomena  are  therefore  no  less  important  in 
their  influence  upon  the  behavior  of  the  engine,  and  upon  its 
efficiency,  and  are  no  less  essential  elements  for  consideration 
in  the  general  theory  of  the  engine  than  those  taken  into 
account  in  pure  thermodynamics.  Such  limitations  are 
studied  in  Chapter  V. 

63.  James  Watt  not  only  discovered  the  fact  of  the  exist- 
ence of  this  method  of  waste,  but  experimentally  determined 
its  amount  in  the  first  engine  ever  placed  in  his  hands.  It 
was  in  1763  that  he  was  called  upon  to  repair  the  little  model 
of  the  Newcomen  engine,  then  and  still  in  the  cabinets  of  the 
University  of  Glasgow.  Making  a  new  boiler,  he  set  up  the 
machine  and  began  his  experiments.  He  found,  to  his  surprise, 
that  the  little  steam-cylinder  demanded  four  times  its  own 
volume,  at  every  stroke,  thus  wasting,  as  he  says,  three  fourths 
of  the  steam  supplied,  and  requiring  four  times  as  much  "in- 
jection-water" as  should  suffice  to  condense  a  cylinderful  of 
steam.  All  of  Watt's  first  inventions  were  directed  toward  the 
reduction  of  this  immense  waste.  He  proposed  to  himself  the 
problem  of  keeping  the  cylinder  "as  hot  as  the  steam  that 
entered  it ;"  he  solved  this  problem  by  the  invention  of  the 
separate  condenser  and  the  steam-jacket,  and  the  discovery  of 


THE  PHILOSOPHY  OF  THE   STEAM-EXGIXE.  269 

these  limitations  of  the  thermodynamic  theory  and  their  re- 
duction was  the  source  of  Watt's  fame. 

John  Smeaton,  a  distinguished  contemporary  of  Watt, 
seems  to  have  been  not  only  well  aware  of  this  defect  of  the 
steam-engine,  but  was  possibly  even  in  advance  of  Watt  in  at- 
tempting to  remedy  it.  He  built  a  large  number  of  Xewcomen 
engines  between  1765  and  1770,  hi  some,  if  not  many,  of  which 
he  attempted  to  check  loss  of  this  "  cylinder-condensation  "  in 
engines,  some  of  which  were  five  and  six  feet  in  diameter  of 
cylinder,  by  lining  pistons  and  heads  with  wood. 

Notwithstanding  the  fact  that  this  waste  was  thus  familiar 
to  engineers,  from  the  time  of  the  invention  of  the  modern 
steam-engine,  and  was  recorded  in  all  treatises  on  engine  con- 
struction and  management,  the  writers  on  the  theory  have 
never  been  aware  that  it  gives  rise  to  the  production,  in  the 
working  cylinder,  of  a  large  amount  of  water  mingled  with  the 
steam.  It  has  often  been  assumed  by  engineers  themselves 
that  this  water  is  always  due  to  "priming"  at  the  boiler. 
Rankine,  while  correctly  describing  the  phenomenon  of  cylin- 
der-condensation, attributed  the  presence  of  the  water  in  steam- 
cylinders  to  the  fact  of  condensation  of  dry  steam  doing  work 
by  expansion,  apparently  not  until  later  having  noted  the  fact 
that  this  would  only  account  for  a  very  small  proportion  of 
the  moisture  actually  present  in  the  average  steam-engine. 
He  considered  incomplete  expansion  the  principal  source  of 
loss,  as  do  usually  other  writers  on  thermodynamics. 

Him  published  his  Memoir e  stir  FUtilitf  dfs  Envehppes  b 
Vapeur  in  1855.*  This  memorable  paper  gives  us  the  first 
precise  analysis  of  experiments  showing  the  quantitative 
measures  of  the  thermal  action  of  the  walls  of  the  steam-cylin- 
der. It  presents  an  exact  and  scientific  treatment  of  the  case, 
and  gives  indisputable  measures  of  the  quantity  of  heat  trans- 
ferred to  the  metal,  and  restored  to  the  steam  when  too  late 
for  transformation  into  its  proportion  of  mechanical  energy. 
In  every  experiment,  Him  measured  the  quantity  of  water  en- 

*  Bulletin  de  la  Soci&£  Indnstrielle  de  Molbouse;  t.  XXVTI.  pp.  105-206. 


2/O  A  MANUAL    OF   THE   STEAM-ENGINE. 

tering  the  boiler,  and  there  converted  into  steam,  and  compared 
it  with  the  quantity  of  steam  found,  at  each  step  in  the  engine- 
cycle,  in  the  cylinder.  He  even  went  so  far  as  to  determine, 
by  the  use  of  his  calorimeter,  the  quality  of  the  steam  entering 
the  engine,  in  order  that  his  measures  of  that  contained  in  the 
cylinder  might  not  be  rendered  uncertain  by  the  action  known 
as  priming  or  foaming  at  the  boiler.  He  also,  for  the  first 
time,  determined  the  weight  of  water  leaving  the  condenser, 
and  its  temperature,  thus  securing  the  elements  for  the  method 
of  computation  now  known  as  that  of  Farey  and  Donkin.  He 
proposed  no  theory,  believing,  as  he  stated  expressly,  that,  at 
the  time,  any  formulation  of  a  theory  was  impossible  without 
further  knowledge. 

As  a  result  of  his  first  series  of  experiments  he  was  able  to 
say :  "  The  influence  of  the  steam-jacket  is  now  clearly  ex- 
plained :  it  consists  in  preventing  the  steam  from  partially  con- 
densing, and  thus  lessening  the  pressure  during  expansion,  by 
that  act  itself.  As  the  heat  taken  from  the  jacket  is,  as  has 
been  seen,  a  small  fraction  of  the  total  heat  expended,  the  power 
so  gained  costs  very  little.  Were  any  doubt  now  to  exist  on 
this  point,  the  following  facts  would  completely  remove  them  : 

"  (i)  When  the  engine  is  working  with  jacket  in  use,  if  we 
suddenly  shut  off  the  steam  and  take  it  directly  to  the  cylinder, 
the  engine  continues  to  work,  as  before,  for  some  time,  as  if 
nothing  had  happened.  The  indicator-diagrams  are  precisely 
the  same  as  before ;  it  is  only  after  10  or  20  minutes  that  the 
power  of  the  engine  falls  off  23^  per  cent  in  this  case.  It  is 
thus  evidently  the  heat  in  the  walls  of  the  cylinder,  and  not  the 
simple  drying  of  the  steam,  which  gives  us  this  economy  of  23^ 
per  cent. 

"  (2)  The  jacket  actually  modifies  very  sensibly  the  tem- 
perature of  the  steam ;  for,  while  it  is  acting,  the  steam  ex- 
hausted into  the  condenser  is  at  64°  C,  at  a  tension  of  ora.o75 
while,  in  the  other  case,  the  temperature  falls  to  58°,  although 
its  tension  rises  to  om.O95.  .  .  ." 

Farther  on  he  says :  "  Since  it  is  the  elevation  of  tempera- 
ture of  the  walls  of  the  cylinder,  heated  by  the  steam  in  the 


THE  PHILOSOPHY  OF  THE  STEAM  ENGIXE.  2JI 

jacket,  which  is  the  cause  of  the  improvement,  it  is  not  to  be 
doubted,  for  an  instant,  that  any  means  of  securing  such  tem- 
perature will  be  equally  effective  and  economical."  He  then 
proposes  the  use  of  a  smoke-jacket :  but  he  finds,  on  trial,  that 
it  is  of  little  value,  the  heat  being  incapable  of  passing  with 
sufficient  rapidity  from  the  gases  in  the  jacket  to  the  metal  of 
the  cylinder. 

Him,  in  this  memoir,  also  expressly  proposed  the  measure 
of  the  heat  consumed  by  the  engine  as  the  true  measure  of  its 
efficiency. 

64.  The  Best  Ratio  of  Expansion  is  that  which  gives 
best  effect  under  the  specified  conditions.    But  this  is  obviously 
greater  or  less,  accordingly  as  the  wastes  of  the  engine  in- 
crease more  or  less  rapidly,  and  as  this  point,  known  practi- 
cally to  exist,  at  which  the  net  effect,  after  balancing  gains 
and  losses,  is  set  at  one  ratio  or  another  by  such  variations. 

The  limit  of  efficiency  in  heat-engines,  as  has  been  seen,  is 
thermodynamically  determined  by  the  limit  of  complete 
expansion.  The  causes  of  the  practical  limitation  of  the  ratio 
of  expansion  to  a  very  much  lower  value  than  those  which 
maximum  efficiency  of  fluid  would  seem  to  demand  have  not 
been  always  considered,  either  with  care  or  with  intelligence, 
by  writers  thoroughly  familiar  with  the  dynamical  treatment, 
apart  from  the  modifying  conditions  here  under  consideration. 
These  problems  are  the  special  subject  of  Chapter  VII. 

65.  Cylinder-condensation  is  now  knowmto  produce  very 
serious  modifications  of  working  conditions.     Watt,  and  prob- 
ably his  contemporaries  and  successors,  for  many  years  sup- 
posed that  the  irregularity  of   motion  due  to   the   variable 
pressure  occurring  with  high  expansion  was  the  limiting  con- 
dition, and  does  not  at  first  seem  to  have  realized  that  the 
cylinder-condensation  discovered  by  him  had  any  economical 
bearing  upon  the  ratio  of  expansion  at  maximum  efficiency. 
It  undoubtedly  is  the  fact  that  this  irregularity  was  the  first 
limiting  condition  with  the  large,  cumbrous,  long-stroked,  and 
slow-moving   engines  of   his    time.     Nearly  every    accepted 
authority,  from  that  day  to  the  present,  has  assumed,  tacitly, 


2J2  A   MANUAL   OF   THE   STEAM-ENGINE. 

that  this  method  of  waste  has  no  influence  upon  the  value  of 
that  ratio. 

Thomas  Tredgold,  writing  in  1827,  who,  but  little  later 
than  Carnot,  puts  the  limit  to  economical  expansion  at  the 
point  subsequently  indicated  and  more  fully  demonstrated  by 
De  Pambour,  exaggerates  the  losses  due  to  the  practical  con- 
ditions, but  evidently  does  perceive  their  nature  and  general 
effect.  He  also  shows  that,  under  the  conditions  assumed,  the 
losses  may  be  reduced  to  a  minimum,  so  far  as  being  depend- 
ent upon  the  form  of  the  cylinder,  by  making  the  stroke  twice 
the  diameter. 

Mr.  D.  K.  Clark,  however,  publishing  his  "  Railway  Ma- 
chinery" in  1855,  was  the  first  to  discuss  this  subject  with 
knowledge,  and  with  a  clear  understanding  of  the  effects  of 
condensation  in  the  cylinder  of  the  steam-engine  upon  its 
maximum  efficiency.  Cornish  engines,  from  the  beginning, 
had  been  restricted  in  their  ratio  of  expansion  to  about  one 
fourth,  as  a  maximum,  Watt  himself  adopting  a  "  cut-off  "  at 
from  one  half  to  two  thirds.  Hornblower,  with  his  compound 
engine  competing  with  the  single-cylinder  engines  of  Watt, 
had  struck  upon  this  rock,  and  had  been  beaten  in  economy 
by  the  latter,  although  using  much  greater  ratios  of  expan- 
sion ;  but  Clark,  a  half-century,  and  more,  later,  was,  neverthe- 
less, the  first  to  perceive  precisely  where  the  obstacle  lay,  and 
to  state  explicitly  that  the  fact  that  increasing  expansion  leads 
to  increasing  losses  by  cylinder-condensation,  the  losses  in- 
creasing in  a  much  higher  ratio  than  the  gain,  is  the  practical 
obstruction  in  our  progress  toward  greater  economy. 

After  a  long  and  arduous  series  of  trials  of  locomotive- 
engines,  and  prolonged  experiment  looking  to  the  measure- 
ment of  the  magnitude  of  the  waste  produced  as  above  de- 
scribed, Clark  concludes :  "  The  magnitude  of  the  loss  is  so 
great  as  to  defeat  all  such  attempts  at  economy  of  fuel  and 
steam  by  expansive  working,  and  it  affords  a  sufficient  expla- 
nation of  the  fact,  in  engineering  practice,  that  expansive 
working  has  been  found  to  be  expensive  working,  and  that, 
in  many  cases,  an  absolutely  greater  quantity  of  fuel  has  been 


THE  Pff/LOSOPJ/Y  OF   THE  STEAM-ENGINE.  "5 

consumed  in  extended  expansion  working,  while  less  power 
has  been  developed."  He  states  that  high  speed  reduces  the 
effect  of  this  cause  of  loss,  and  indicates  other  methods  of 
checking  it.  He  states  that  "  the  less  the  period  of  admission, 
relative  to  the  whole  stroke,  the  greater  the  quantity  of  free 
water  existing  in  the  cylinder."  His  experiments  revealing 
these  facts  were,  in  some  cases,  made  prior  to  1852.  But  the 
men  handling  the  engines  had  observed  this  effect  even  before 
Clark :  he  states  that  they  rarely  voluntarily  adopted  "  a  sup- 
pression of  above  30  per  cent,"  as  they  found  the  loss  greater 
than  the  gain.  Describing  the  method  of  this  loss,  this  author 
goes  on  to  say  that,  "  to  prevent  entirely  the  condensation  of 
steam  worked  expansively,  the  cylinder  must  not  only  be  sim- 
ply protected  by  the  non-conductor :  it  must  be  maintained,  by 
independent  external  means,  at  the  initial  temperature  of  the 
steam."  He  thus  reiterates  the  principle  expressed  by  Watt 
three  quarters  of  a  century  before. 

The  same  author,  writing  in  1 877,  says :  '•  The  only  ob- 
stacle to  the  working  of  steam  advantageously  to  a  high 
degree  of  expansion  in  one  cylinder,  in  general  practice,  is  the 
condensation  to  which  it  is  subjected,  when  it  is  admitted  into 
the  cylinder  at  the  beginning  of  the  stroke,  by  the  less  hot  sur- 
faces of  the  cylinder  and  piston ;  the  proportion  of  which  is 
increased  so  that  the  economy  of  steam  by  expansive  working 
ceases  to  increase  when  the  period  of  admission  is  reduced 
down  to  a  certain  fraction  of  the  stroke,  and  that,  on  the  con- 
trary, the  efficiency  of  the  steam  is  diminished  as  the  period 
of  admission  is  reduced  below  that  fraction."  The  magnitude 
of  this  influence  may  be  understood  from  the  fact  that  the 
distinguished  engineer,  Loftus  Perkins,  using  steam  of  300 
pounds  pressure,  and  attaining  the  highest  economy  known, 
up  to  his  time,  found  his  engine  to  consume  1.62  pounds 
of  fuel  per  hour  and  per  horse-power ;  while  this  figure  is  now 
reached  by  engines  using  steam  at  one  third  that  pressure, 
and  expanding  about  the  same  amount,  and  sometimes  less. 

Mr.  Humphreys,  writing  a  little  later  than  Clark,  shows 
the  consumption  of  fuel  to  increase  seriously  as  the  ratio  of 


2/4  A   MANUAL   OF   THE   STEAM-ENGINE. 

expansion  is  increased  beyond  the  very  low  figure  which  con- 
stituted the  limit  in  marine  engines  of  his  time. 

66.  Him  was  the  first  scientific  and  practical  investigatoi 
on  the  Continent  of  Europe. 

A  few  writers  on  thermodynamics  had  finally  come  to  un- 
derstand the  fact  that  such  a  limitation  of  applied  theory 
existed,  and  Mons.  G.  A.  Hirn,  who,  better  than  probably  any 
authority  of  his  time  or  earlier,  combined  a  knowledge  of  the 
scientific  principles  involved,  with  practical  experience  and 
experimental  knowledge,  in  his  treatise  on  thermodynamics 
(1876),  concludes :  "  quit  est  absolument  impossible  d'e'difier  a 
priori  une  the'orie  de  la  machine  a  vapeur  d'eau  douce  d"un  cha- 
racttre  scientifiqnc  et  exact"  in  consequence  of  the  operation  of 
the  causes  here  detailed.  While  working  up  his  experiments 
upon  the  performance  of  engines,  comparing  the  volume  of 
steam  used  with  that  of  the  cylinder,  he  had  always  found  a 
great  excess,  and  had,  at  first,  attributed  it  to  the  leakage  of 
steam  past  the  piston ;  but  a  suggestion  of  M.  Leloutre  set  him 
upon  the  right  track,  and  he  came  to  the  same  conclusion  as 
had  Watt,  so  many  years  before.  He  explains  that  errors  of 
thirty,  or  even  up  to  seventy,  per  cent  may  arise  from  the 
neglect  of  the  consideration  of  this  loss.  Combes  had  per- 
ceived the  importance  of  this  matter,  and  De  Freminville 
suggested  the  now  familiar  expedient  of  compression,  on  the 
return-stroke,  as  nearly  as  possible  to  boiler-pressure,  as  a 
good  way  to  correct  the  evil.  Hirn  was  the  first  to  show  in 
detail  the  distribution  of  heat-wastes  and  to  prove  with  cer- 
tainty, on  such  grounds,  that  the  benefit  of  extended  expan- 
sion in  real  engines  can  only  be  approximated  to  that  pre- 
dicted, by  the  theory  of  the  ideal  engine,  by  special  arrange- 
ments having  for  their  object  the  reduction  of  cylinder-waste, 
such  as  superheating,  "steam-jacketing,"  and  "compounding." 

His  experimental  work  began  at  a  very  early  date  and  in  a 
purely  scientific  spirit.  He  had  noted  the  discoveries  of 
Mayer  (1842)  and  of  Joule  (1846  and  later)  only  after  he  had 
himself  sought  to  ascertain  the  true  nature  of  heat.  He  pub- 
lished his  conclusions,  correct  conclusions,  in  1848,  relating  to 


THE  PHILOSOPHY  OF   THE  STEAM-EMG1NE.  2/5 

this  question  as  determined  by  his  researches  on  heat  and  fric- 
tion. In  1855  he  was  able  to  show  that  Cannot  had  accepted 
the  wrong  theory  in  his  now  famous  work ;  proved,  by  experi- 
ment, that  heat  actually  disappears,  as  heat,  in  the  operation  of 
tile  steam-engine,  and  showed  that,  in  the  actual  engine,  the 
steam-jacket,  an  element  in  itself  wasteful,  may  be  a  very  im- 
portant source  of  economy  by  checking  extra-thermodynamic 
wastes. 

Him  showed  that  Mayer's  ideas  were  completely  sustained, 
and  that  the  Rankine  and  Clausius  phenomenon  of  condensa- 
tion of  steam  and  similar  vapors,  during  their  adiabatic  expan- 
sion,, is  actually  observable  in  the  steam-engine.  His  great 
work  on  Thermodynamics  *  was  published  in  1876,  and  in  it 
he  gave  as  clear  an  account  of  the  physical  operations  taking 
place  within  the  engine-cylinder  as  had  dark  or  Isherwood. 
and  produced  a  theory  of  the  real  engine — an  **  experimental 
theory"  as  he  called  it — which  has  served  as  the  basis  for 
nearly  all  subsequent  work  in  that  direction. 

Mons.  V.  Dwelshauvers-Dery  supplemented  this  work  of 
Him  by  further  development  of  the  theory  and  its  application 
in  fuller  detail  to  the  processes  of  heat-transfer  in  the  steam- 
engine  in  the  years  subsequent  to  1878.+  From  1873,  this  in- 
vestigator worked  with  Him  and  his  lieutenant,  Hallauer,  and 
with  M.  Grossteste  in  the  construction,  upon  the  basis  of  ex- 
periment, of  a  correct  theory  of  the  real,  as  distinguished  from 
the  ideal,  engine  and  its  reduction  to  a  practically  valuable 
form.  He  gives  in  an  "  Expose,"  in  the  Revue,  in  1882,  a 
carefully-written  account  of  this  development  of  the  most 
modern  form  of  the  theory  of  heat-engines.  This  latest  theory 
was  finally  completely  established  by  a  long  and  instructive 
discussion  in  which  the  ablest  physicists  and  engineers  of 
Europe  were  engaged.  In  its  current  form,  its  algebraic  ex- 
pression is  that  of  Dwelshauvers-Dery;  but  it  still  requires 
further  development. 


*  Thterie  Mecaniqoe  de  Cbaknr;  z  tomes;  Finis,  1816. 
f  Revue  UmretseSe  des  Mines,  de  Liege. 


2/6  A   MANUAL   OF   THE   STEAM-ENGINE. 

67.  Isherwood's  Researches  were  the  first  systematically 
conducted  investigations  of  the  latest  phase  of  the  problem  of 
steam-engine  efficiency  in  the  United  States. 

Mr,  B.  F.  Isherwood  was,  in  1860,  a  Chief  Engineer  in  the 
United  States  navy,  and  Chief  of  the  Bureau  of  Steam  Engi- 
neering. He  seems  to  have  been  the  first  to  have  attempted 
to  determine,  by  systematically  planned  experiment,  the  law  of 
variation  of  the  amount  of  cylinder-condensation  with  varia- 
tion of  the  ratio  of  expansion.  Experimenting  on  board  the 
U.  S.  S.  Michigan,  a  naval  vessel  fitted  with  simple  and  un- 
jacketed  engines,  he  found  that  the  consumption  of  fuel  and 
of  steam  was  greater  when  the  ratio  of  expansion  was  carried 
beyond  about  two  than  when  restricted  to  lower  ratios.  He 
determined  the  quantity  of  steam  used,  and  the  amount  con- 
densed, at  expansions  ranging  from  full  stroke  to  a  "  cut-off" 
at  one  tenth.  His  results  permit  the  determination  of  the 
method  of  variation,  with  practically  satisfactory  accuracy,  for 
the  engine  upon  which  the  investigation  was  made,  and  for 
others  of  its  class.  It  was  the  first  of  a  number  of  such  inves- 
tigations made  by  the  same  hand,  and  these  to  day  constitute 
the  principal  part  of  our  data  in  this  particular  direction.  The 
author,  studying  these  results,  found  that  the  cylinder-conden- 
sation there  varied  sensibly  as  the  square-root  of  the  ratio  of 
expansion,  and  the  method  of  variation  is  apparently  substan- 
tially similar  for  other  forms  and  proportions  of  engine.  The 
amount  of  such  condensation  usually  lies  between  one  tenth 
and  one  fifth  the  square-root  of  that  ratio,  if  estimated  as  a 
fraction  of  the  quantity  of  steam  demanded  by  a  similar  engine 
having  a  non-conducting  cylinder,  it  being  here  assumed  that 
the  engine  is  one  of  fair  size.  The  proportion  of  loss  is  some 
inverse  function  of  the  size  of  engine — probably  nearly  in- 
versely as  the  diameter  of  cylinder. 

Mr.  Isherwood,  in  his  works,  gives  admirably-expressed 
descriptions  of  the  modus  operandi,  when  considering  this 
waste.*  He  summarizes  his  own  work,  and  explains  with  un- 

*  Engineering  Researches;  a  vols.  410;  Philadelphia,  1860.  See  especially 
the  introduction  to  volume  n. 


THE  PHILOSOPHY  OF   THE   STEAM-EXGIXE.  -~~ 

exampled  clearness  the  method  of  modification  of   the  best 
ratio  of  expansion  by  these  internal  and  previously  unfamiliar 

v   IStCSi 

Professor  Cotterill  gives  more  attention  to  this  subject  than 
any  writer  up  to  his  time.  He  devotes  a  considerable  amount 
of  space  to  the  study  of  the  method  of  absorption  and  surren- 
der of  heat  by  the  metal  surfaces  enclosing  the  steam,  con- 
structs diagrams  which  beautifully  illustrate  this  action,  and 
solves  the  problems  studied  by  him  with  equal  precision  and 
elegance  of  method.  He  summarizes  the  experimental  work 
done  to  the  date  of  writing,  and  very  fully  and  clearly  exhibits 
the  mode  of  transfer  of  heat  past  the  piston  without  trans- 
formation into  work.  Professor  Cotterill's  treatise  on  the 
steam-engine,  "  considered  as  a  heat-engine,"  is  thus  most 
valuable  to  the  engineer.* 

Mr.  Sutcliffe  states,  as  early  as  1875,  that  engines  of  ap- 
proved type  may  sometimes  exhibit  losses  by  cylinder-waste 
exceeding  40  per  cent.t  He  gives  the  following  figures  for 
these  losses  in  the  Corliss  engines  at  Saltaire : 


7.4  27       per  cent. 

9-04  36.37    "       " 

11.4  46.67    "       " 

These  figures  approach  those  previously  obtained  by  Isher- 
wood  from  a  much  less  approved  form  of  engine. 

68.  The  Status  of  the  Theory  of  the  Steam-engine, 
about  1850.  was  becoming  well  settled  as  a  thermodynamic 
system,  and  even  the  most  recent  phase  had  begun  to  take 
vague  shape. 

Dr.  Albans,  writing  about  1840,  says  of  the  choice  of  best 
ratio  of  expansion :  "  Practical  considerations  form  the  best 
guide,  and  these  are  often  left  entirely  out  of  view  by  mathe- 
maticians. Many  theoretical  calculations  have  been  made  to 

*  The  Steam-engine  considered  as  a  Heat-engine ;  London,  1878. 
4  Hopkinson  on  the  Steam-engine  Indicator;  7th  ed. ;  1875. 


278  A   MANUAL   OF   THE   STEAM-ENGINE. 

determine  the  point,  but  they  appear  contradictory  and  unsat- 
isfactory." Renwick,  in  1848,  makes  the  ratio  of  initial  divided 
by  back  pressure  the  proper  ratio  of  expansion,  but  correctly 
describes  the  effect  of  the  steam-jacket,  and  suggests  that  it 
may  have  peculiar  value  in  expansive  working,  and  that  the 
steam  may  receive  heat  from  a  cylinder  thus  kept  at  the  tem- 
perature of  the  "  prime  "  steam.  John  Bourne,  the  earliest  of 
now  acknowledged  authorities  on  the  management  and  con- 
struction of  the  steam-engine,  pointed  out,  at  a  very  early  date, 
the  fact  of  a  restricted  economic  expansion.  Rankine  recog- 
nized no  such  restriction  as  is  here  under  consideration,  con- 
sidered the  ratio  of  expansion  at  maximum  efficiency  to  be  the 
same  as  that  stated  by  Carnot,  and  by  other  early  writers,  and 
only  perceived  its  limitation  by  commercial  considerations,  a 
method  of  limitation  of  great  importance,  but  often  of  less 
practical  effect  than  is  the  waste  by  condensation.  In  his  life 
of  Elder  (1871),  however,  he  indicates  the  existence  of  a  limit 
in  practice,  and  places  the  figure  at  that  previously  given  by 
Isherwood  for  unjacketed  engines. 

Thus  the  theory  of  the  steam-engine  stands,  at  this  date,  in- 
complete, but  on  the  verge  of  completion,  needing  only  a  little 
well-directed  experimental  work  to  supply.the  doubtful  elements. 
Even  these  are  becoming  determined.  Isherwood  and  later  engin- 
eers give  facts  showing  waste  to  be  proportional,  very  nearly,  if 
not  exactly,  to  the  square-root  of  the  ratio  of  expansion  ;  and 
Escher,  of  Zurich,  has  shown  the  loss  to  be  also  proportional 
to  the  square-root  of  the  time  of  exposure,  or,  in  other  words, 
to  the  reciprocal  of  the  square-root  of  the  speed  of  rotation  ; 
and  it  only  remains  to  determine  the  exact  method  of  variation 
of  loss  with  variation  of  range  of  temperature  and  a  rational 
basis  to  give  the  whole  of  the  necessary  material  for  the  con- 
struction of  a  working  theory  which  may  enable  the  engineer 
to  estimate,  in  advance  of  construction,  the  economic  perform- 
ance of  his  machine. 

Dwelshauvers  has  done  much  to  popularize  the  modern  and 
accepted  theory  of  the  real  engine.  He  has  endeavored  to 
exhibit  the  action  of  the  steam-jacket,  to  show  what  is  the 


TOE  PHILOSOPHY  OF  THE  STEAM-EJtTGWE.  2J9 

modification  of  die  action  of  the  metallic  interior  of  the  gngntr, 
by  the  introduction  of  that  wasteful  dement,  to  counteract. 
in  many  cases,  a  greater  waste  ;  and  he  has  sought  to  show 
the  influence  of  the  experimental  philosophy  of  the  engine 
upon  the  proportions  and  the  working  of  the  condenser.  He 
has  observed  the  fact  of  a  maximum  ratio  of  expansion  appro- 
priate to  the  condition  of  maximum  efficiency,,  as  determined 
by  the  variation  of  this  waste,  previously  unobserved,  and  has 
engaged  in  the  construction  of  its  theory  in  accordance  with 
his  published  theory  of  heat-expenditure,  reducing  all  to  a 
common  basis  and  philosophy. 

Some  of  the  work  of  Dwelshau  vers-Dery  has  been  trans- 
lated by  Donkin.  and  published,  from  time  to  time  in  London 
EmgimetTrsmg  ;  other  portions  remain  untranslated,  xm\  are  onlv 
to  be  found  in  the  Rfzue  Umtn-ersiHe  dies  Mines.  Simigagiia 
jia<  summarized  it  welL 

It  probably  cannot  be  long  before  direct  investigation  will 
secure  all  essential  knowledge.  When  this  becomes  the  case, 
the  remarks  of  those  distinguished  physicists  and  engineers, 
Hallauer  and  his  great  teacher,  Him,  wfll  be  no  longer  based 
upon  apparent  fact. 

Says  Him.  on  this  subject  "  Ma  commctiom  reste  amjomrdkm 
qtiflU  ctedt  il  y  a  vimgt  ams,  mme  tkeorie  proprememt  dite  de  la 
machine  a  Tzapcmr  est  impossible;  la  titanic  cjcpcnmemtale,etabKe 
atr  If  motemr  bdmeme  et  dams  toutes  les  formes  oil  il  a  fit  fssave. 
cm  me'camiqme  afpliqxe  pent  semle  comdmire  a  des  rcsmhats  rigom- 


60,  Three  Periods  of  this  Philosophy  of  the  steam-en- 
gine may  be  discerned.  Chronologically  considered,  the  his- 
tory of  the  growth  of  the  theory  divides  itself  distinctly  into 
three  parts  :  the  first  extending  up  to  the  middle  of  the  present 
century,  and  mainly  distinguished  by  the  attempts  of  Cannot 
and  of  Clapeyron  to  formulate  a  physical  theory  of  the  thermo- 
dynamics of  the  machine  ;  the  second  beginning  with  the  date 
of  the  work  of  Rankine  and  Clausius,  who  constructed  a  correct 
thermodynamk  theory  ;  and  the  third  beginning  nearly  a  gen- 
eration later,  and  marked  by  the  introduction  into  the  general 


280  A    MANUAL    OF    THE  STEAM-ENGINE. 

theory  of  the  physics  of  the  conduction  and  transfer  of  that 
heat  which  plays  no  part  in  the  useful  transformation  of  energy 
and  its  application. 

The  first  period  may  be  said  to  include,  also,  the  inaugura- 
tion of  experimental  investigation,  and  the  discovery  of  the 
nature  and  extent  of  avoidable  wastes  and  attempts  at  their 
amelioration  by  James  Watt  and  by  John  Smeaton.  The 
second  period  is  marked  by  the  attempt,  on  the  part  of  a  num- 
ber of  engineers,  to  determine  the  method  and  magnitude  of 
these  wastes  by  more  thorough  and  systematic  investigation, 
and  by  the  exact  enunciation  of  the  law  governing  the  neces- 
sary rejection  of  heat,  as  revealed  by  the  science  of  thermody- 
namics. The  third  period  is  opening  with  promise  of  a  com- 
plete and  practically  applicable  investigation  of  all  the  methods 
of  loss  of  energy  in  the  engine,  and  of  the  determination,  by, 
both  theoretical  and  experimental  research,  of  all  the  data 
needed  for  the  construction  of  a  working  theory. 

Hirn  has  recognized  these  three  periods,  and  has  proposed 
to  call  the  second  the  "  theoretical  "  and  the  third  the  "  experi- 
mental "  stage.  The  Author  would  prefer  to  make  the  nomen- 
clature somewhat  more  accordant  with  what  has  seemed  to 
him  to  be  the  true  method  of  development  of  the  subject.  It 
has  been  seen  that  the  experimental  stage  really  began  with 
the  investigations  of  Watt  in  the  first  period,  and  that  the 
work  of  experimentation  was  continued  through  the  second 
into  the  present,  the  last,  period. 

It  is  also  evident  that  the  theoretical  stage,  if  it  can  be 
properly  said  that  such  a  period  may  be  marked  off  in  the  his- 
tory of  the  theory  of  the  steam-engine,  actually  extends  into 
the  present  epoch ;  since  the  work  of  the  engineer  and  the 
physicist  of  to-day  consists  in  the  application  of  the  science  of 
heat-transfer  and  heat-transformation,  together,  to  the  engine. 
During  the  second  period  the  theory  included  only  the  thermo- 
dynamics of  the  engine ;  while  the  third  period  is  about  to 
incorporate  the  theory  of  conduction  and  radiation  into  the 
general  theory  with  the  already  established  theory  of  heat- 
transformation.  The  writer  would  therefore  make  the  classifi- 


THE  PHILOSOPHY  OF  THE   STEAM-EXGIXE.  28 1 

cation  of  these  successive  stages  in  the  progress  here -described 
thus: 

1.  Primary  Period — that  of   incomplete  investigation  and 
of  earliest  systematic,  but  inaccurate,  theory. 

2.  Secondary  Period — that  of  the  establishment  of  a  cor- 
rect thermodynamic  theory,  the  Theory  of  the  Idtal  Engine. 

3.  Tertiary  Period — that  of  the  production  of  the  complete 
theory  of  the  engine,  of  the  true  Theory  of  the  Real  Engine. 

70.  Work  remaining  to  be  done,  as  may  be  now  readily 
seen,  is  that  of  determining,  by  experiment,  precisely  what  are 
the  physical  laws  governing  the  transfers  of  heat  between 
metal  and  vapor,  in  the  engine-cylinder,  and  to  apply  these 
laws  in  the  theory  of  the  machine.  Cotteriil  has  shown  how 
heat  penetrates  and  traverses  the  metal,  and  Grashof  has  indi- 
cated the  existence  of  an  intermediate  and  approximately  con- 
stant temperature  between  the  temperatures  of  the  initial 
steam  and  of  the  exhaust,  and  both  have  given  us  some  new 
methods.  The  Author,  while  pointing  out  the  nature  of  the 
true  **  curve  of  efficiency"  of  the  steam-engine  which  he  was  so 
fortunate  as  to  discover,  has  shown  how  it  may  be  made  useful 
in  the  solution  of  practical  and  of  theoretical  problems  in- 
volved in  the  applied  theory  of  heat-engines,  and  many  able 
minds  are  now  engaged  upon  the  theory.  There  can  be  little 
doubt  that  it  will  soon  become  satisfactorily  complete. 

The  determination  of  physical  constants  and  the  experi- 
mental checking  of  the  scientific  treatment  of  the  case  will 
undoubtedly  furnish  employment  to  able  and  skilful  investi- 
gators for  many  years,  and  the  study  of  the  modification  of  the 
general  theory  in  its  application  to  the  present  and  the  com- 
ing types  of  engine  will  offer  a  no  less  important  and  attrac- 
tive field  of  labor  for  those  competent  to  take  up  the  work 
and  finding  opportunities  to  do  so.  The  philosophy  of  the 
construction  and  of  the  operation  of  the  multiple-cylinder  and 
of  new  forms  of  engine  is  already  well  understood,  and  the 
algebraic  and  numerical  equations  applying  to  them  as  a  mathe- 
matical theory  are  now  in  process  of  development.  Messrs. 
Him  and  Hallauer,  Donkin,  Dwelshauvers-Dery,  Zeuner  and 


282  A    MANUAL    OF    THE    STEAM-ENGINE. 

Kirsh  have  already  succeeded  in  effecting  some  valuable  ad- 
vances in  the  theory  of  the  real  engine,  by  the  introduction  of 
data  previously  secured  by  Clark  and  others. 

The  experimental  investigation  of  Messrs.  Gately  and 
Kletschy,  to  be  considered  later,  and  the  more  exact  work  since 
undertaken  will  ultimately  supply  all  needed  data.  That  in- 
vestigation, the  first  attempt  at  systematic  investigation  of  the 
methods  of  variation  of  the  several  main  losses  and  wastes,  in 
the  steam-engine,  with  variation  of  the  principal  quantities  de- 
termining their  magnitudes,  was  made  in  the  spring  of  1884, 
and  upon  a  plan  schemed  out  by  the  Author  some  years 
earlier  (1878).  The  results  gave,  roughly,  the  needed  data  for 
the  provisional  theory  of  the  engine,  including  physical  as  well 
as  thermodynamic  wastes,  the  theory  of  heat-transfer  and 
that  of  heat-transformation.  It  has  now  become  practicable 
to  make  intelligent  and  useful  estimates  of  the  relative  value 
of  alternative  plans  of  construction  of  proposed  new  engines, 
of  probable  costs  of  operation,  and  of  efficiencies  and  best  pro- 
portions of  size  of  engine  to  power  demanded  for  any  given 
type,  size,  and  design.  Some  of  the  most  satisfactory  data 
are  those  obtained  by  Messrs.  Hill,*  Willans,f  Schneider,;}; 
English,§  and  Kennedy. | 

71.  The  Plan  of  this  Work  thus  logically  includes  the 
philosophical  study  of  the  gradual  development  of  the  modern 
steam  engine  out  of  the  germ  which  existed  in  ancient  times  ; 
the  description  of  the  machine  of  our  own  day,  in  its  principal 
forms  ;  the  tracing  of  the  evolution  of  scientific  knowledge  of 
its  philosophy  to  the  present  time  ;  the  discussion  of  the  sci- 
entific principles  involved  in  the  production,  utilization,  and 
wastes  of  energy  in  the  apparatus  and  mechanisms  employed  ; 
and  the  useful  application  of  such  principles,  in  the  design,  the 
proportioning,  the  constructing,  and  the  economical  operation 
of  engines  and  transmitting  machinery. 

The  succeeding  subjects  then  follow  in  logical  and  natural 

*  Mark's  Steam-engine  Design.         f  Trans.  Brit.  Inst.  C.  E.,  1888. 

t  Delaford's  Report,  1884.  §  Trans.  Brit.  Inst.  Mech.  Engrs.,  1887. 

||  Trans.  Brit.  Inst.  Mech.  Engrs.,  1890. 


THE  PHILOSOPHY  OF  THE   STEAM-ENGINE.  283 

order,  thus:  Chemistry  of  Combustion  ;  Physics  of  Heat-trans- 
fer and  Storage;  Thermodynamics:  Theory  of  the  Steam- 
engine,  ideal  and  real ;  Design ;  Construction ;  Operation  and 
Management;  Tests  of  the  Machine;  Theory  of  Efficiencies, 
including  finance;  Establishments;  Specifications,  Contracts, 
and  Legal  Forms  and  Business  Principles.  We  thus  trace  the 
production  of  energy  in  available  form  and  its  progress  in  the 
process  of  its  utilization,  from  its  first  appearance  with  the 
combustion  of  the  fuel  in  which  it  had  been  stored,  through 
the  several  steps  by  which  it  passes  into  the  boiler,  becomes 
stored  in  the  steam,  and  is  finally  transferred  to  the  engine 
and  there  converted  in  part  into  mechanical  energy,  to  be  use- 
fully or  wastefully  applied  to  the  performance  of  the  intended 
task  or  to  overcome  the  friction  of  the  mechanism  employed. 

The  Fundamental  Mechanical  Principles  involved  are,  in 
brief,  the  following : 

The  object  of  all  mechanism  is  to  produce  a  certain  defi- 
nite motion  of  some  part  or  parts — the  position  and  form  and 
the  methods  of  connection  of  which  are  known  and  fixed — 
against  any  resistance  that  may  be  met  with  in  the  course  of 
such  movement.  Every  machine  and  every  train  of  mechanism 
is  therefore  a  contrivance  by  means  of  which  energy  or  power 
available  at  one  point,  usually  in  definite  amount  and  acting 
in  a  definite  direction  and  with  definite  velocity,  is  transferred 
to  other  points,  there  to  do  work  of  definite  amount,  and  there 
to  overcome  known  resistances  with  known  velocities, 

The  object  of  the  engineer  in  designing  mechanism  is  to 
effect  this  transfer  of  energy  and  these  transformations  at  the 
least  cost  and  with  least  running  expense,  and  hence  with 
maximum  efficiency  of  apparatus.  It  is  often  important  tc 
secure  minimum  volume  and  weight  of  machine,  as  well  as 
maximum  effectiveness  in  operation. 

The  work  of  a  machine  is  measured  by  the  magnitude  of 
the  resistance  encountered  and  the  velocity  with  which  it 
is  overcome.  The  nature  of  the  work,  aside  from  its  simple 
kinetic  character,  is  as  widely  variable  as  are  the  details  of 
human  industry. 


284  A  MANUAL   OF   THE    STEAM-ENGINE. 

Prime  Movers  are  those  machines  which  receive  energy 
directly  from  natural  sources,  and  transmit  it  to  other  machines 
which  are  fitted  for  doing  the  various  kinds  of  useful  work. 
Thus,  the  steam-engine  derives  its  power  from  the  heat-energy 
liberated  by  the  combustion  of  fuel ;  water-wheels  utilize  the 
energy  of  flowing  streams  ;  windmills  render  available  the  power 
of  currents  of  air;  the  voltaic  battery  develops  the  energy  of 
chemical  action  in  its  cells;  and,  through  the  movement  of 
electro-dynamic  mechanism,  this  energy  is  communicated  to 
other  machinery,  and  thus  caused  to  do  work. 

Machinery  of  Transmission  is  used  in  the  transformation 
of  energy  supplied  by  the  prime  mover  into  available  form, 
for  the  performance  of  special  kinds  of  work,  or  for  simple 
transmission  of  power  from  the  prime  mover  to  machines  doing 
that  work. 

The  work  to  be  done  may  be  the  raising  of  weights,  as  in 
hoisting  and  pumping  machinery;  the  transportation  of  loads, 
as  on  the  railway  or  in  the  steamship ;  the  alteration  of  the 
form  of  solid  masses,  as  in  machine-tools ;  the  overcoming  or 
even  the  utilizing  of  frictional  resistances,  as  in  brakes ;  or  any 
other  of  the  numberless  operations  performed  in  mills  and 
factories  by  machinery. 

Machines  and  Machine-tools  receive  energy,  derived  originally 
from  prime  movers,  and  transferred  to  them  through  machinery 
of  transmission,  and  apply  that  energy  to  special  kinds  of  work 
to  which  they  are  precisely  adapted  by  their  design  and  con- 
struction. Thus,  looms  apply  such  energy  to  the  weaving  of 
cloth  ;  lathes  are  especially  fitted  for  the  production  of  parts 
having  circular  sections;  planing-machines  produce  straight- 
lined  surfaces. 

The  power  demanded  by  a  machine  is  that  needed  to 
do  the  work  for  which  the  machine  is  designed,  plus  the  addi- 
tional amount  expended  by  the  machine  itself,  in  transferring 
the  first-mentioned  quantity  from  the  source  of  power  to  which 
the  machine  is  connected,  by  transmitting  mechanism  to  the 
point  at  which  the  work  is  to  be  done.  Where  the  machine  is 
subject  to  shock  and  jar  sufficient  to  permanently  distort  its 
parts,  or  the  bearing  surfaces,  a  portion  of  the  power  demanded 


THE  PHILOSOPHY  OF  THE  STEAJt-EA'CIXE.  -  *  f 

is  wasted  in  doing  this  work  ;  where  the  journals  heat,  consider- 
able amounts  of  energy  are  sometimes  lost  as  heat-energy:  in 
all  cases  some  loss  occurs  in  this  way.  Where  power  is  trans- 
mitted by  the  expansion  and  compression  of  elastic  fluids,  also, 
energy  is  often  lost  in  large  amounts  by  transformation  into 

" 


The  power  demanded  by  any  machine  thus  always  exceeds 
that  expended  by  the  machine  upon  its  proposed  task.  Were 
these  wastes  not  to  occur,  the  power  transmitted  would  be  the 
same  in  amount  at  every  point  in  the  machine. 

Work,  as  a  term  in  the  science  of  engineering,  may  be 
defined  as  that  action  by  which  motion  is  produced  against  the 
resistance  continuously  or  intermittently  opposed  to  any  mov- 
ing body.  It  is  measured  by  the  product  of  the  direct  com- 
ponent of  the  resistance  into  the  space  traversed.  Where  the 
resistance  is  variable,  its  mean  value  is  taken.  Thus,  if  R  be 
the  resistance  and  5  the  space,  the  work  is,  for  constant 
fijnbtance, 

U=RS,  ........    (i) 

in  which  U  is  measured   in  foot-pounds  or  kilogrammetres. 
For  a  variable  resistance,  R*  acting  through  a  space,  sr 


(2) 


which  can  be  integrated  when  R  is  known  as  a  function  of  s. 

Resistances,  and  the  forces  by  which  they  are  overcome, 
are  measured  by  engineers,  usually,  either  in  British  or  in 
metric  units,  as  the  pound  or  the  kilogramme.  Work,  and  the 
energy  expended  in  doing  work,  are  thus  both  measured  by 
the  product  of  the  pounds  or  the  kilogrammes  of  resistance 
or  of  effort  into  spaces  of  which  the  measure  is  usually  given 
in  feet  or  in  metres.  The  unit  of  work  and  of  energy  is  thus 
either  the  foot-pound  or  the  kUogrammetre. 

The  British  and  metric  measures  have  definite  relations, 
which  are  given  in  tables  to  be  found  in  all  engineers*  table- 
books, 


286  A    MANUAL    OF    THE    STEAM-ENGINE. 

Where  the  motion  of  the  machine  or  of  the  part  doing  v^ork 
is  circular,  the  space  traversed  may  be  measured  by  the  angu- 
lar motion,  a,  multiplied  by  the  lever-arm,  /,  and  their  pro- 
duct, multiplied  by  the  force,  R,  exerted,  gives  the  measure 
of  the  work  done.  Thus  : 


U=aRl 


in  which  last  expression  n  is  the  number  of  revolutions  made 
in  the  unit  of  time. 

These  values  are  equivalent  to  the  product  of  the  angular 
motion  into  the  moment  of  the  resistance. 

Work  may  also  be  measured,  as  in  steam,  air,  gas,  or  water- 
pressure  engines,  by  the  product  of  the  area  of  piston,  A,  the 
mean  intensity  of  pressure  upon  it,/,  the  length  of  stroke  of 
piston,  /,  and  the  number  of  strokes  made.  Thus, 

U=Apln 
=  Aps 

=fir>  .........   (4) 

when  Fis  the  volume  of  the  working  cylinder  multiplied  by 
the  number  of  strokes  ;  in  other  words,  the  volume  traversed 
by  the  piston. 

Where  the  force  acting,  or  the  resistance,  acts  obliquely  to 
the  path  traversed,  it  is  evident  that  only  the  component  in 
that  path  is  to  be  considered. 

Diagrams  exhibiting  the  amount  of  work  done  and  the 
method  of  its  variation  are  often  found  useful.  In  such 
diagrams  the  ordinate  is  usually  made  proportional  to  the 
force  acting  or  to  the  resistance,  while  the  abscissas  are  made 
to  measure  the  space  traversed.  The  curve  then  exhibits  the 
relations  of  these  two  quantities,  and  the  enclosed  area  is  a 
measure  of  the  work  performed.  With  a  constant  resistance, 
the  figure  is  rectilinear  and  a  parallelogram  ;  with  variable 
velocities  and  resistances,  it  has  a  form  characteristic  of  the 
methods  of  operation  of  the  part  or  of  the  machine  the  action  of 


THE  PHILOSOPHY  OF   THE   STEAM  ENGINE.  287 

which  it  illustrates.  In  the  first  case,  the  area  can  be  obtained 
by  multiplication  of  the  difference  of  the  ordinates  by  the 
difference  between  maximum  and  minimum  abscissas;  in  the 
second  case,  it  may  be  obtained  by  any  convenient  system  of 
integration,  of  which  systems  that  of  mechanical  integration, 
as  by  the  "  planimeter,"  is  usually  best. 

Power  is  defined  as  the  rate  of  work,  and  is  measured 
by  the  quantity  of  work  performed  in  the  unit  of  time,  as  in 
foot-pounds  or  in  kilogrammetres,  per  minute  or  per  second. 
The  unit  commonly  employed  by  engineers  is  the  "horse- 
power," which  was  defined  by  Watt  as  33,000  foot-pounds  per 
minute,  equivalent  to  550  per  second,  or  1,980,000  foot-pounds 
per  hour.  This  is  considered  to  be  very  nearly  the  amount  of 
work  performed  by  the  very  heavy  draught-horses  of  Great 
Britain  ;  but  it  considerably  exceeds  the  power  of  the  average 
dray-horse  of  that  and  other  countries,  for  which  25,000  foot- 
pounds may  be  taken  as  a  good  average  amount. 

The  metric  horse-power,  called  by  the  French  the  chevaL- 
vafeur,  or  force  de  cheval,  is  about  i£  per  cent  less  than  the 
British,  being  542^  foot-pounds  or  75  kilogrammetres  per 
second,  4500  kilogrammetres  per  minute,  or  270,000  per  hour. 
These  quantities  are  almost  invariably  employed  to  measure 
the  power  expended  and  work  done  by  machines. 

It  is  evident  that  power  is  also  measured  by  the  product  of 
the  resistance,  or  of  the  effort  exerted  into  the  velocity  of  the 
motion  with  which  that  resistance  is  overcome,  or  that  force 
exerted.  Since  s  =  vt, 

U=  Rs  =  Rvt; 

and  when  /  becomes  unity,  the  measure  of  the  power,  or  of 
the  equivalent  work  done  in  the  unit  of  time,  is 


(5) 


in  which  the  terms  are  given  in  units  of  force  and  space  as 
above. 

The  power  of  a  prime  mover  is  usually  ascertained  by  experi- 
mentally determining  the  work  done  in  a  given  time,  the  trial 


288  A    MANUAL    OF    THE   STEAM-ENGINE. 

usually  extending  over  some  hours,  and  often  several  days. 
It  is  measured  in  foot-pounds  or  kilogrammetres;  the  total 
work  so  measured  is  then  divided  by  the  time  of  operation 
and  by  the  value  of  the  horse-power  for  the  assumed  unit  of 
time  and  the  mean  value  of  the  power  expended  thus  finally 
expressed  in  horse-powers.* 

The  forces  acting  in  machines  are  distinguished  into  driv- 
ing and  resisting  forces.  That  component  of  the  force,  act- 
ing to  produce  motion  in  any  part  which  lies  in  the  line  of  motion 
only,  is  that  which  does  the  work;  and  this  component  is 
distinctively  called  the  "  Effort."  Similarly,  only  that  compo- 
nent of  the  resistance  which  lies  in  the  line  of  motion  is  con- 
sidered in  measuring  the  work  of  resistance.  In  either  case, 
if  the  angle  formed  between  the  directions  of  the  motion  of 
the  piece  and  of  the  driving  or  the  resisting  force  be  called  a, 
the  effort  is 

P  =  R  cos  a (6) 

The  other  component,  acting  at  right  angles  to  the  path  of 
the  effort,  is 

.  Q  =  R  sin  a (7) 

and  has  no  useful  effect,  but  produces  waste  of  power  by  in- 
troducing lateral  pressures  and  consequent  friction. 

Energy,  which  is  defined  as  capacity  for  performing  work, 
is  either  actual  or  potential. 

Actual  or  Kinetic  Energy  is  the  energy  of  an  actually  mov- 
ing body,  and  is  measured  by  the  work  whichjt  is  capable  of 
performing  while  being  brought  to  rest,  under  the  action  of  a 
retarding  force  ;  this  work  is  equal  to  the  product  of  its  weight, 

v* 
W,  into  the  height,  h  =  —  ,  through  which  it  must  fall  under 

the  action  of  gravity  to  acquire  that  velocity,  v,  with  which  it 
is  at  the  instant  moving;  i.e., 

E-U=Wh=  W— (8) 

<5 

*  Custom  has  not  yet  settled  the  proper  form  of  the  plural  of  this  word;  there 
is  no  reason  why  it  should  not  follow  the  rule. 


THE  PHILOSOPHY  OF    THE   STEAM-ENGINE.  289 

A  change  of  velocity  vt  to  vv  causes  a  variation  of  actual 
energy,  E^  —  Ev  and  can  be  effected  only  by  the  expenditure 
of  an  equal  amount  of  work  — 


.    .    (9) 


This  form  of  energy  appears  in  every  moving  part  of  evc-ry 
machine,  and  its  variations  often  seriously  affect  the  working 
of  mechanism. 

The  total  actual  energy  of  any  system  is  the  algebraic  sum 
of  the  energies,  at  the  instant,  of  all  its  parts  ;  i.e., 


(10) 


and  when  this  energy  is  all  reckoned  as  acquired  or  expended 
at  any  one  point,  as  at  the  driving-point,  the  several  parts 
having  velocities,  each  n  times  that  of  the  driving-point,  which 
latter  velocity  is  then  v,  the  total  energy  becomes 


Actual  energy  is  usually  reckoned  relatively  to  the  earth  ; 
but  it  must  often  be  reckoned  relatively  to  a  given  moving 
mass,  in  which  case  it  measures  the  work  which  the  moving 
body  is  capable  of  doing  upon  that  mass,  when  brought  by  it 
to  its  own  speed. 

Potential  Energy  is  the  capacity  for  doing  work  possessed 
by  a  body  in  virtue  of  its  position,  of  its  condition,  or  of  its 
intrinsic  properties.  Thus,  a  weight  suspended  at  a  given 
height  possesses  the  potential  energy,  in  consequence  of  its 
position,  E  =  Wh,  and  may  do  work  to  that  amount  while  de- 
scending through  the  height,  h,  under  the  action  of  gravity. 
A  bent  bow  or  coiled  spring  has  potential  energy,  which  be- 
comes actual  in  the  impulsion  of  the  arrow  or  is  expended  in 
the  work  of  the  mechanism  driven  by  the  spring.  A  mass  of 
gunpowder  or  other  explosive  has  potential  energy  in  virtue 


2QO  A    MANUAL    OF   THE   STEAM-ENGINE. 

of  the  unstable  equilibrium  of  the  chemical  forces  affecting  its 
molecules.  Food  has  potential  energy  in  proportion  to  the 
amount  of  vital  and  muscular  energy  derivable  by  its  consump- 
tion and  utilization  in  the  human  or  animal  system.  These 
potential  energies  are  not  measured  by  the  observed  actual 
energies  derived  from  these  substances  in  any  case,  but  are 
the  maximum  quantities  possibly  obtainable  by  any  perfect 
system  of  development  and  utilization.  In  practical  applica- 
tion, more  or  less  waste  is  always  to  be  anticipated. 

The  law  of  persistence  of  energy  affirms  that  the  total 
energy,  actual  and  potential,  of  the  universe,  or  of  any  isolated 
system  of  bodies,  is  of  invariable  amount,  and  that  all  energy 
is  thus  indestructible,  although  capable  of  transformation  into 
various  forms  of  physical  and  chemical  energy. 

Every  instance  of  disappearance  of  actual  energy  involves 
the  performance  of  work,  and  the  production  of  potential  or 
of  some  new  form  of  actual  energy  in  precisely  equal  amount. 
A  stone  thrown  vertically  upward  loses  kinetic  energy  as  it 
rises  in  precisely  the  amount — resistance  of  the  air  being  ne- 
glected— by  which  it  gains  potential  energy.  A  falling  mass 
striking  the  earth  surrenders  the  actual  energy  acquired  by 
loss  of  potential  energy  during  its  fall,  and  the  equivalent  of 
the  quantity  so  surrendered  is  found  in  the  work  done  upon  the 
soil ;  it  finally  passes  away  as  the  equivalent  energy  of  heat 
motion  produced  by  friction  and  impact.  The  potential  chem- 
ical energy  of  the  explosive  is  the  equivalent  of  the  kinetic 
energy  of  the  flying  projectile,  and  the  latter  has  its  equivalent 
in  the  work  done  at  the  instant  of  striking  and  coming  to  rest, 
and  in  the  heat  produced  by  the  final  change  of  mass-motion 
into  molecular  or  heat  motion. 

Energy  in  all  its  many  forms  is  thus  transferable  in  defi- 
nite quantivalent  proportions,  and  in  all  cases  changes  form 
when  work  is  done.  Work  may  therefore  be  defined  as  that 
operation  which  results  in  a  change  in  the  method  of  manifes- 
tation of  energy,  and  Energy  as  that  which  is  transferred  or 
transformed,  when  work  is  done.  The  motion  of  a  projectile 
is  the  transfer  of  energy  from  one  place  to  another.  It  is 
generated  at  the  point  of  departure,  stored  as  actual  or 


THE  PHILOSOPHY  OF  THE  STEAM-ENGINE.  2QI 

kinetic  energy,  transferred  to  the  point  of  destination,  and 
there  restored  and  applied  to  the  production  of  work. 

Acceleration  and  retardation  of  masses  in  motion  can 
only  be  produced  by  doing  work  upon  them,  or  by  causing 
them  to  do  work,  and  thus,  by  the  communication  of  energy 
to  them  or  by  its  absorption  from  them,  in  precisely  the  amount 
which  measures  the  variation  of  their  actual  energy  as  so  pro- 
duced. Every  body  which  is  increasing  in  velocity  of  motion 
thus  receives  and  stores  energy  ;  every  mass  undergoing  re- 
tardation must  perform  work,  and  thus  must  restore  energy 
previously  communicated  to  it.  In  every  machine  which  works 
continuously,  and  in  which  parts  are  alternately  accelerated  and 
retarded,  energy  is  stored  at  one  period  and  restored  at 
another,  in  precisely  equal  amounts. 

Work  done  upon  any  machine  may  thus  be  expended  partly 
in  doing  the  useful  work  of  the  system,  and  partly  in  storing 
energy  ;  and  the  same  machine  may  do  work  at  another  instant 
partly  by  expending  the  energy  received  by  it,  and  partly  by 
expending  stored  energy  previously  accumulated. 

Storage  or  restoration  of  energy  thus  always  occurs 
when  change  of  speed  takes  place.  It  is  evident,  since  the 
storage  or  restoration  of  energy  implies  variation  of  speed, 
that  the  condition  of  uniform  speed  is  that  the  work  done  upon 
the  machine  shall  at  each  instant  be  precisely  equal  to  that 
done  by  it  upon  other  bodies.  The  work  applied  must  be 
equal  to  that  of  resistance  met  at  the  driving-point.  Thus, 


^^Ri/',  J  Pdv=J*Rdv'\     .    .     .    (12) 

and  the  effort  at  each  point  in  the  machine  will  be  equal  to 
the  resistance,  and  inversely  as  the  velocity  of  the  point  to 
which  it  is  applied  ;  i.e., 


03) 


In  the  starting  of  every  machine  energy  is  stored  during 
the  whole  period  of  acceleration  up  to  maximum  speed,  and 
this  energy  is  restored  and  expended  while  the  machine  is 


2Q2  A   MANUAL   OF   THE   STEAM-ENGINE. 

coming  to  rest  again.  This  latter  quantity  of  energy  is  usually 
expended  in  overcoming  friction. 

The  useful  and  the  lost  work  of  a  machine  are,  together, 
equal  to  the  total  amount  of  energy  expended  upon  the 
machine,  i.e.,  to  the  work  done  upon  it  by  its  "driver."  The 
Useful  Work  is  that  which  the  machine  is  designed  to  perform  ; 
the  Lost  Work  is  that  which  is  absorbed  by  the  friction  and 
other  prejudicial  resistances  of  the  mechanism,  and  which  thus 
waste  energy  which  might  otherwise  be  usefully  applied. 
These  two  quantities,  together,  constitute  the  Total  Work  or 
the  Gross  Work  of  a  machine,  or  of  a  train  of  mechanism.  In 
every  case  some  energy  is  wasted,  and  the  work  done  by  the 
machine  is  by  that  amount  less  than  the  work  performed  in 
driving  it.  In  badly  proportioned  machines  the  lost  work  is 
often  partly  expended  in  the  deformation  and  destruction  c* 
the  members  of  the  construction  ;  in  well  designed  and  properly 
worked  machinery  loss  occurs  wholly  through  friction.  In 
machines  acting  upon  fluids  this  lost  work  is  usually  partly 
wasted  in  the  production  of  fluid  friction — i.e.,  of  currents  and 
eddies ;  thus  producing  new  forms  of  actual  energy  in  ways 
which  are  not  advantageous :  even  this  waste  energy  is  finally 
converted,  like  the  preceding  form,  by  molecular  friction  into 
heat,  and  is  dissipated  in  that  form  of  molecular  energy.  Thus 
all  wasted  work  is  lost  by  conversion  from  the  energy  of  mass- 
motion  into  molecular  energy  and  ultimately  disappears  as  heat. 

The  efficiency  of  mechanism  is  measured  by  the  quan- 
tity obtained  by  dividing  the  amount  of  useful  work  per- 
formed by  the  gross  work  of  the  piece  or  of  the  system.  It 
is  always,  therefore,  a  fraction,  and  is  less  than  unity  ;  which 
latter  quantity  constitutes  a  limit  which  may  be  approached 
more  and  more  nearly  as  the  wastes  of  energy  and  work  are 
reduced,  but  can  never  be  quite  reached.  If  the  mean  useful 
resistance  be  R,  and  the  space  through  which  it  is  overcome 
be  s',  and  if  the  mean  effort  driving  the  machine  be  P,  and  the 
space  through  which  it  acts  be  s,  the  total  and  the  net  or 
useful  work  will  be,  respectively,  Ps,  Rs'\  the  lost  work  will  be 
Ps  —  Rs'  and  the 

Efficiency  =        <  i.     .  '.  ' "...  ';' '  .     (14) 


THE  PHILOSOPHY  OF   THE   STEAM-EXGrXE.  2Q3 

Counter-efficiency,  C,  is  the  reciprocal  of  the  efficiency  ;  Le., 


The  efficiency  and  the  counter-efficiency  of  a  machine,  or 
of  any  train  of  mechanism,  is  the  product  of  the  efficiencies  or 
of  the  counter-efficiencies  of  the  several  elements  constituting 
the  train  transmitting  energy  from  the  point  at  which  it  is 
receivetd  to  that  at  which  the  work  is  done,  i.e.,  from  the 
M  driving"  to  the  "  working"  point. 

Friction  is  thus  the  principal  cause,  and  usually  the  only 
cause,  of  loss  of  energy  and  waste  of  work  in  machinery.  A 
given  amount  of  energy  being  expended  upon  the  driving- 
point  in  any  machine,  that  amount  will,  in  accordance  with 
the  principle  of  the  persistence  of  energy,  be  transmitted  from 
piece  to  piece,  from  element  to  element,  of  the  machine  or 
train  of  mechanism,  without  diminution,  if  no  permanent  dis- 
tortion takes  place  and  no  friction  occurs  between  the  several 
elements  of  the  train,  or  between  those  parts  and  the  frame 
or  adjacent  objects.  Temporary  distortion,  within  the  limit 
of  perfect  elasticity,  causes  no  waste  of  energy;  permanent 
distortion,  however,  causes  a  loss  of  energy  equal  to  the  total 
work  performed  in  producing  it.  But  permanent  distortion  is 
due  to  deficiency  of  strength  and  defective  elasticity,  and  is 
never  permitted  in  well-designed  machinery  properly  operated  ; 
and  hence  the  important  principle  : 

The  only  cause  of  lost  work  in  mechanism,  which  is  to  be 
anticipated  in  design  and  calculated  upon  in  deducing  the 
theory  of  special  mechanism,  is  the  friction  necessarily  conse- 
quent upon  the  relative  motion  of  parts  in  contact  and  under 
pressure. 

The  study  of  the  laws  of  friction,  the  construction  of  its 
theory,  and  the  experimental  investigation  of  the  conditions 
which  determine  the  loss  of  efficiency  in  machinery  by  friction, 
are  thus  obviously  of  supreme  importance  to  the  engineer 
who  designs,  the  mechanic  who  constructs,  and  the  operator 
or  manufacturer  who  makes  use  of  machinery. 


294  A    MANUAL   OF   THE  STEAM-ENGINE. 

In  engineering,  therefore,  the  principles  of  pure  mechan. 
ism,  of  theoretical  mechanics,  and  of  pure  theory  in  the  science 
of  energetics,  or  of  thermodynamics,  are  to  be  studied  as  intro- 
ductory to  a  science  of  application  in  which  all  actions  and  all 
calculations  are  to  be  considered  with  reference  to  the  modi- 
fications produced  by  the  wastes  of  energy  and  the  alteration 
of  the  magnitudes  and  other  properties  of  forces  consequent 
upon  the  occurrence  of  friction.  This  is  to  the  engineer  a 
vitally  important  branch  of  applied  science,  and  it  is  coexten- 
sive with  the  applications  of  mechanical  science. 

The  magnitude  of  the  lost  work  in  machinery  and  mill- 
work  is  variable,  but  is  always  very  large.  It  may  prob- 
ably be  fairly  estimated  that  one  half  the  power  expended  in 
the  average  case,  whether  in  mill  or  workshop,  is  wasted  in 
lost  work,  being  consumed  in  overcoming  the  friction  of  lubri- 
cated surfaces.  That  this  is  true,  is  evident  from  the  fact  that 
the  power  demanded  to  drive  the  machinery  of  such  establish- 
ments has  been  found  by  Cornut  and  others  to  be  variable  to 
the  extent  of  15  or  20  per  cent  by  simple  change  of  tempera- 
ture indoors  from  summer  to  winter,  and  a  reduction  of  50 
per  cent  in  the  work  lost  by  friction  has  often  been  secured 
by  change  of  lubricant.  Mr.  Fairbairn  has  found  a  change  to 
the  extent  of  10  to  15  horse-power  in  a  cotton-mill  from  the 
former  cause. 

The  friction  of  shafting  in  mills  varies,  with  size  and  load- 
ing, from  0.33  to  1.5  horse-power  per  100  feet  (31  m.)  length, 
averaging  for  the  "  main  line,"  with  good  lubrication,  about 
I  horse-power.  The  loss  of  power  in  mills  ranges,  with  differ- 
ent machines,  from  5  to  90  per  cent,  averaging  for  cotton  and 
flax  mills  about  60  per  cent,  with  good  management,  and  in 
woollen  mills  about  40  per  cent,  the  efficiencies  being  there- 
fore about  40  and  60  per  cent  for  the  two  cases.  The  friction 
of  heavy  iron-working  tools  maybe  taken  at  about/  =0.15, 
the  efficiency  at  0.85.  The  loss  in  the  steam-engine  is  usually 
nearly  constant  at  all  powers,  and  ranges  from  4  pounds  per 
square  inch  (0.27  atmosphere)  on  smail  engines  of  25  to  50 
horse-power,  down  to  I  pound  (0.07  atmosphere)  in  very  large 
marine-engines:  this  gives  efficiencies  ranging  from  0.84  to  95 


THE  PHILOSOPHY  OF   THE   STEAM-ENGINE.  295 

or  97  per  cent.  In  a  "high-speed"  engine  intended  to  drive 
electric  lights  the  Author  found  the  efficiency  to  be 

_.„  .                      0.06 
Efficiency  =  i -=j-, 

in  which  U  is  the  work  done,  calling  work  "  at  full  stroke" 
unity.  Rules  for  calculating  the  magnitude  of  this  loss  will 
be  given  in  later  chapters. 

"Absolute"  Power  is  that  measured  on  the  indicator-dia- 
gram, taken  down  to  the  line  of  zero-pressure,  that  of  perfect 
vacuum.  Taking  the  steam  used  per  horse-power,  per  hour, 
on  this  basis,  permits  a  comparison  to  be  made,  irrespective  of 
differences  of  back-pressure,  either  in  determining  the  intrinsic 
merits  of  different  types  or  of  individual  engines  of  the  same 
type. 

"Nominal"  power  is  that  at  which  the  machine  is  rated. 
It  may  represent,  as  in  the  now  usual  rating  of  boilers,  that 
which  the  engine  may  reasonably  be  expected  to  produce 
under  usual  conditions;  or  it  may,  as  in  old  British  practice, 
which  assumes  a  mean  effective  pressure  of  7  pounds  per 
square  inch,  simply  give  a  clue  to  the  dimensions  of  the 
machine;  while  its  actual  working  power  may  be  several  times 
greater. 

The  British  rule  for  finding  the  nominal  horse-power  of  an 
engine  is :  Multiply  the  square  of  the  diameter  by  the  speed  of 
the  piston,  and  divide  the  product  by  6000.  Thus  : 

Let  d  =  diameter  of  piston, 

/  =  the  length  of  the  stroke, 
»  =  the  revolutions  per  minute. 

The  speed  of  the  piston  is  =  /  X  2  X  «. 

Area  of  piston  =  d*  X  .7854. 

Work  done  per  minute  =  </*  X  .7854  X  7  X  (/  X  2  X  «). 

d*  X  7854  X  7  X  (/  X  2  X  «) 
H'P-  =  33000 

d*  X  speed  of  piston  , 
= 6000  -  (very  nearly). 


CHAPTER  IV. 

THERMODYNAMICS   OF   THE    IDEAL   ENIGNE. 
HEAT-UTILIZATION  BY  TRANSFORMATION. 

72.  The  Thermodynamics  of  the  Steam-engine  in- 
cludes simply  the  science  of  its  heat-transformations,  result- 
ing in  the  production  of  mechanical  energy  and  the  perform- 
ance of  work.  As  will  be  fully  shown  later,  this  constitutes  but 
a  part  of  the  theory  of  the  steam-engine;  although  it  was 
long  assumed  by  writers  on  the  subject  that  the  theory  of  the 
machine  was  purely  thermodynamic.  The  progress  of  discovery 
and  the  growth  of  the  elements  of  the  complete  theory  have 
been  traced  at  some  length  in  an  earlier  chapter.  The  design 
of  the  present  chapter  is  to  exhibit  the  relations  of  the  science 
of  heat-transformation  to  the  complete  theory  of  the  steam- 
engine. 

Since  the  differences  between  the  older  and  the  more 
recent  philosophy  of  the  heat-engines  grow  out  of  the  facts 
that  the  thermodynamic  treatment  of  the  case  is  thoroughly 
ideal  and  that  the  real  engine  exhibits  a  vastly  more  compli- 
cated and  wasteful  operation  than  does  the  ideal,  the  proposed 
treatment  includes,  first,  the  study  of  the  ideal  case  as  a  problem 
in  pure  thermodynamics  ;  secondly,  the  examination  of  the  real 
engine  and  its  comparison  with  the  ideal  ;  and,  thirdly,  the 
study  of  the  real  problem,  as  modified  by  all  the  conditions 
which  characterize  the  actual  engine  in  its  ordinary  operation. 
73.  Thermodynamics,  defined  as  that  science  which  treats 
of  the  laws  and  phenomena  of  those  processes  which  result  in 
the  conversion  of  thermal  and  of  dynamic,  of  heat  and  of 
mechanical  energy,  the  one  into  the  other,  is  the  science  of  the 
perfect  heat-engine.  In  this  science,  no  other  phenomena  are 

296 


THERMODYNAMICS  OF   THE  IDEAL  ENGINE.          2OJ 

considered;  no  other  thermal  or  mechanical  processes  are 
taken  cognizance  of ;  and  all  other  forms  of  energy  are,  in  its 
study,  ignored. 

Thus  the  wastes  of  heat  in  all  forms  of  heat-engine,  in  so 
far  as  they  consist  of  losses  by  conduction  or  radiation,  as 
heat,  without  transformation,  or  in  so  far  as  they  consist  in,  or 
involve,  conversion  into  other  forms  of  energy  than  heat  and 
dynamic,  are  extra-thermodynamic  and  must  be  separately 
considered.  Thermodynamics  is  that  science  which  relates  to 
systems  in  which  but  two  forms  of  energy  act  by  transfer  and 
natural  reaction  through  transformation. . 

74.  Thermodynamics  and  Energetics  are  related  as  a  part 
is  related  to  a  whole.  As  will  be  seen  presently,  the  former 
comprehends  laws  which  are  restricted  statements  of  the  more 
general  code  which  constitutes  the  broader  science,  and  its 
phenomena  are  forms  of  energy-transformation  which  illustrate, 
in  a  narrow  field,  principles  and  processes  as  extended  as  the 
universe  and  which  include  all  its  effects  of  active  or  stored 
energies  of  whatever  kind. 

An  intelligent  understanding  of  the  one  science  thus  pre- 
supposes an  understanding  of  the  fundamental  principles  of 
the  other  and  of  their  general  bearing  upon  all  physical  and 
chemical,  as  well  as  mechanical,  phenomena ;  in  other  words, 
upon  all  nature's  movements ;  whether  atomic,  molecular,  or 
mass  motion  be  illustrated. 

Energetics,  and  its  progeny,  Thermodynamics,  are  thus  the 
great  sciences  which  have  grown  out  of  the  discovery  of 
the  nature  of  heat  and  the  relations  of  the  various  forms  of 
energy.  They  are  the  product  of  the  present  century  and 
mainly  of  the  last  generation.  They  represent  the  highest 
achievement  of  man  in  the  substitution  of  the  deductive  for  the 
speculative  methods  in  science,  in  the  substitution,  rather,  of 
science  for  speculation.  But  while  they  are  spoken  of  as  the 
two  sciences  of  energetics  and  thermodynamics,  it  would  be 
more  correct  to  say  that  the  science  of  energetics  comprehends, 
among  other  of  its  subdivisions,  that  of  thermodynamics. 
There  might  also  be  a  branch  to  be  called  that  of  thermcelec- 


298  A   MANUAL   OF   THE  STEAM-ENGINE. 

tries,  or  one  called  electrodynamics,  as,  in  fact,  is  the  case. 
But  the  science  of  energetics  itself  is  but  one  division  of  a 
broader  science,  that  of  Mechanics — that  great  science,  which 
bears  more  or  less  directly  upon  every  phenomenon  of  nature 
and  of  the  universe,  and  which  is  at  the  foundation  of  all  the 
applied  sciences,  of  all  the  arts  of  construction,  of  all  the  exact 
science  of  physics  and  chemistry,  of  astronomy,  and  of  forces 
and  motions. 

Mechanics,  as  we  have  seen,  includes  four  principal  divisions: 

(1)  Statics  treats  of  the  relations  of  forces  acting  in  any 
system  when  no  motion  results  from  their  action. 

(2)  Kinematics  treats  of  the  relations  of  motions  simply,  of 
their  composition  and  resolution,  and  of  their  resultant  effects. 

(3)  Dynamics  or  Kinetics  treats  of  the  motions  produced  in 
bodies  by  the  action  of  forces. 

(4)  Energetics  treats  of  the  measurement,  the  transfer,  and 
the  transformations  of  energy,  under  the  action  of  forces,  and 
of  their  result  in  the  variation  of  the  method  of  its  manifestation. 

75.  Energetics  is  defined  as  that  science  which  treats  of 
all  natural  phenomena  which,  through  the  action  of  force  upon 
matter,  result  in  the  production  of  motion ;  whether  it  be  a 
relative  motion  of  atoms,  of  molecules,  or  of  masses.  It  is  that 
science  "whose  subjects  are  material  bodies  and  physical 
phenomena."  *  We  may  here  repeat  (§  51) : 

Energetics  thus  treats  of  modifications  of  energy  under  the 
action  of  forces,  and  of  its  transformation  from  one  mode  of 
manifestation  to  another,  and  from  one  body  to  another ;  and 
within  this  broader  science  is  comprehended  that  latest  of  the 
minor  sciences — of  which  the  heat-engines  and  especially 
the  steam-engine  illustrate  the  most  important  applications — 
Thermodynamics.  The  science  of  energetics  is  simply  a  wider 
generalization  of  principles  which  have  been  established  one  at 
a  time,  and  by  philosophers  widely  separated,  both  geographi- 
cally and  historically,  by  both,  space  and  time,  and  which  have 
been  slowly  aggregated,  to  form  one  after  another  of  the  physi- 

*  Rankine:  Proc.  Phil.  Soc.  Glasgow;  vol.  in.  No.  6. 


THERMODYNAMICS  OF   THE  IDEAL  EXGINE.          299 

cal  sciences,  and  out  of  which  we  are  slowly  evolving  wider 
generalizations,  thus  tending  toward  a  condition  of  scientific 
knowledge  which  renders  more  and  more  probable  the  truth  of 
a  principle,  still  broader  than  this  science,  even,  and  which  was 
enunciated  before  Science  had  a  birthplace  or  a  name  ;  i.e. : 

All  that  exists,  whether  matter  or  force,  and  in  wliatever 
form,  is  indestructible  by  any  finite  power. 

As  already  remarked,  that  matter  is  indestructible  by  finite 
power  became  admitted  as  soon  as  the  chemists,  led  by  Lavoi- 
sier, began  to  apply  the  balance,  and  were  thus  able  to  show 
that  in  all  chemical  change  there  occurs  only  a  modification 
of  form  or  of  combination  of  elements,  and  no  loss  of  matter 
ever  takes  place.  The  "persistence"  of  energy*  was  a  later 
discovery,  consequent  largely  upon  the  experimental  deter- 
mination of  the  convertibility  of  heat-energy  into  other  forms 
and  into  mechanical  work,  for  which  we  are  indebted  to  Rum- 
ford  and  Davy,  and  to  the  determination  of  the  quantivalence 
anticipated  by  Newton,  shown  and  calculated  approximately 
by  Colding  and  Mayer,  measured  with  great  accuracy  by  Joule 
and  Rowland. 

It  is  now  generally  understood  that  all  forms  of  energy  are 
mutually  convertible  with  a  definite  quantivalence ;  and  it  is 
not  certain  that  even  vital  and  mental  energy  do  not  fall  within 
the  same  category. 

The  essentially  important,  as  well  as  interesting,  fact,  in  this 
connection,  to  the  engineer  as  well  as  to  the  physicist,  it  should 
be  noted,  is  that  the  laws  of  energetics  apply  unqualifiedly  to 
atomic  and  molecular  phenomena,  as  well  as  to  energies  of 
masses,  and  to  all  transformations  of  energy  in  either  class  and 
of  any  kind.  There  is,  dynamically,  absolutely  no  distinction, 
in  this  respect,  between  the  methods  and  processes  of  chem- 
istry, of  physics,  and  of  the  mechanics  of  masses.  All  illustrate 
phases  of  one  science,  and  all  are  energies  of  matter  in  motion. 

76.  Matter,  Force,  and  Energy  are  the  only  quantities 
known  to  the  departments  of  natural  science.  The  science  of 

*  The  term  "  energy  "  was  first  used  by  Dr.  Young  as  the  equivalent  of  the 
Work  of  a  moving  body,  in  his  "  Lectures  on  Natural  Philosophy  "  (1807). 


300  A   MANUAL    OF   THE   STEAM-ENGINE. 

Chemistry  deals  with  the  forms  which  matter  assumes  under 
the  action  of  measurable  atomic  molecular  forces  affecting  dis- 
similar kinds  of  matter;  Physics  is  that  science  which  deals 
with  all  the  other  forms  of  sensible  force  and  their  effects.  The 
science  of  Energetics  treats  of  the  action  of  forces  when  motion 
is  produced,  whatever  the  kind  of  force,  whatever  the  kind  of 
matter ;  it  thus  covers  the  whole  range  of  chemistry  and 
physics. 

Matter  is  that  which  is  capable  of  directly  affecting  the 
senses,  and  which  occupies  space.  Nothing  is  known  of  the 
ultimate  nature  of  matter,  and  we  are  acquainted  with  it  only 
as  it  affects  the  organs  of  the  body.  It  is  usually  divided  into 
four  classes :  solids,  liquids,  gases,  and  imponderable  matter,  or 
that  which  cannot  be  assigned  a  finite  specific  measure  of  mass 
or  weight ;  the  luminiferous  aether  is  an  example  of  this  last ; 
the  other  three  are  familiar  forms. 

A  Body  is  a  limited  portion  of  matter. 

Force  is  that  which  produces,  or  tends  to  produce,  motion, 
or  change  of  motion,  in  bodies ;  it  is  measured,  statically,  by 
the  -weight  which  will  counterpoise  it,  or  by  comparison  with  a 
known  standard  of  force,  and,  dynamically,  by  the  velocity 
which  it  will  give  to  a  known  mass,  in  a  stated  time,  i.e.,  by  the 
"  acceleration  "  which  it  is  capable  of  producing. 

Work  is  always  performed  by  the  expenditure  of  energy, 
and  is  the  product  of  the  resistance  overcome  by  a  force,  or  of 
the  effort  exerted  by  it,  into  the  space  through  which  that  ac- 
tion takes  place.  That  resistance  may  be  constant,  or  variable, 
and  due  to  an  active,  opposing  force,  to  resisting  pressure,  to 
the  inertia  of  masses,  or  of  molecules  compelled  to  submit  to 
acceleration  or  retardation  ;  or  it  may  be  due  to  any  one  of  the 
physical  or  chemical  forces.  Thus,  if  U  represents  the  work 
done  by  a  force,  F,  acting  through  a  space,  s, 

U=Fs (i) 

For  variable  motion, 

dU=Fds (2) 


THERJIODYXAAIICS  OF   THE  IDEAL  ENGIXE.  3OI 

For  variable  forces, 

dU=sdF.    ........    (3) 

For  forces  and  motion  variable, 

dU  =  *Fs)  ........    (4) 

The  Unit  of  Work  is  the  product  of  the  units  of  its  factors 
force  and  space,  as  the  foot-pound,  the  kilogrammetre,  the  foot- 
ton,  the  gramme-centimetre. 

Useful  Work  is  that  which  is  applied  to  the  production  of  a 
specified  useful  effect  ;  Lost  Work  is  that  which  is  incidentally 
wasted,  in  the  endeavor  to  perform  useful  work,  in  overcoming 
prejudicial  resistances,  and  in  doing  useless  work  ;  this  waste 
occurs  usually  and  principally  in  overcoming  friction  of  moving 
parts. 

Work  of  Acceleration  is  work  expended  in  producing  in- 
creased velocity  in  a  freely-moving  body.  The  effort  exerted, 
and  the  resistance  met,  is  dependent  upon  the  inertia  of  the 
mass,  and  is  measured  thus  :  A  body  moving  freely  under  the 
action  of  gravity,  Le.t  of  a  force  equal  to  its  own  weight,  ac- 
quires, in  this  latitude,  a  velocity  of  32.2  feet  (9.81  metres), 
nearly,  in  one  second,  and  the  acceleration,  or  retardation,  of 
any  freely-moving  body  is  proportional  to  the  effort  applied,  as 
to  the  resistance  met  by  it.  If  f  is  the  actual  acceleration,  if  g 
measures  that  produced  by  gravity,  if  F  is  the  statical  measure 
of  the  effort,  and  W  is  the  weight  of  the  body,  we  have 

F'.Wr.f'.g;   /:  i  ::*,-*.:/; 


(5) 


i\  and  p,  being  the  initial  and  final  velocities,  and  /  the  time  of 
action  of  the  accelerating  force. 


302  A   MANUAL    OF   THE   STEAM-ENGINE. 

For  variable  acceleration, 

-  /-$: W 

dv     W 

p=*i--g w 

The  space,  s,  is  equal  to  -J —  t,  and  the  work  done  is,  for 

uniform  acceleration, 


For  variable  acceleration, 

U=d(Fs}=W.d.^=WV-^- (9) 

Since  --  =  k,  the  height  due  the  velocity  v,  the  work  is 

equal  to  that  required  to  raise  the  body  through  the  difference 
of  the  two  heights  due  the  initial  and  the  final  velocities,  re- 
spectively. 

Energy,  the  product  of  these  forces  acting  upon  this  matter, 
may  be  defined  as  capacity  for  doing  work,  or  to  effect  physical 
change ;  it  is  measured,  either  by  the  measure  of  the  work 

which  it  can  perform,  Fs,  or  by  the  available  vis  viva,  W L 

or  the  work  of  acceleration.    The  quantity,  W  —-,  is  the  "actual 

energy"  of  the  mass,  W.  When  the  body  is  relatively  at  rest, 
and  thus  without  available  actual  energy,  but  yet  is  so  situated 
that  it  may  do  work  by  change  of  position,  or  of  affecting 
conditions,  under  the  action  of  existing  or  available  forces,  as, 
for  example,  when  it  may  do  work  by  falling  from  a  height, 


THERMODYNAMICS  OF  THE    IDEAL  EXGINE.          303 

ft   possesses  "potential    energy";    this   is    measured  by  the 

tf 
product,  Wh  —  W-,  of  the  weight  into  the  height  of  fall,  or 

into  the  height  due  the  final  velocity  which  may  be  acquired. 

Energy,  whether  of  Masses,  or  of  Molecules,  wherever  ex- 
isting, has  the  same  character,  quality,  and  measure ;  yet  its 
availability  for  useful  purposes  depends  very  greatly  upon  the 
nature  of  the  body  through  which  it  acts,  and  upon  the  method 
of  its  exhibition.  The  two  methods  of  exhibition  of  energy 
are,  thus,  in  the  forms  of  energy  of  masses  and  of  molecular  or 
of  atomic  energy.  A  falling  stone,  flowing  water,  a  flying 
shot,  are  illustrations  of  the  first,  and  the  energy  of  heat,  of 
electricity,  and  of  chemical  combination  of  the  second. 

Energy  may  be  potential  as  well  as  actual  in  either  class, 
as  the  potential  energy  of  a  suspended  weight,  or  of  water  in 
the  reservoir  in  the  one.  or  that  of  unignited  fuel,  or  gun- 
powder or  of  the  open  voltaic  circuit  in  the  other. 

Energy  of  the  second  form  is  often,  but  never  necessarily, 
measured  in  other  units  than  those  customarily  adopted  in 
mechanics,  as  in  ** thermal  units,"  in  "ergs,"  or  in  "volt- 
amperes-"  All  such  units  are  capable  of  reduction  to  a  com- 
mon standard,  which  will  here  be  taken  as  either  British,  as 
in  foot  pounds,  or  metric,  as  in  kilogram  metres.  Work  and 
energy  must  evidently  have  this  same  measure. 

The  quantity  of  work  done,  or  of  energy  transformed,  in 
the  unit  of  time,  is  measured  by  the  Unit  of  Power,  which,  in 
engineering,  is  usually  the  horse-power;  this  is,  reckoned  in 
British  units, 

550  foot-pounds  per  second; 
33,000    •«          •          «    minute; 
1,980,000    "  hour; 

in  metric  units,  the  horse-power  is  taken  as 

75  kilogrammetres  per  second ; 
-  4,500  "   minute; 

270,000  *:  **  hour. 


304  A    MANUAL   OF   THE   STEAM-ENGINE. 

These  units  are,  however,  slightly  different,  the  British 
horse-power  being  1.014  metric  horse-power;  i.e.,  instead  of 
550  foot-pounds  per  second,  or  33,000  per  minute,  the  latter 
is  542-J  per  second,  or  32,549  per  minute.  Neither  unit  is  the 
measure  of  the  power  of  a  horse,  which  is  usually  lower,  aver- 
aging 20  or  25  per  cent  less  than  the  above  figures. 

77.  The  Laws  of  Energetics,  the  basis  of  the  science 
which  it  has  been  proposed  to  call  by  that  name,  are : 

(1)  The  Law  of  Persistence,  or  of  Conservation  of  Energy, 
viz. — Existing  energy  can  never  be  annihilated  ;  and  the  total 
energy,  actual  and  potential,  of  any  isolated  system  can  never 
change. 

This  is  evidently  a  corollary  of  that  grander  law,  asserting 
the  indestructibility  of  all  the  work  of  creation,  which  has  al- 
ready been  enunciated. 

(2)  The  Law  of  Dissipation,  or  of  Degradation  of  Energy, 
viz. — All  energy  tends  to  diffuse  itself  throughout  space,  with 
a  continual  loss  of  intensity,  with  what  seems,  now,  to  be  the 
inevitable  result  of  complete  and  uniform  dispersion  through- 
out the  universe,  and  consequently  of  entire  loss  of  availability. 

It  is  only  by  differences  in  the  intensity  of  energy,  and  the 
consequent  tendency  to  forcible  dispersion,  that  it  is  possible 
to  make  it  available  in  the  production  of  work. 

(3)  The  Law  of  Transformation   of  Energy,   viz. — Energy 
may  be  transformed  from  one  condition   to  another,  or  from 
anyone  kind  or  state  to  any  other  ;  changing  from  mass-energy 
to  molecular  energy  of  any  kind,  or  from  one   form  of  molecu- 
lar energy  to  another,  with  a  definite  quantivalence. 

These  laws  lead  to  the  conclusion  that,  in  any  isolated 
system  of  bodies,  or  in  any  isolated  mass,  the  total  of  all  energy 
present  is  always  the  same ;  though  it  may  be  transformed  in 
various  ways,  and  to  an  extent  only  limited  by  the  special  con- 
ditions affecting  the  system.  They  lead  to  the  conclusion  that 
energy  of  higher  intensity  than  the  mean  must  occupy  a  lim- 
ited space,  and  will  continually  tend  to  dissipate  itself  by  dis- 
semination through  a  greater  volume,  affecting  larger  and 
larger  quantities  of  matter,  with  proportional  reduction  of  in- 


THERMODYNAMICS  OF   THE  IDEAL  EXCIXE.          y>5 

tensity,  until  the  whole  system  is  occupied  by  the  originally 
existing  energy,  at  a  finally  uniform  and  minimum  intensity. 
Energy  confined  within  a  limited  space  thus  continually  tends 
to  expand,  and  to  break  through  its  boundaries,  and,  if  not 
freed  from  this  constraint,  it  produces  a  pressure  upon  the  sur- 
rounding surfaces,  which,  e.g.,  is  exhibited  as  tension  of  en- 
closed vapors  and  gases.  Freed  from  confinement,  it  tends  to 
indefinitely  expand. 

Either  form  of  energy  may  produce  either  other  form 
under  suitable  conditions. 

Rankine's  statement  of  the  **  General  Law  of  the  Transfor- 
mation of  Energy"  is  as  follows:  * 

"  The  effect  of  the  whole  actual  energy  present  in  a  sub- 
stance, in  causing  transformation  of  energy,  is  the  sum  of  the 
effects  of  all  its  parts." 

The  ajciom,  as  Rankine  calls  it,  that  "  any  kind  of  energy 
may  be  made  the  means  of  performing  any  land  of  work"  is 
derived  by  "  induction  from  experiment  and  observation."  and 
confirmed  by  all  experience.  The  science  of  energetics  may 
be  based  either  upon  this  principle,  so  derived,  or.  probably 
better,  upon  the  fundamental  law  stated  as  underlying  all  ex- 
istences :  although  the  latter  has,  after  all,  the  same  basis. 
The  science  is  one  of  which,  as  its  great  student  has  said,  the 
subjects  are  boundless ;  and  never  can,  by  human  labors,  be 
exhausted,  nor  the  science  brought  to  perfection. 

Professor  Balfour  Stewart  considered  the  universe  to  be 
"composed  of  atoms  with  some  sort  of  medium  between  them 
as  the  machine,  and  the  laws  of  energy  as  the  laws  of  working 
of  this  machine." 

The  Sources  of  Energy  are :  (i)  Potential:  ia)  fuel;  (S) 
food  :  if)  head  of  water ;  (</)  chemical  forces.  (2)  Actual :  (a)  air 
in  motion ;  (£)  gravity  in  waterfalls  ;  (c)  tides. 

78.  "  Newton's  Laws"  follow  directly  from  the  general 
law  of  persistence  of  energy,  a  corollary  to  which  may  be  stated 
thus :  Change  of  energy  can  only  be  produced  by  the  action  of 
force,  and  by  doing  work.  Newton's  Lar&s  are : 

*  Proc.  Phfl.  Soc.  of  Glasgow:  vol.  in.  Xo.  V  ;  iS5J. 


306  A   MANUAL    OF    THE   STEAM-ENGINE, 

(1)  A  free  body  tends  to  continue  in  the  state  in  which  it, 
at  any  instant,  exists,  either  of  rest  or  of  uniform  rectilinear 
motion. 

(2)  All  change  of  motion  in  a  body  free  to  move  is  propor- 
tional to  the  force  impressed,  and  is  in  the  direction  of  that 
force. 

(3)  The  reaction  of  the  body  acted  upon  by  the  impressed 
force  is  equal,  and  directly  opposed,  to  that  force. 

Inertia  is  that  property,  observed  in  all  bodies,  in  conse- 
quence of  the  existence  of  which  they  are  capable  of  exhibit- 
ing the  action  of  these  laws.  The  laws  of  Newton  themselves 
are  all  easily  verified  by  experiment.  The  "  Atwood  Machine," 
illustrated  in  nearly  all  works  on  physics,  is  constructed  for  this 
special  purpose. 

While  Newton's  laws  are  readily  verified  by  experiment, 
the  more  general  laws  of  energetics  are  accepted  simply  as 
being  in  accordance  with  universal  experience.  The  generally 
accepted  theory  of  the  constitution  of  matter  being  assumed 
as  a  premise,  however,  the  general  laws  of  energy  are  all  easily 
deducible  from  Newton's  laws.  Thus:  the  first  law  is  but  a 
differently  worded  statement  of  Newton's  three  laws  combined. 

To  assert  that  every  moving  body  tends  to  persist  in  its 
rate  of  motion,  exerting  an  effort  always  equal  to  the  retarding 
or  accelerating  force,  and  exerting  such  effort  in  the  line  of 
action  of  such  force,  is  to  assert  that  its  energy  can  only  be 
altered  by  the  performance  of  an  equivalent  amount  of  work, 
and  an  equal  amount  of  energy  of  opposite  sign  ;  and  this 
latter  assertion  is  a  declaration  of  the  indestructibility  of  en- 
ergy. To  assert  that  all  bodies,  whether  masses  or  molecules, 
when  in  motion  tend  to  move  in  rectilinear  paths,  is  to  assert  a 
tendency  to  unlimited  dissipation  of  energy  through  space. 
To  assert  that  all  matter  in  motion  is  subject  to  Newton's  laws 
is  to  assert  the  laws  of  universal  conservation  of  energy,  and 
of  the  quantivalence  of  all  transformations,  as  stated  in  the 
third  general  law.  Whenever  it  becomes  established  that  any 
phenomenon,  as  the  transfer  of  heat,  of  light,  of  electricity,  or 
of  sound,  is  a  mode  of  motion  affecting  bodies  of  whatever 


TffEKMODYXAJf/CS  OF   THE  IDEAL  EXCIA'E.          JOJ 

class,  Newton's  laws  bring  that  phenomenon  within  the  scope 
of  the  general  laws  of  energy.  Every  phenomenon,  molecular 
or  other,  which  involves  relative  motion  of  masses,  vibrations 
of  parts,  or  pulsations  in  fluid  media,  is  now  well  understood  to 
lie  subject  to  these  laws. 

Tait  *  finds  in  the  Prinripia  of  Xewton,  in  the  scholium  to 
his  Third  Law,  the  enunciation  of  the  principle  of  D'Alembert, 
and  also  of  the  Law  of  Conservation  of  Energy.  He  para- 
phrases this  statement  thus : 

*•  Work  done  in  any  system  of  bodies  has  its  equivalent  in 
the  form  of  work  done  against  friction,  molecular  forces,  or 
gravity,  if  there  be  no  acceleration ;  but  if  there  be  accelera- 
tion, part  of  the  work  is  expended  in  overcoming  resistance  to 
acceleration ;  and  the  additional  energy  developed  is  equiva- 
lent to  the  work  so  spent." 

70.  Algebraic  Expressions  of  the  transformabflity  of  the 
energies  are  now  readily  deduced.  If  in  any  isolated  system  a 
certain  quantity  of  energy  exists,  homogeneous  in  character 
and  heterogeneously  distributed ;  and  if,  by  any  process,  other 
and  various  forms  of  energy  appear  in  that  system,  these  latter 
must  be  the  result  of  transformations  of  parts  of  the  initial 
stock  of  energy  by  conversion  into  the  new  forms.  But  every 
such  change  must  be  effected  by  a  perfectly  definite  and  exact 
MpantivaleBOt: 

Assume  this  ratio  of  values  of  customary  units  reduced  to  a 
system  of  equivalents,  then  it  becomes  at  once  practicable  to 
measure  all  these  energies  in  the  same  units ;  as,  for  example, 
when  Joule  measures  either  heat  or  mechanical  energy-,  taking 
f  =  772  foot-pounds  as  the  equivalent  of  a  British  thermal  unit, 
orj=  about  423  kilogrammftrcs.as  the  equivalent  of  one  metre 
or  thermal  unit  alone ;  the  thermal  unit  being  defined  as  the 
quantity  of  beat  or  energy-equivalent  demanded  to  raise  the 
temperature  of  unit  weight  of  water  one  degree  from  the  tem- 
perature of  maximum  density. 

Taking  either  kind  of  unit  in  thus  measuring,  we  shall  have 

«  Sketch  of  TbenBadj»anks;  Revised  Ed.,  PL  65. 


308  A   MANUAL    OF    THE   STEAM-ENGINE. 

the  initial  stock  of  the  one  kind  of  energy  altered  by  the  quan- 
tity which,  in  the  same  units,  measures  the  aggregate  several 
quantities  of  energy  resulting  from  the  change  ;  and 


where  E,  T,  U,  V,  etc.,  are  the  symbols  representing  the  several 
energies,  initial  and  other. 

If  T  measure  heat-energy,  and  U  be  taken  as  potential  en- 
ergy of  the  molecular  kind,  Fthe  potential  energy  of  an  elastic 
fluid  varying  in  volume,  W  the  work  of  some  mechanism  or  a 
dynamic  process,  the  total  variation  of  the  initial  energy,  £, 
will  be  equal  to  the  total  of  all  the  new  energies,  and  the  new 
work,  in  proportions  which  become  known  as  soon  as  the  par- 

tial coefficients  -jy,  etc.,  are  determined. 

If  two  energies  only,  as  thermal  and  mechanical,  are  affected, 
and  if  the  original  stock  were  simply  heat-energy,  we  should 
have  a  change,  dE,  in  the  initial  stock  of  heat-energy,  which 
would  be  the  precise  equivalent  of  the  sum  of  the  two  changes 
taking  place,  simultaneously,  in  the  initial  store  and  in  the 
temperature,  T,  of  the  system,  and  in  work  by  the  change  of 
volume,  F,  against  a  pressure  of,  say,  the  intensity/.  Then, 
obviously, 


and,  since  (^j^   measures  the  specific  heat,  Km  for  constant 

volume,  and  as  [~^j     must  measure  the  intensity  of  pressure 
producing,  or  resisting,  the  change  of  volume, 

dE  =  KvdT  +  pdV.     ...    V.     .     (3) 

If  but  one  kind  of  transformation  occurs,  as  by  conversion  of 
any  original  form  of  energy,  E,  into  work, 

dE=pdV\     or,     dE—RdS\     ....     (4) 


THERMODYNAMICS  OF   THE  IDEAL  EA'CIXE.  309 

accordingly  as  the  work  is  performed  in  compressing  a  fluid, 
or  in  overcoming  a  resistance,  R,  through  a  space.  dS. 

80.  Energetics  and  Thermodynamics  are  thus  seen  to  be 
sciences  of  similar  general  character,  of  which  the  first  involves 
the  second,  together  with  all  other  applications  of  the  founda- 
tion-principles of  the  persistence  of  energy,  and  of  equivalence 
in  transformation  of  energy  from  one  form  to  another. 

Energetics,  as  first  defined  by  Rankine.  comprehends  all 
physical  phenomena  involving  transfer,  or  change,  of  energy. 
Thermodynamics  confines  itself  to  such  as  involve  simply  trans- 
fer, or  transformation  of  energy,  in  the  related  forms  of  heat 
and  mechanical  energy.  The  general  laws  of  transformation 
of  energy  are  here  limited,  in  their  application,  to  cases  in  which 
heat  is  transformed  into  mechanical  energy,  or  by  the  produc- 
tion of  mechanical  work,  and  to  instances  of  the  opposite  kind, 
in  which  mechanical  energy  or  work  produces  heat  by  its  own 
transformation  into  thermal  energy. 

When  heat  enters  into  any  substance,  the  operation  is  a 
process  of  adding  to  the  total  energy  of  that  mass,  and  it  may 
increase  either  its  kinetic  or  its  potential  energy,  or  both  ;  the 
loss  of  heat  from  a  body  is  the  loss  of  a  definitely  measurable 
quantity  of  energy. 

The  usual  effects  are  these  : 

(1)  To  increase  the  energy  of  molecular  motion,  by  intensi- 
fying the  energy  of  vibration  of  the  particles. 

(2)  To  separate  molecules,  thus  producing  an  increase  of 
potential  energy. 

(3)  Expanding  the  whole  mass  against  external  pressure ; 
Le.,  doing  external  work. 

The  sum  of  all  work  in  these  three  ways  is  the  mechanical 
equivalent  to  the  heat-energy  transferred. 

Heat  being  energy,  there  can  be  no  restricted  kinematic 
science  of  Thermotics ;  this  science  is  purely  thermodynamical. 

TJie  Science  of  Thermodynamics  is  defined  as  comprehending 
all  facts  and  principles  which  are  involved  in  the  transforma- 
tion of  heat-energy  into  mechanical  energy,  or  work,  or  in  the 
reverse  process.  This  science  consists  of  a  system  of  definitely 


3IO  A  MANUAL    OF   THE   STEAM-ENGINE. 

stated  laws,  based  on  observed  facts,  and  united  to  form  a  con- 
sistent physical  theory. 

Thermodynamics  is  sometimes  called  the  "  Mechanical 
Theory  of  Heat ;"  but  it  is  more  than  this ;  and,  based  on  that 
theory,  it  comprehends  all  the  physical  laws  and  all  the  phe- 
nomena involved  in  dynamic  changes  in  which  heat-energy 
plays  a  part.  The  mechanical  theory  of  heat — i.e.,  the  theory, 
now  considered  established,  that  heat  is  a  form  of  energy — is 
simply  the  expression  of  a  fact  which  underlies  the  science  of 
thermodynamics.  Thermodynamics  is  thus  a  branch  of  the 
division,  "  Energetics,"  of  the  still  broader  science,  "  Me- 
chanics." 

81.  The  Basis  of  the  Science  of  Thermodynamics  is 
found  in  the  fundamental  laws  of  persistence  of  energy  and  of 
existing  forms  of  matter,  which  have  been  already  enunciated, 
which  laws  are  here  restricted  to  their  applications  in  the  rela- 
tions of  interchanging  heat  and  work ;  they  are,  therefore, 
restricted  statements  of  the  more  general  laws  of  energy,  and 
are  all  comprehended  in  the  larger  science.  The  science  of 
thermodynamics  is  thus  based  upon  the  experimentally  proven 
facts  that  heat  is  a  form  of  energy ;  that  "  it  is  a  kind  of  mo- 
lecular disturbance ;  that  the  motion  is,  in  solids,  one  of  vibra- 
tion, in  fluids,  of  translation,  of  molecules ;  that  it  is  possible 
to  transfer  this  molecular  energy  from  part  to  part  of  any 
mass,  and  from  one  body  to  another,  by  contact — i.e.,  by  con- 
duction— and  by  radiation  through  space,  the  "  luminiferous 
aether"  supplying  the  necessary  medium  ;  that  this  molecular 
energy  may  become  transformed  into  other  kinds  of  energy, 
and  that  such  transformation  is  definite  in  its  extent  and  in  its 
effects. 

As  will  be  hereafter  seen  more  fully,  therefore,  the  Science 
of  Thermodynamics  is  based,  primarily,  upon  the  great*  laws  of 
the  persistence  of  energy,  of  the  equivalence,  in  transformation, 
of  one  form  of  energy  into  another,  and  of  the  tendency  of  all 
kinds  of  energy  to  indefinite  expansion,  with  indefinite  reduc- 
tion of  intensity ;  it  rests  directly  upon  two  sets  of  well-estab- 
lished relations : 


THERMODYNAMICS  OF   THE  IDEAL  ENGINE.  $11 

(1)  The  relation,  qualitatively  known,  and  quantitatively 
established  with  a  considerable  degree  of  accuracy,  between 
heat,  considered  as  one  form  of  energy,  and  mechanical  work 
and  energy,  either  actual  and  kinetic  or  stored  and  potential. 

(2)  The  relation  between  variations  of  quantities  of  heat 
and  of  mechanical  work  or  energy,  during  a  process  of  transfer 
or  transformation,  and  the  temperature  at  which  such  trans- 
formation, or  transfer,  takes  place. 

These  relations  being  determined,  equations  are  easily  de- 
duced from  them  expressing  the  efficiency  of  heat-engines,  and 
applicable  to  all  physical  actions  illustrating  such  changes. 

The  Methods  of  Transformation,  in  such  thermodynamic  op- 
eration in  heat-engines,  involve,  simply,  the  variation  of  the 
volume  and  pressure  of  a  confined  "working  substance,"  which 
expands  with  accession  of  heat  and  contracts  with  its  refection. 
The  resistance  to  expansion  by  heat  during  the  first  operation 
is  less  than  that  met  with  in  the  second,  and  the  mean  differ- 
ence measures  the  mean  external  resistance,  the  continuous 
overcoming  of  which  constitutes  the  work  of  the  system.  It 
is  evident  that  such  changes  are  essential  to  the  production 
of  mechanical  energy;  as  no  work  can  be  done  at  constant 
volume,  either  externally  or  internally. 

This  working  substance  may  be  either  solid,  liquid,  or  gas- 
eous ;  is  almost  invariably  of  the  latter  class,  and  is  always  of 
this  class  in  the  familiar  forms  of  heat-motors. 

Tlie  First  Law  of  TJiermodynamics  may  be  stated  thus : 

Where  work  is  done  by  expenditure  of  heat,  the  quantity  of 
heat  consumed — i.e.,  transformed  or  converted — is  a  measure 
of  the  quantity  of  work  done,  or  of  energy  acquired,  in  the  new 
form ;  and,  conversely,  the  transmutation  of  work  into  heat- 
energy  occurs  by  a  definite  equivalence. 

This  first  law,  or  fundamental  principle,  has  several  impor- 
tant corollaries : 

(i)  When  mechanical  energy  is  expended  upon  bodies 
which  do  not  transfer  it  to  others,  or  do  not  in  any  way  trans- 
form it,  heat  is  produced  in  equivalent  amount,  and  the  tem- 
perature of  the  mass  is  thus  correspondingly  elevated. 


312  A    MANUAL    OF    THE   STEAM-ENGINE. 

Conversely :  When  mechanical  energy  is  expended  by  an 
expanding  body  exhibiting  no  mass-energy,  and  without  trans- 
fer of  heat,  the  substance  loses  an  equivalent  amount  of  heat, 
and  its  temperature  is  correspondingly  depressed. 

(2)  When  internal  work  is  gained  or  lost  during  changes  or 
transfers  of  energy,  the  amount  of  that  work  measures  a  corre- 
sponding external  loss  or  gain  of  heat  or  work. 

(3)  No  internal  work  being  done,  all  isothermal  changes  are 
accompanied  by  a  transfer  of  heat  to  or  from  the  substance, 
precisely  equal  in  amount  to  the  work  done  by  that  substance 
upon  other  bodies,  or  by  other  bodies  upon  it. 

(4)  Whatever  the  character  of  the  work  done  by,  or  upon, 
any  substance,  the  actual  thermal,  or  internal,  energy,  whether 
kinetic  or  potential,  will  remain  unchanged  only  when  the  en- 
ergy  so  transferred  has  an  equivalent  in  the  quantity  of  heat  re- 
ceived by  it,  in  the  one  case,  or  discharged  from  it,  in  the  other. 

The  principle  of  equivalence  of  energy  thus  applies  in  ther- 
modynamic  changes  as  it  does  whenever  transformation  occurs 
between  any  existing  forms  of  energy,  whether  mechanical, 
physical,  or  chemical ;  and,  evidently,  since  the  algebraic  sum  of 
all  energies  communicated  to  any  substance  is  equal  to  the 
algebraic  sum  of  all  work  done,  both  within  the  substance  and 
by  it  upon  other  bodies,  and  of  all  energies  stored  within  it,  or 
transferred  by  it  to  adjacent  masses,  the  same  principle  and  its 
converse  obviously  hold  with  respect  to  this  limited  class,  in- 
volving only  thermal  and  mechanical  energies. 

The  Second  Law  of  Thermodynamics,  which  relates  to  the 
proportion  of  energy  present  in  any  thermodynamic  operation, 
which  may  be  converted  from  the  one  into  the  other  of  the 
two  forms,  and  in  accordance  with  the  First  Law,  will  be  stated 
later. 

82.  Algebraic  Expressions  of  the  First  Law  of  Ther- 
modynamics, illustrating  the  operations  seen  wherever  one  of 
the  two  forms  of  energy  is  converted  into  the  other,  are  readily 
deduced : 

As  illustrating  the  transformability  of  heat  into  mechanical 
energy,  suppose  a  quantity  of  heat,  Q,  in  thermal  measure, 


THERMODYNAMICS  OF   THE  IDEAL  ENGIXE.  313 

given  in  dynamic  measure,  H  =  JQ,  to  be  expended  in  raising 
a  weight  Wto  a  certain  height,  h,  thus  performing  mechanical 
work,  Wh  \  let  the  body  thus  raised  fall  again,  and  measure  its 
height,  //',  and  velocity,  r',  at  any  given  altitude,  thus  deter- 
mining the  actual  and  potential  energies  at  that  point.  We 
should  thus  find  several  equivalent  measures  of  energy,  taking 
as  before  /  =  H  H-  Q  ; 


.      .    (i) 


Should  the  falling  mass  strike  an  inelastic  body  on  reaching 
the  ground,  transferring  to  it  all  its  energy  without  producing 
movement  of  the  mass  struck  ;  or  should  it  be  arrested  by 
friction,  the  equivalent  of  all  this  energy  would  reappear  in  its 
original  form  of  heat,  and  might  be  measured  by  the  quantity 

W(v  *  _  v  *\  W 

~^-2  -  —  ,  in  which  W  is  the  weight,  or  —  =  J/  the  mass,  of 

the  heated  body,  i\  the  mean  velocity  of  its  molecules  at  the 
instant  before  and  rt  the  velocity  after  the  shock.  Thus  energy, 
originally  heat,  is  changed  from  one  form  to  another,  as  it 
passes  from  point  to  point  ;  but  it  always  finally  eludes  obser- 
vation by  dissipation  as  heat  of  continually  decreasing  intensity, 
extending  throughout  constantly  enlarging  space. 

Every  transformation  of  energy  illustrates  some  one  of  these 
changes,  and,  in  every  case  throughout  the  series,  we  have 
energy  transformed  by  transfer  from  one  body  to  another,  and 
by  change  in  mode  of  motion,  until  a  cycle  is  completed  and 
all  energy  originally  heat  becomes  heat  again  of  "  lower  grade" 
—  i.e.,  of  lower  intensity,  but  affecting  a  greater  mass  of  matter. 
In  ever}'  step  of  the  series,  we  find  the  equality  : 

Energy  exerted  (i.e.,  Energy  transformed)  =  Work  done, 

In  any  machine,  the  energy  exerted  'is  partly  transferred 
through  the  machine  to  its  legitimate  work,  partly  transformed 
into  heat-motion  by  friction,  and,  in  some  cases,  partly  tem- 
porarily stored  in  the  machine  by  acceleration  of  velocity  of 


314  A    MANUAL    OF    THE   STEAM-ENGINE. 

heavy  parts,  in  which  cases  it  is  restored  when  retardation  takes 
place.  In  all  such  instances  the  First  Law  is  exemplified,  the 
work  and  heat  observed  having  definite  relations  of  quantity. 

Heat,  or  energy,  taking  effect  in  expansion  of  solids,  the 
evaporation  of  liquids,  or  expansion  of  vapors,  is  precisely 
equivalent  to  the  mechanical  work  done  in  altering  molecular 
velocity,  and  in  producing  changes  of  relative  position  among 
the  molecules  of  the  substance,  thus  doing  work  against  ex- 
ternal pressures  and  internal  molecular  forces.  In  such  cases, 
we  have  a  definite  quantity  of  heat,  H,  or  JQ,  transformed, 
and  an  equally  definite  internal  and  external  total  mean  re- 
sistance, f-\-p,  overcome  through  a  certain  space  v  in  each 
unit  of  time  ;  then 

/f  =  /<2  =  *</+/).    ......    (2) 

For  variable  pressures  and  volumes,  the  heat  transformed, 
and  thus,  as  heat,  expended,  between  configurations  a,  b,  is 

Pds.     ...    (3) 

The  mechanical  equivalent  of  heat  is  the  specific  heat  of  water 
at  its  temperature  of  maximum  density  expressed  in  dynamic 
units. 

The  value  of  the  mechanical  equivalent  of  heat  has  been 
commonly  taken  as  first  adopted  by  Joule,  although  recent  and 
most  carefully  conducted  investigations  indicate  a  value  higher, 
by  perhaps  one  per  cent,  to  be  more  accurate.  Existing  tables, 
and  nearly  all  work  done  in  this  field  to  date,'have,  however, 
been  based  upon  Joule's  figure.*  The  First  Law  may  be  thus 
enunciated  : 

Thermal  and  Mechanical  Energy  are  mutually  interconverti- 
ble in  the  proportion  of  one  British  Thermal  Unit  for  each  772  or 
778  foot-pounds,  or  of  one  Calorie  for  each  424  or  427  kilogram, 
metres  of  energy  or  of  work. 

*  Professor  Peabody  bases  all  his  work  on  the  later  value.    See  "  Thermo- 
dynamics of  the  Steam-engine";  N.  Y.,  J.  Wiley  &  Sons;  1889. 


THERMODYNAMICS  OF   THE  IDEAL  ENGINE.          315 

This  "  Mechanical  Equivalent"  of  the  heat-unit,  or  "  Dy- 
namical Equivalent"  of  heat,  known  as  "Joule's  Equivalent," 
is  represented  by  the  symbol  J. 

As  is  seen  from  the  above,  the  metric  unit  has  nearly  four 
times  the  magnitude  (3.968  times)  of  the  British  unit. 

83.  The  Steam-engine  illustrates  the  First  Law  as  well 
as  does  any  other  apparatus  or  machine  converting  heat  into 
work.     The  performance  of  work  by  heat-engines  invariably 
results  in  the  conversion,  or  destruction  by  transformation,  of 
a  definite  quantity  of  heat  into  mechanical  energy ;  and,  con- 
versely, the  expenditure  of  a  given  amount  of  mechanical  en- 
ergy will  produce  a  similarly  definite  and  equivalent  quantity 
of  heat-energy. 

When  a  steam-engine  is  in  regular,  steady,  operation,  doing 
its  stated  work,  the  stream  of  energy  sent  to  it  from  the  boiler, 
in  the  steam  which  is,  to  that  point,  its  vehicle,  divides  into  two, 
the  one  passing  out,  as  mechanical  energy,  to  do  the  prescribed 
work,  the  remainder,  usually,  vastly  the  greater  part,  flowing 
on,  unchanged  in  kind,  to  be  rejected  into  the  condenser  or 
into  the  atmosphere,  losing,  however,  en  route  through  the 
machine,  a  part,  usually  small,  by  conduction  and  radiation  to 
surrounding  objects. 

Could  the  magnitude  of  these  currents  of  energy  be  con- 
tinually observed  and  measured,  it  would  be  found  that  the 
quantity  of  energy  leaving  the  machine  by  these  several  routes 
would  be,  at  every  instant,  precisely  the  quantity  entering  the 
engine ;  but  that  the  amount  rejected  and  lost  as  heat  would 
Sc  less  by  precisely  the  amount  of  mechanical  energy  pro- 
duced. 

84.  The  Second  Law  of  Thermodynamics  asserts  that  the 
total  of  any  single  effect  of  any  given  quantity  of  heat  acting  in 
any  thermodynamic  operation  is  proportional  to  the  total  amount 
of  heat-energy  so  acting* 

Experiment  and  general  experience  indicate  that  actual 
heat-energy  is  homogeneous  in  condition  and  attributes,  and 

*  This  principle  is  substantially  that  first  accepted  by  Rankine  as  the  sec- 
M  :  fa*. 


316  A  MANUAL    OF    THE   STEAM-ENGINE. 

that  the  effect  of  any  one  portion  of  the  total  amount  acting  to 
produce  any  single,  definite,  effect,  as  change  of  pressure,  or 
change  of  volume,  is  precisely  the  same  as  that  of  every  other 
equal  portion. 

In  other  words,  the  units  of  which  it  may  be  assumed  to  be 
composed  are  all  of  precisely  the  same  nature,  and  are,  under 
similar  conditions,  capable  of  producing  precisely  equal  effects. 
Since,  in  accordance  with  this  law,  the  magnitude  of  any  and 
every  effect  of  heat-energy  is  proportional  to  the  quantity  of 
that  energy  acting  in  its  production,  it  follows  that  every  such 
effect  has  for  its  measure  the  product  of  that  quantity  of  heat 
into  some  function ;  the  form  and  magnitude  of  which  are  de- 
termined by  the  conditions  under  which  the  change  takes  place. 

Thus,  if  we  call  the  quantity  of  heat  undergoing  transfer 
H,  the  total  heat  Q,  and  the  function  above  referred  to,  called 
by  Rankine  the  "  Thermodynamic  Function"  0 ;  then  any  ele- 
mentary quantity  of  work,  produced  by  transformation  of  heat, 

dH=Qd<l>, (i) 

and  the  value  of  H  can  be  determined  by  integration  when  the 
method  and  the  rate  of  variation  of  heat  and  the  Thermody- 
namic Function  are  known. 

Since,  in  any  case,  the  quantity  of  heat,  Q,  is  known  to  be 
proportional  to  the  absolute  temperature,  T,  it  follows,  also,  that 

dH  —  Td<t>, (2) 

and  the  value  of  H  can  be  obtained  when  (f>  is  known  in  terms 
of  T  and  of  constants,  or  of  other  independent  variables  so  ex- 
pressed as  to  make  the  above  equation  integrable.  This  ex- 
pression, the  basis  of  the  whole  theory  of  heat-engines,  shows 
that  the  amount  of  energy  transformed  is  measured  by  the 
product  of  the  absolute  temperatures  of  transformation  into 
some  function  of  the  changes  of  condition  of  the  working  sub- 
stance. 

This  Second  Law  is  also  more  generally  expressed  by  Ran- 
kine as  follows  :*  If  the  total  actual  heat  of  a  homogeneous  and 

*  Steam-engine;  p.  306. 


THERMODYNAMICS  OF   THE  IDEAL   E  \GI\E.  $\7 

uniformly  hot  substance  be  contrived  to  be  divided  into  any  num- 
ber of  equal  parts,  the  effects  of  those  parts  in  causing  uvrk  to  be 
performed  are  equal.  This  law  is  one  case  of  a  general  law  ap- 
plicable to  every  kind  of  actual  energy  ;  that  is,  of  capacity  for 
performing  work,  constituted  by  a  certain  condition  of  each 
particle  of  a  substance,  how  small  soever,  independently  of  the 
presence  of  other  particles.  The  symbolical  expression  of  the 
Second  Law  of  Thermodynamics  is  given  as  follows  :  Let  unity 
of  weight  of  a  homogeneous  substance,  possessing  the  actual 
heat  Q,  undergo  any  indefinitely  small  change,  so  as  to  perform 
the  indefinitely  small  amount  of  work  dU.  It  is  required  to 
find  how  much  work  is  performed  by  the  disappearance  of 
heat.  Conceive  Q  to  be  divided  into  an  indefinite  number  of 
indefinitely  small  equal  parts,  each  of  which  is  SQ.  Each  of 
those  parts  will  cause  to  be  performed  the  quantity  of  work 
represented  by 


consequently  the  quantity  of  work  performed  by  the  disap- 
pearance of  heat  will  be 

V=Q.±*U.    or    £=£ 

which  quantity  is  known  when  Q,  and  the  law  of  variation  of 
4?Cf  with  Q,  are  known. 

From  the  mutual  proportionality  of  actual  heat  and  abso- 
lute temperature,  there  follows  — 

The  Second  Law  of  ThermodynamicSj  expressed  with  ref- 
erence to  absolute  temperature.  If  the  absolute  temperature  of 
any  uniformly  hot  substance  be  divided  into  any  number  of  equal 
farts,  the  effects  of  those  parts  in  causing  work  to  be  performed  are 
equal.  This  law  is  expressed  algebraically  as  follows  :  From  the  t 
relation  between  absolute  temperature  (r)  and  actual  heat  (0 
it  follows  that 

L-Q. 
dr~  dQ' 


318  A  MANUAL   OF   THE   STEAM-ENGINE. 

consequently  the  expression  above,  for  the  work  performed  by 
the  disappearance  of  heat,  is  transformed  into 

U_  _  r_ 
dU  ~  ~dr 

The  first  and  second  laws  constitute  the  basis  of  the 
Theory  of  Thermodynamics. 

Rankine  has  shown  that  the  second  law  must  follow  from 
the  hypothesis  that  "sensible  heat  consists  of  any  kind  of 
steady,  molecular  motion  within  limited  space  ;"  and  it  is  now 
considered  as  well  established,  both  that  heat  does  consist  of 
such  molecular  motion,  and  that  the  second  law  is  correct. 
The  magnitude  of  heat-energy  must  thus  be  proportioned  to 
the  weight  of  matter 'affected  by  it,  and  to  the  mean  square  of 
the  velocity  of  molecular  motion.  Absolute  temperature,  prop- 
erly defined,  is  proportional  to  the  actual  molecular  energy  of 
the  matter  so  affected ;  and  it  thus  again  follows  that  any  con- 
version of  such  energy,  during  any  change  in  the  dimensions  of 
the  space  enclosing  it,  is  proportional  to  the  absolute  tem- 
perature.* 

Clausius'  enunciation  of  this  law  is  as  follows :  f  "  The  work 
which  heat  is  capable  of  performing,  in  any  variation  of  the 
arrangement  of  parts  of  any  body,  is  proportional  to  the  abso- 
lute temperature  at  which  such  change  occurs." 

This  law  evidently  asserts  the  independence  of  the  quantity 
of  work  done  and  the  nature  of  the  "working  substance;" 
and  it  may  be  taken  as  a  corollary  that — 

When,  in  any  heat-engine  tracing  a  cycle,  the  working  sub- 
stance operates  between  two  fixed  temperatures,  the  work 
done,  or  the  energy  produced,  is  precisely  proportional  to  the 
quantity  of  heat  transmitted  from  the  source  of  heat  to  the 
refrigerator,  without  regard  to  the  nature  of  the  substance 
adopted  as  its  vehicle — as  shown  by  Carnot  in  1824. 

*See  Rankine,   "On  the  Second  Law  of  Thermodynamics  ;"  Trans.  Brit. 
Assoc.,  1865;  Phil.  Mag.,  Oct.  1865. 
f  Poggendorff's  Annalen,  1862. 


THERMODYNAMICS  OF    THE  IDEAL    ENGINE.  319 

This  was  demonstrated  by  Clausius,  who  made  the  princi- 
ple '*  it  is  impossible  for  heat  to  pass,  of  itself,  from  a  colder  to 
a  warmer  body"  the  basis  of  his  argument. 

Thus,  of  the  whole  quantity  of  heat  passing  from  the  heater 
to  the  working  substance,  one  part  is  always  transmuted  into 
mechanical  work,  or  energy ;  while  the  remainder  goes  to  the 
refrigerator,  and  the  ratio  of  the  one  quantity  to  the  other  is 
perfectly  definite. 

Professor  Wood  expresses  this  law  thus  : 

"  If  all  the  heat  absorbed  be  at  one  temperature,  and  that 
rejected  be  at  one  lower  temperature,  then  will  the  heat  which 
is  transmuted  into  work  be  to  the  entire  heat  absorbed  in  the 
same  ratio  as  the  difference  between  the  absolute  temperatures 
of  source  and  refrigerator  is  to  the  absolute  temperature  of  the 
source."* 

85.  The    Steam-engine    illustrates    the  Second   Law, 
both  in  its  operation  as  a  whole  and  in  the  details  of  energy- 
transformation  going  on  in  its  inner  workings.    Not  only  is  it 
true  that  two  perfect  engines,  of  different  power,  working  under 
the  same  thermodynamic  conditions  perform  work  by  the  con- 
version of  precisely  proportional  quantities  of  heat ;  but  it  is  also 
true  that  the  work-effect  of  heat  at  any  instant,  in  the  midst  of 
the  steam  so  doing  work  by  its  expansion,  is  proportional  to 
the  quantity  of  heat  at  that  instant  there  present  and  taking 
its  part  in  the  thermodynamic  action  of  the  fluid. 

As  will  be  seen,  however,  presently,  the  second  law  finds 
important  application  simply  in  enabling  us  to  ascertain  the 
total  quantity  of  work,  external  and  internal,  required  to  pro- 
duce changes  of  volume  and  energy  in  fluids,  like  the  vapors, 
in  which  we  cannot  measure  directly  the  internal  forces  and 
internal  work. 

86.  General  Algebraic  Expressions  for  Thermodynamic 
Changes  of  Energy  may  be  readily  deduced  directly  from  the 
First  Law  of  Thermodynamics.     Since  only  transfers  of  heat 
and  transformations  into  mechanical  energy,  actual  or  poten- 

*  Thermodynamics,  §  40. 


32O  A   MANUAL   OF   THE   STEAM-ENGINE. 

tial,  are  considered,  assuming  any  small  variation  of  heat,  dH, 
measured  dynamically,  to  take  place,  producing  variations  of 
the  physical  state  of  any  substance ;  if  the  change  of  sensible 
heat  be  called  dS,  that  of  "  latent "  heat.  dL,  and  of  external 
work,  dU,  then  the  first  law  of  thermodynamics  is  expressed  by 
the  equations : 

dff=dS+dL  +  dU, (A) 

and 

.......  (E) 

. (C) 

where,  in  the  last  two  expressions,  dE  =  dS  -\-  dL,  and  is  the 
variation  of  energy,  actual  and  potential ;  while  dW '=  dL  -\-  dU, 
and  is  the  total  work  done,  externally  and  internally.  These 
are  primary  and  general  equations. 

The  quantity  E  is  often  called  the  intrinsic  energy  of  the 
substance  ;  L  is  evidently  a  potential  energy ;  while  S  is  a  form 
of  molecular  kinetic,  or  actual,  energy,  which  may  sometimes 
be  regarded  as  also  in  a  sense  potential. 

The  above  are  completely  general  expressions  of  the  GEN- 
ERAL FUNDAMENTAL  EQUATION  OF  THERMODYNAMICS. 

It  will  be  observed,  however,  that,  while  the  law  enables  us 
to  say  that,  a  given  amount  of  work,  dU,  being  done,  and  a 
known  quantity  of  sensible  heat,  dS,  being  transferred  from 
the  source  without  transformation,  the  total  quantity  of  heat 
demanded  for  the  two  changes,  occurring  simultaneously  or 
successively,  will  be  precisely  the  sum  of  the  thermal  equiva- 
lent of  the  first  and  the  thermal  measure  of  the  second ; 
that  law  does  not  enable  us  to  say  what,  in  any  given  case  of 
heat-expenditure,  will  be  the  method  of  distribution  of  energy 
in  the  two  forms,  or  the  magnitude  of  either  of  the  two  parts 
into  which  it  is  thus  divided.  We  must  evidently  find  a  way 
of  determining  dU\  and  this,  when  it  includes  internal  work, 
may  be  impracticable,  as  a  matter  of  observation  and  direct 
measurement.  It  is  this  subsidiary  problem  which  the  second 
law  is  called  in  to  solve. 


THERMODYNAMICS  OF   THE  IDEAL   ENGIXE.  321 

87.  The  Relations  of  the  Two  Laws  of  Thermodynamics 

to  the  theory  of  thermodynamic  operations  and  heat-engines 
are  now  readily  defined.  The  First  Law  states  that,  wherever 
thermal  and  mechanical  energies  are  converted,  the  one  into 
the  other,  such  conversion  takes  place  in  the  proportion  of  one 
thermal  unit  to  each  "  mechanical  equivalent,"  as  previously 
defined  :  while  the  Second  Law  asserts  that,  during  such  conver- 
sion, whatever  proportion  of  the  thermal  energy  present  may 
be  so  converted,  that  proportion  is  equal  to  the  product  of  the 
quantity  of  heat,  or  of  the  absolute  temperature,  into  another 
factor,  the  form  and  magnitude  of  which  are  determined  by 
other  physical  conditions.  The  first  law  gives  no  clue  to  the 
method  of  transformation,  and  no  measure  of  the  total  quan- 
tity of  energy  transformed  in  any  case ;  it  simply  asserts  that 
so  much  heat-energy  as  is  converted  into  the  other  form  is  so 
transmuted  with  a  definite  quantivalence.  The  second  law, 
while  merely  asserting  that  the  quantity  transformed  is  propor- 
tional to  the  total  heat  present,  and  to  the  absolute  tempera- 
ture at  which  transformation  takes  place,  enables  a  determina- 
tion to  be  made,  by  its  combination  with  the  first  law,  of  the 
actual  quantity  of  energy  so  changing  form. 

The  first  law  enables  us  to  construct  the  second  equation  of 
thermodynamics ;  the  second  law,  as  will  be  more  fully  shown 
later,  gives  the  form  and  value  of  its  second  term.  Thus  heat, 
from  whatever  source  derived,  once  stored  within  any  mass  of 
working  substance,  becomes  subject  to  these  two  laws ;  and 
while  the  first  law  determines  what  amount  of  mechanical  en- 
ergy may  be  produced  per  unit  of  heat-energy  transformed,  the 
second  law  prescribes  both  the  proportion  of  the  total  stored 
heat  which,  under  the  given  conditions,  maybe  so  transformed, 
and  the  proportion  of  utilized  to  unutilized  heat.  A  reservoir 
containing  any  given  amount  of  heat-energy,  no  additional 
amount  can  be  transferred  into  it,  except  it  be  heat  of  higher 
temperature  ;  and,  once  the  added  energy  enters  the  reservoir, 
it  cannot  be  again  removed  as  a  distinct  quantity  of  heat  of 
high  temperature,  but  becomes  a  part  of  the  whole  stock  of 
energy,  and,  in  common  with  the  original  store,  becomes  sub- 


322  A    MANUAL    OF    THE    STEAM-ENGINE. 

ject,  unqualifiedly,  to  the  second  law  of  thermodynamics,  in  all 
operations  involving  transformation. 

88.  The  Thermodynamics  of  the  Constitution  of  Mat- 
ter and  its  physical  and  chemical  changes  must  be  considered 
before  the  heat-engines  can  be  intelligently  studied  ;  since,  in 
all  of  them,  variations  of  temperatures,  pressures,  and  volumes 
of  one  or  another  form  of  "working  fluid  "  constitute  the  pro- 
cess of  their  action. 

The  physical  state  of  matter  is  determined  by  the  intensity 
of  internal  forces  and  by  the  quantity  of  internal  heat,  i.e.,  of 
heat-energy  present  in  the  mass,  and  it  varies  as  transfer  takes 
place  to  it  or  from  it  by  communication  with  external  bodies. 
The  intrinsic  energy  of  the  solid  body  is  a  form  of  potential 
energy,  or  energy  of  position  ;  equilibrium  being  maintained 
by  the  adjustment  of  volume  to  temperature,  and  this  energy 
being  developed  as  kinetic,  or  in  the  production  of  work,  as 
temperature  and  the  stock  of  sensible  heat  are  reduced.  The 
same  is  true  of  liquids,  which,  however,  have  a  larger  stock  of 
molecular,  potential,  energy,  and  have,  by  expansion,  lost  sta- 
bility of  form.  The  change  of  state,  traced  further,  passes 
through  that  of  the  vapors  and  of  the  permanent  gases,  and 
finally  is  exhibited  the  condition  of  the  perfect  gas,  in  which 
equilibrium  exists  between  external  confining  pressures  and 
the  total  tension  due  the  pressure  of  heat-energy ;  in  which, 
also,  no  internal  condensing  forces  are  observable.  In  the  lat- 
ter case  the  total  heat-energy  is  exactly  proportional  to  the 
absolute  temperature,  and  is  measured  by  the  continued  prod- 
uct of  weight,  real  specific  heat,  and  absolute  temperature. 

89.  Solids,  Liquids,  and  Gases  constitute  the  three  forms 
of  matter  into  which  all  kinds  are  classed.     The  exact  structure 
and  constitution  of  matter  are  well  understood  only  so  far  as  the 
senses,  aided  by  physical  apparatus,  can  observe  it ;  of  its  ulti- 
mate nature  nothing  is  known.     So  far  as  our  knowledge  goes, 
all  forms  may  be  assigned  to  one  or  another  of  three  classes. 
All  known  kinds  of  matter  are  probably  capable  of  taking, 
under  different  conditions,  definite  for  each  case,  either  of  these 
forms.     Nearly  all   known  liquids,  for  example,  under  certain 


THERMODYNAMICS  OF   THE  IDEAL  ENGINE.          323 

definite  conditions  of  temperature  and  pressure,  may  be  solidi- 
fied, or  may  be  vaporized ;  solids  are  liquefied  and  vaporized 
by  elevation  of  temperature ;  and  all  familiar  gases  may  be 
liquefied,  and  have  even  been  solidified,  by  subjecting  them  to 
pressure  and,  at  the  same  time,  reducing  their  temperature. 

All  matter,  so  far  as  is  known,  may  be  considered  as  con- 
sisting of  an  aggregation  of  collections  of  "atoms,"  or  particles, 
which  collections  are  called  molecules,  separated  by  intermo- 
lecular  spaces  of  greater  or  less  extent,  attracting  each  other  with 
a  force  which  is  dependent  upon  the  nature  of  the  substance, 
and  upon  its  volume,  and  yet  held  apart  by  repellent  forces, 
which  seem,  usually,  to  have  an  intensity  dependent  principally 
upon  temperature,  and  may  probably  be  due  solely,  and  in  all 
cases,  to  the  heat-energy  present,  stored  m  the  substance.  The 
attractive  forces  are  considered  to  be  of  two  kinds,  the  one 
purely  attractive,  the  other  giving  permanence  of  form ;  the 
first  is  the  force  of  "  cohesion,"  the  second  that  of  "  polarity." 

ox).  Solids  have  stability  both  of  form  and  of  volume,  re- 
sisting every  attempt  to  alter  either;  liquids  are  stable  as  to 
volume,  but  destitute  of  stability  of  form  ;  gases  have  no  sta- 
bility either  of  form  or  volume ;  and,  at  all  measurable  tem- 
peratures, constantly  tend  to  indefinite  diffusion  throughout 
space.  Solids  have  molecules  bound  together  by  cohesive 
attraction,  and  held  in  definite  relations  of  position  by  polarity ; 
in  liquids  polarity  becomes  unobservable ;  in  gases  only  the 
repellent  forces  are  seen,  and  equilibrium  between  attraction 
and  repulsion  of  molecules  can  no  longer  exist. 

In  the  passage  from  one  state  to  another,  in  many  cases,  mat- 
ter passes  through  intermediate  states,  solids  becoming  viscous 
when  liquefying,  and  liquids  becoming  imperfectly  gaseous  be- 
fore fairly  attaining  the  perfectly  gaseous  state.  The  perfect 
gas  is  absolutely  free  from  the  influence  of  attractive  molecular 
forces.  All  known  gases  are  more  or  less  imperfect ;  but  a  few, 
as  oxygen,  hydrogen,  nitrogen,  in  their  ordinary  conditions, 
may.  for  all  purposes  of  the  engineer,  be  considered  perfect. 

The  Fusing  and  Boiling  Points,  or  the  freezing  and  liquefy 
ing  temperatures,  are,  as  already  stated,  fixed  for  each  fluid  for 


324  A    MANUAL    OF   THE    STEAM-ENGINE. 

every  pressure,  but  variable  with  change  of  pressure.  Increased 
pressure  usually  increases  the  former  and  always  elevates  the 
latter.  An  exception,  in  the  case  of  ice,  for  example,  is  seen 
when  fusion  is  accompanied  by  contraction  ;  the  melting-point 
is  lowered,  in  such  cases,  by  increase  of  pressure.  The  pressure 
/>  at  which  the  boiling-point  becomes  a  given  temperature,  T, 
on  the  absolute  srale  is  very  exactly  given,  for  several  liquids, 
by  a  formula  constructed  by  Rankine*  to  represent  Regnault's 
experiments : 

com.  log p  =  A  —  -^  —  ™  ;     .     .     .     .     (i) 
and,  for  the  reverse  determination, 

T= ,  ,    (2) 


C          '  4£TV       2C 

in  which,  for  the  Fahrenheit  scale  and  pressures  in  pounds  on 
the  square  foot,  the  several  quantities  are : 

A          log  B        logC  —  —j 

Water 8.2591  3.43642  5.59873  0003441  0.00001184 

Alcohol 7.9707  3.31233  5.75323  0.001812  0.00003282 

Ether 7-5732  3.31492  5.21706  0.006264  0.00003924 

Carbon  disulphide 7-3438  3.30728  5.21839  0.006136  0.00003765 

Regnault's  own  formula,  as  adapted  to  the  Centigrade  scale 
and  to  pressures  in  millimetres  of  mercury,  for  temperatures, 
/„,  exceeding  100°  C.,  is  as  follows : 

logp  =  a  —  bo?  —  c/3x, (3) 

in  which  x=.tm-\-  20,  and 

a—      6.2640348;  log  b  =  0.1397743  ; 

log  a  =  9.994049292  —  10  ;         "  c  =  0.6924351. 
"  ft  =  9-998343862  -  10  ; 


*  Philosophical  Magazine;  1854. 


THERMODYNAMICS  OF   THE  IDEAL  ENGIXE.  $2$ 

For  temperatures  between  the  freezing  and  boiling  points, 

logp  =  a  -j-  bet  —  c&t 
in  which,  as  corrected  by  Moritz,* 

a=  4-7393707;  kg  £  =  8.13199071 12  —  10 ; 

log  a  —  0.0x368649371 52  ;  "  c  =  o/5 1 17407675. 

"  ft  =  9-996725536856-  10  ; 

The  temperatures  of  fusion  of  metals  and  those  of  fusion 
and  of  boiling  of  other  substances  are  given  in  works  on  physics 
and  on  special  materials. 

The  "  luminiferous  ether  "which  apparently  pervades  all 
space,  and  which  transmits  light  and  heat  to  us  from  the  sun, 
is  a  gas  of  such  exceeding  tenuity  that  it  opposes  no  meas- 
urable resistance  to  the  bodies  of  the  solar  system  and  of  the 
universe,  and  is  of  such  slight  density  and  high  elasticity  as  to 
transmit  vibrations  with  nearly  two  hundred  and  fifty  thousand 
times  the  velocity  of  those  traversing  hydrogen  gas ;  it  has 
therefore  one  five-hundredth  the  density  of  any  hydrogen 
which  may  exist  in  the  interstellar  spaces. 

The  Kinetic  Theory  of  Matter  is  now  generally  accepted  by 
men  of  science.  According  to  this  theory,  a  gas  consists  of  a 
collection  of  molecules,  simple  or  complex,  which  are  in  ex- 
tremely rapid  motion,  and  which  intermingle  freely,  coming 
into  collision  with  each  other,t  and  with  the  confining  surfaces, 
with  a  violence  which  depends  upon  their  velocities ;  which 
velocities,  in  turn,  are  determined  by  the  temperature  of  the 
mass.  The  intermolecular  spaces,  and  therefore  the  free  paths 
of  the  molecules,  are  of  comparatively  great  extent.  In  liquids, 
the  free  paths  of  the  molecules  become  very  greatly  restricted 
by  the  action  of  now  measurable  attractive  forces;  and  in 
solids,  in  consequence  of  the  confining  action  of  cohesion  and 
of  polarity,  brought  into  play  by  the  condensation  marking  the 

*  Clausios. 

f  Boltzmann  suggests  that  collisions  may  be  rare,  if  not  absolutely  impos- 
sible, the  molecules  swinging  about  each  other  in  hyperbolic,  comet-like  orbits, 
without  contact. 


326  A    MANUAL   OF   THE   STEAM-ENGINE, 

further  change  from  the  liquid  state,  the  particles  can  only  vi. 
brate  about  a  fixed  point  without  change  of  mean  position  rela- 
tively to  adjacent  particles. 

The  state,  or  the  form,  of  matter  is  thus  determined  by  the 
action  of  forces  external  and  internal.  The  intensity  of  inter- 
nal attractive  and  repulsive  forces,  and  of  external  pressure, 
determines  whether  a  substance  may  exist  in  the  liquid  or  the 
gaseous  condition,  and  the  action  of  polarity  produces  when 
the  particles  are  brought  closely  together,  the  solid  state  ;  while 
rise  in  temperature,  by  modifying  the  intensity  of  the  molecu- 
lar forces  and  separating  molecules,  causes  the  solid  to  pass 
through  the  pasty  and  viscous  condition,  and  to  become  liquid 
at  higher  temperatures ;  it  then  vaporizes,  and  finally  becomes 
gaseous,  in  consequence  of  separation  of  particles  by  the  repul- 
sion produced  by  heat-motion. 

The  size  of  the  molecule  is  probably  always  the  same  in  the 
same  kind  of  matter ;  but  different  in  different  substances.  Sir 
William  Thomson  estimates  a  molecule  of  glass  as  probably 
less  than  one  twenty-five  millionth  and  more  than  one  two 
hundred  and  fifty  millionth  of  an  inch  in  diameter  (less  than 
ioolooo  and  more  than  TFsVtrFor  millimetre).  He  states  that, 
were  a  drop  of  water  as  large  as  a  pea  magnified  to  the  size  of 
the  earth,  its  molecules  would  then  appear  to  be,  in  size,  be- 
tween that  of  a  small  leaden  shot  and  that  of  a  cricket-ball.* 
He  calculates  the  number  of  molecules  present  in  a  cubic  inch 
of  any  perfect  gas  at  atmospheric  pressure,  and  at  the  freezing 
point  in  temperature,  to  be  10",  or  one  hundred  thousand  mil- 
lion million  million.  According  to  Avogadro's  law,  this  number 
is  the  same  for  all  perfect  gases. 

Plateau  f  concludes,  from  experiments  made  by  him  upon 
the  tenuity  of  liquid  bubbles,  that  the  radius  of  molecular  at- 
traction is  less  than  one  seven-hundredth  of  an  inch  (i  milli- 
metre). WartmannJ  makes  the  range  still  less.  Robison  had 


*  Nature;  1870.     Silliman's  Journal  of  Science  and  Art;  July  1870. 
f  Smithsonian  Report;  1856. 
j  Trans.  Soc.  Geneva;  1862. 


THERMODYNAMICS  OF   THE  IDEAL  ENGINE.          $2? 

long  before  *  inferred,  from  experiments  with  Newton's  rings, 
that  the  effect  of  pressure  is  observable  before  actual  contact, 
at  a  distance  of  about  one  five-thousandth  of  an  inch  (y^ 
millimetre),  and  Powell  t  detects  this  action  at  one  eleven-hun- 
dredth of  an  inch  (^  millimetre). 

90.  Internal  and  External  Work,  when  change  of  physi- 
cal state  occurs,  are  always  the  immediate  cause  of  change  of 
volume  and  molecular  arrangement.  As  this  alteration  of  con- 
dition involves,  internally,  the  application  of  force  to  overcom- 
ing atomic  or  molecular  resistance,  or  the  reverse,  with  altera- 
tion of  volume,  work  is  consumed  or  is  developed  in  the  process, 
and  an  equivalent  amount  of  energy  is  transformed  into,  or  out 
of,  work.  Work  so  done  is  entirely  independent  of  external 
forces  and  conditions,  and  its  amount  is  a  function,  solely,  of 
the  forces  acting,  and  of  the  spaces  traversed,  or  of  the  altera- 
tion of  volume  incident  to  the  physical  changes  occurring. 
Such  work  is  called  Internal  Work,  and  energy  operating  in 
this  manner  is  known  as  Internal  Energy. 

Changes  of  volume  occurring  in  any  mass,  in  the  presence 
of  other  substances,  involve  the  overcoming  of  external  pres- 
sure, or  are  facilitated,  to  some  extent,  by  the  action  of  exter- 
nal forces.  This  is  equivalent  to  the  production,  or  to  the 
consumption,  of  a  certain  amount  of  work,  which  is  known  as 
External  Work. 

Energy  may  thus  be  expended  in  the  production  of  either 
internal  or  external  work,  or  both  ;  and,  on  the  other  hand,  in- 
ternal energy  may  be  transformed  into  external  work ;  or  the 
reverse  operation  may  take  place. 

The  amount  of  external  work  so  performed  is  evidently  de- 
termined by  the  magnitude  of  the  change  of  volume,  and  by 
the  intensity  of  external  pressures,  solely,  and  is  thus  not 
necessarily  dependent  upon  internal  conditions.  An  equation 
involving  both  internal  and  external  work,  or  energy,  is  evi- 
dently an  equation  involving  two  independent  variables. 


Mechanical  Philosophy;  voL  L  f  Phil.  Trans.;  1834. 


328  A    MANUAL    OF   THE   STEAM-ENGINE. 

Thus>  when  steam,  air,  or  gas  expands  behind  the  piston  of 
a  heat-engine,  the  internal  work  done  is  measured  by  the 
product  of  the  mean  intensity  of  molecular  attraction  into  the 
change  of  volume  occurring;  and  this  quantity  may  be  much 
greater  than  the  external  work ;  in  the  case  of  steam,  it  far  ex- 
ceeds the  external  work  done  in  driving  the  piston  ;  its  amount 
is  comparatively  small,  and  is  very  difficult  to  measure,  in  the 
case  of  air,  and  it  becomes  indefinitely  small  in  the  case  of  the 
perfect  gas ;  it  is  a  function  of  volumes,  and  of  molecular 
forces.  The  external  work  is  measured  by  the  product  of  the 
mean  intensity  of  pressure  on  the  piston  by  the  volume  trav- 
ersed, and  is  limited  by  the  resistance  to  the  motion  of  the 
piston  on  the  one  hand,  and  by  the  intensity  of  molecular  re- 
pulsion on  the  other.  An  equilibrium  always  exists  between 
this  latter  force  and  the  sum  of  internal  attractive  and  exter- 
nal compressive  forces.  When  the  fluid  expands  freely  into  a 
vacuum,  evidently  no  external  work  is  done.  External  work  is 
usually  ultimately  converted,  through  mechanical  energy,  into 
heat. 

The  Internal  Energy  of  a  body  is  the  potential  energy,  or 
the  capacity  to  do  work,  possessed  in  virtue  of  the  existence  of 
internal  repulsive  force.  The  potential  energy  of  a  mass  ca- 
pable of  condensation  under  the  action  of  internal  attractive 
forces  is  another  similar  and  equally  important  form  of  energy. 

Rotational  Motion  evidently  can  only  be  produced  or  de- 
stroyed in  a  fluid  by  the  action  of  a  force  which  may  be  de- 
nominated internal  friction,  or  molecular  friction  ;  hence,  such 
motion  cannot  exist  in  a  perfect  fluid,  or,  if  existing,  may  be 
neglected,  as  being  invariable,  and  need  not  be  taken  into  ac- 
count in  any  accepted  theory. 

91.  Heat,  denned  and  measured,  as  a  Form  of  Energy, 
constitutes  the  principal  subject  of  treatment  in  the  branch  of 
applied  physics  here  studied.  The  term  heat  may  be  used  in 
either  of  the  two  senses ;  it  may  represent  the  sensation  due 
to  that  physical  action  which  has  been  described,  or  it  may 
mean  that  phenomenon  itself.  It  is  in  the  latter  of  these  two 
senses  that  the  term  is  here  used ;  and  heat  is  to  be  here  con- 


THERMODYNAMICS  OP  THE  IDEAL  ENGINE.  329 

sidered  only  as  a  form  of  the  energy  of  molecular  motion,  or 
vibration,  capable  of  transfer  from  one  body  to  another,  and 
of  transformation  into  other  forms  of  energy.  In  its  measure- 
ment, it  is  necessary  to  consider  two  magnitudes,  the  one 
defining  intensity,  the  other  its  quantity.  Since  any  given 
amount  of  energy  may  exist,  whatever  its  form,  either  as  the 
energy  of  a  small  quantity  of  matter  in  rapid  motion,  or  as 
that  of  a  larger  quantity  in  less  violent  motion,  the  rate  of  heat- 
motion,  and  the  consequent  "intensity"  of  the  heat,  must  be 
observed,  as  well  as  the  quantity. 

Since  heat  is  energy,  and  since  it  is  measured  by  the  pro- 
duct of  the  mass  of  matter  pervaded  by  it  into  its  intensity  of 

Wtf 
action,  i.e.,  by  the  quantity  \Mtf  = ,  it  is  evident  that, 

whether  it  pervades  one  substance  or  another,  and  whatever 
the  mode  of  transfer,  the  quantity  of  heat-energy  is  the  same, 
when  the  same  work  is  done,  or  the  same  kinetic  energy  is 
present,  and  that  it  is  entirely  independent  of  the  nature  of  the 
substance,  having  the  weight  W,  or  the  mass  M,  and  the  mo- 
lecular velocity  v,  which  simply  serves  as  its  vehicle. 

The  Physical  Effects  of  Heat,  as  a  form  of  energy  intro- 
duced into  matter,  are  seen  in  several  distinct  classes  of  phe- 
nomena : 

(1)  The  temperature  of  the  substance  rises,  the  sensation  of 
heat,  produced  upon  the  nerves  of  touch  by  contact  with  the 
body,  is  intensified,  and  the  tendency  to  transfer  heat  to  adja- 
cent bodies  is  increased. 

(2)  The  elasticity  of  volume  of  the  substance  is  increased, 
and  its  stability  of  form  is  decreased. 

(3)  The  substance  is  given  increased  volume,  and,  reaching 
certain  definite  points  in  the  scale  of  temperature,  is  caused  to 
change  its  physical  state,  as  from  solid  to  liquid,  or  from  the 
liquid  to  the  gaseous  form. 

(4)  External  work  is  performed,  i.e.,  work  is  done  against 
forces  affecting  the  mass  from  without. 


330  A  MANUAL    OF    THE   STEAM-ENGINE. 

(5)  As  a  secondary  effect,  the  chemical  composition  of 
bodies  is  often  altered,  elements  uniting  more  readily  to  form 
compounds,  and  compounds  changing  their  constitution,  some- 
times at  fixed,  sometimes  at  variable,  temperatures;  combina- 
tion being,  within  certain  limits,  usually,  but  not  always,  accel- 
erated by  increase  of  temperature.  Dissociation  sometimes 
occurs. 

Reversal  of  the  phenomenon,  causing  a  reversal  in  the 
direction  of  movement  of  heat,  produces  heat  where  it  had 
been  expended,  and  decreases  temperature  where  increase  had 
previously  taken  place. 

Dynamically,  the  effects  of  transfer  of  heat  are : 

(1)  Change  of  temperature  ;  i.e.,  variation  of  sensible  heat- 
energy,  or  of  the  kinetic  energy  of  molecular  motion. 

(2)  Performance  of  internal  work;  i.e. : 

(a)  Molecular  work,  which  is  often  considered  to  include 
the  preceding. 

(b)  Intermolecular  work ;   i.e.,  work  done  against  molecular 
cohesion,  or  other  attractive  forces. 

(c)  Interatomic  work  ;  or  similar  work  done  within  the  mo- 
lecular, and  against  the  chemical,  forces. 

Temperature  measures  the  intensity  of  heat  and  its  tendency 
to  transfer  itself  to  surrounding  bodies.  When  two  bodies  are 
at  the  same  temperature,  they  exhibit  no  tendency  to  change 
by  transfer  of  heat  from  one  to  the  other.  Whenever  two 
bodies  are  brought  together,  heat  is  exchanged  between  them, 
the  hotter  yielding  to  the  colder  more  than  it  receives  from  the 
latter,  until  they  attain  a  state  of  common  and  uniform  tem- 
perature at  which  the  flow  of  heat  ceases,  each  receiving  pre- 
cisely as  much  as  it  loses.  The  higher  the  temperature  of  any 
body  the  greater  the  tendency  to  expand,  and  the  greater  its 
elasticity  of  volume,  and  the  less  its  elasticity  and  stability  of 
form  ;  and  the  colder  the  mass  the  more  marked  the  opposite 
qualities.  Two  dissimilar  substances,  however,  do  not  exhibit, 
usually,  the  same  elasticities  at  the  same  temperatures. 

Temperatures  are  usually  measured  by  means  of  thermome- 
ters of  which  the  scales  are  conventional,  and  often  differ  in 


THERMODYNAMICS  OF   THE  IDEAL  EXGIXE.          33! 

different  instruments.  Standard  temperatures  are  so  chosen 
that  they  may  be  easily  identified  and  that  comparison  may 
be  readily  effected.  The  temperature  of  fusion  of  ice  and  the 
boiling-point  of  pure  water,  under  mean  barometric  pressure  at 
the  sea-level,  are  universally  accepted  standards,  and  are  readily 
determined  and  are  invariable.  The  scale  of  the  Centigrade 
thermometer  is  constructed  by  dividing  the  space  between 
these  two  temperatures  into  100  degrees,  the  lower  point  being 
made  the  zero.  The  Fahrenheit  scale  is  thus  divided  to  180 
degrees,  and  the  lower  reference-point  is  called  32.  To  trans- 
form these  scales,  the  one  to  the  other,  we  have 


.......    (2) 

in  which  C  and  F  represent  the  readings  of  a  common  tem- 
perature on  the  Centigrade  and  Fahrenheit  scales,  respectively. 
The  Absolute  Scale  of  Temperature  is  constructed  on  the 
assumption  that  its  zero  represents  the  real  zero  of  heat-energy, 
that  point  at  which  either  the  pressure  of  a  perfect  gas  retained 
at  constant  volume,  the  volume  of  such  a  gas  under  constant 
pressure,  or  the  product  of  pressure  and  volume,  when  both  are 
variable,  will  vanish  by  complete  abstraction  of  heat.  Experi- 
ment shows  that  the  ratio  of  /Or0,  this  product  at  the  melting- 
point  of  ice,  to/,1",  ,  the  magnitude  of  the  same  product  at  the 
boiling-point,  as  above,  is,  for  nearly  perfect  gases, 


£=i^6i'neariy' (3) 

and 

Ag«  —  A*V      0-36$ 

-*£—=— (4) 

If  the  difference  p,vt  — pj>9  corresponds  to  lotf,  as  on  the 
Centigrade  scale,  we  have,  for  the  absolute  scale, 

7\      ptvt  —  o      1-365  * 


332  A    MANUAL   OF   THE   STEAM-ENGINE. 

and  the  temperatures  TQ  and  Tl  will  have  the  relation 

T,  -  r.  _  0.365  A"..       _  I^T,  _   100   _ 

~  0.365  ~274 


For  the  Fahrenheit  division, 

T,  -  T0        1  80 


(7) 


Generally,  any  temperature,  /,  on  the  common  scale,  may 
be  determined  from  the  expressioa 


t         >-* 

-'•-  0.365" 


pv  —  POVQ   „      .       , 
=  274 ,  Centigrade ; 


\   -    (9) 
=  493  *"  Jt*0"0-,  Fahrenheit,  j 


pv  —  p0v0 


The  Absolute  Zero  is  thus  found  at 

-274°C,     or    -(493.2-32)  =  -461  °.2  F.    .    (10) 

The  freezing  and  boiling  points,  on  the  absolute  scale,  are 
thus   found    at   -J-  274   C.,  or   -|-  493  F.,  and  at  -|-  374°  C,  or 


The  absolute  zero  has  never  been  reached  experimentally, 
and  its  existence  and  its  location  on  the  scale  of  temperature 
have  only  been  determined  by  theory,  based  upon  the  now 
universally  recognized  laws  of  transfer  of  heat-energy.  The 
exact  value  of  the  coefficient  of  expansion  for  the  perfect  gas 
is  not  known  with  absolute  correctness.  It  was  made  0.3646 
to  0.3648  by  Rudberg,  for  air,  between  the  freezing  and  boiling 
points,  and  by  Regnault  0.3665  to  0.3670.  Rankine  assumes 


THERMODYNAMICS  OF   THE  IDEAL  ENGINE.  333 

that  the  perfect  gas  would  give,  approximately,  0.365,  as 
above. 

Taking  Regnault's  value  for  air  at  constant  volume, 
0.3665  =  ^J-y,  as  is  often  done,  the  absolute  zero  would  be 
found  at  —  459°  F.,  or  —  272°. 9  C.,  instead  of  —  461  °.2  F.,  or 
—  274°  C.  The  freezing  and  boiling  points,  on  the  absolute 
scale,  then  become  respectively  -j-  49i°-4  F.,  or  -}-  273°  C.,  and 
-f  671°^  F.,  or  -f  373°  C.,  instead  of  -f  493°.2  F.,  or  +  274° 
C.,  and  -f-  673°.2  F.,  or  -j-  374°  C.  The  second  set  of  figures 
are  obtained  on  the  assumption  that  the  values  for  air  and  the 
perfect  gas  are  substantially  the  same,  and  both  sets  on  the 
hypothesis  that  the  coefficient  remains  constant  throughout 
the  scale.* 

92.  Quantity  of  Heat  is  thus  seen  to  be  entirely  distinct 
from  temperature,  and  is  measured  by  an  essentially  different 
unit.  Heat  as  a  form  of  energy  and  the  equivalent  of  the 
work,  of  whatever  kind,  expended  in  producing  that  energy, 
may  evidently  be  measured  by  any  unit  of  energy.  But  any 
unit  of  energy  is  a  product  of  two  factors,  the  one  measuring 
a  force,  the  other  a  space  traversed  under  the  action  of  that 
force.  Quantity  of  heat,  therefore,  is  a  quantity  of  energy  and 
it  may  be  similarly  measured,  by  either  of  the  familiar  measures 
of  energy,  or  by  its  own  peculiar  unit. 

The  Thermal  Unit,  or  unit  of  heat-energy,  is  that  invariable 
quantity  of  heat  which  is  found  to  be  required  to  raise  the 
temperature  of  unity  in  weight  of  water  one  degree  in  tem- 
perature when  at  the  lower  standard  temperature  at  o°  Centi- 
grade, or  32°  Fahrenheit.  The  British  Thermal  Unit  is  the 
heat  so  required  when  the  unit  of  weight  is  the  pound,  and  the 
scale  Fahrenheit ;  the  Metric  Thermal  Unit,  or  Calorie,  meas- 
ured that  demanded  to  heat  one  kilogramme  of  water  from  o° 
C.  to  i°  C.  Rankine  and  Maxwell  take  this  quantity  at  the 
temperature  of  maximum  density ;  but  for  the  purposes  of  this 

*  Professor  Holman  concludes  that,  as  the  absolute  zero  is  approached,  the 
value  of  this  coefficient  approximates  a  = Cent.,    or    a  = Fahr. 


334  A   MANUAL    OF   THE   STEAM-ENGINE. 

work  the  two  measures  are  taken  as  substantially  equal ;  they 
are  sensibly  the  same.  Calling  the  quantity  of  heat,  in  any 
case,  measured  in  British  units,  Q,  and  in  metric  units,  Qmi 

Q  =  3.968320,; 

&„  =  0.25 1996  <2; 
log  Q  =  log  Qm  -fa  5986065  ; 
log  Qm  —  log  Q  +  14013935. 

The  magnitude  of  the  thermal  unit  is  necessarily  invariable ; 
and  the  number  of  thermal  units  required  to  produce  any 
given  change  of  temperature  in  any  substance  usually  increases 
slightly  as  that  range  is  higher  on  the  scale  of  temperatures. 

Heat  is  often,  especially  in  applied  thermodynamics,  most 
conveniently  measured  in  mechanical  units.  The  determina- 
tion of  the  magnitude  of  the  "  mechanical  equivalent  of  heat" 
has  been  made  by  processes  which  involve  a  comparison  of  these 
units  both  by  transformation  of  mechanical  energy  into  heat 
and  by  the  reverse  operation,  but  usually  by  the  former  method. 

Calorimeters  are  instruments  constructed  for  the  purpose  of 
Calorimetry,  or  heat-measurement.  They  are  of  various 
forms,  but  that  principally  used  in  physical  and  engineering 
researches  consists  of  an  apparatus  containing  water  and  fitted 
with  thermometers  and  scales  for  measuring  variations  of  tem- 
perature and  quantities  of  water.  The  quantity  of  heat  pass- 
ing into  the  instrument  becomes  determinable  when  the  quan- 
tity of  water  flowing  through  it  and  its  variation  of  tempera- 
ture become  known. 

It  is  sometimes  convenient  to  measure  the  volume,  rather 
than  the  weight,  of  water.  In  this  case,  the  density  must  be 
known  to  permit  the  calculation  of  the  weight  of  the  liquid. 

Volkmann  has  compiled  the  results  of  the  experiments  of 
Hagen,  Matthiessen,  Pierre,  Kopp,  and  Jolly,  on  the  expansion 
of  water,  and  has  obtained  the  following  mean  results  for  the 
volume  and  density  of  water  at  various  temperatures  on  the 
Centigrade  scale  : 


THERMODYNAMICS  OF   THE  IDEAL  ENGINE. 


335 


Temf 
Odeg 

I 
2 
3 
4 
5 
6 
7 
: 

9 
10 

I           Volume. 
T  C   ..   ..I  OOOI22   » 

Density. 
5.999878 
>-999933 
.999972 
-999993 

.OOOOOO 

.999992 
.999969 
•999933 
•  19988s 

.999819 

>.QQQ7iQ 

Temp.                  1 
15  dcgr.  C  

Volume. 
.000847 
.001731 
.002868 
.004250 
.007700 
.011970 
.016940 
.022610 
.028910 
-035740 
-04-52-W 

20   " 

2=    ** 

30       

60   "    .... 

80   "   

I  OOOlSl 

...1.000261   < 

100    " 

The  law  governing  the  expansion  of  water  is  very  exactly 
expressed  by  a  simple  form  of  equation.  Buel  has  thus  calcu- 
lated in  British  units  the  following  table,  following  Watt  :* 
the  figures  agree  with  the  above  to  the  third  place  of  decimals. 

VOLUME  AND  WEIGHT  OF  DISTILLED  WATER   AT   DIFFERENT 
TEMPERATURES  ON  THE  FAHRENHEIT   SCALE. 


Temper- 
ature, 
iUn» 

;-.=.-.. 

Ratio  of  volume  to  vol- 
ume of  equal   weight  at 
the  temperature  of  maxi- 

m_~   -er.~::v. 

Difference. 

Weight  of  a  cubic 
foot  in  pounds. 

Differ, 
ence. 

32= 
39  -2 
40 
50° 
60° 
70° 
8oe 
90* 

100° 

no* 

120* 

.000129 
.OOOOOO 
.000004 

.000253 

.000020 

.001981 

.00332 
.00492 
.00686 

.00902 
.01143 

.OOOI29 
.000004 
.000249 
.000676 
.001052 

.001339 
.00160 
•00194 
.00216 
.00241 
OO263 

62.417 
62.425 
62.423 
62.409 
62.367 
62.302 
02.213 
62.119 
62.000 
61.867 
61.720 

.OOS 
.OO2 
.014 
.042 
.065 
.084 
•099 
.119 

•133 
.147 

ifii 

130° 
140' 

I5ov 
160° 
170° 
180* 
ioo: 

200= 
2IO= 
2I2C 
220° 
230= 
240" 

.01411 
.01690 
.01095 
.02324 
.02671 
1-03033 
1.03411 
.03807 

.04226 

.04312 
.04668 
.05142 

-05633 

.00279 
-00305 
.00329 
.00347 
.00362 
.00378 
.00396 
.00419 
.OOOS6 
.00356 
-00474 
.00491 

61.556 
61.388 
61.204 
61.007 
6o.8oi 
60.587 
60.366 
60.136 
59-394 
59.707 
59-041 
59-372 
59.096) 

.168 
.184 
.197 
.206 
•214 

.221 
.230 
.242 
.I37 
.066 
.269 
.276 

*  Watt's  Dictionary  of  Chemistry;  art.  H« 
ii.  p.  113. 


Weisbach's  Mechanics;  vol. 


336 


A  MANUAL    OF    THE    STEAM-ENGINE. 


Temper- 
ature, 
Fahren- 
heit. 

Ratio  of  volume  to  vol- 
ume  of    equal  weight  at 
the  temperature  of  maxi- 
mum density. 

Difference. 

Weight  of  a  cubic 
foot  in  pounds. 

Differ- 
ence. 

250° 

.06144 

.00511 

58.812 

.284 

26o° 

.06679 

•00535 

58.517 

.295 

270° 

.0/233 

•00554 

58.214 

•303 

280° 

.07809 

.00576 

57-903 

.311 

290° 

.08405 

.00596 

57.585 

.318 

300° 

.09023 

.00618 

57-259 

.326 

310° 

.09661 

.00638 

56.925 

•334 

320° 

.  10323 

.00662 

56.584 

•  341 

330° 

.IIOO5 

.00682 

56.236 

•  348 

340° 

.11706 

.00701 

55-883 

•353 

350° 

.12431 

.00725 

55-523 

•  360 

360° 

•I3I75 

.00744 

55-I58 

.365 

370° 

•13942 

.00767 

54-787 

•  371 

380° 

•14729 

.00787 

54-4H 

•  376 

390° 

•15538 

.00809 

54.030 

.381 

400° 

.  16366 

.00828 

53-645 

•385 

410° 

.  17218 

.00852 

53-255 

•  390 

420° 

.18090 

.00872 

52.862 

•393 

430° 

.18982 

.00892 

52-466 

.396 

440° 

.19898 

.00916 

52.065 

.401 

450° 

.20833 

•00935 

51.662 

•  403 

460° 

.21790 

.00957 

51.256 

.406 

470° 

.22767 

.00977 

50.848 

.408 

480° 

•23766 

.00999 

50.438 

.410 

490° 

.24785 

.01019 

50.026 

.412 

500 

.25828 

.01043 

49.611 

•415 

5io° 

.  26892 

.01064 

49-195 

.416 

520° 

•27975 

.01083 

48.778 

.417 

530° 

.29080 

.01105 

48.360 

.418 

540° 

30204 

.01124 

47-941 

.419 

550° 

•31354 

.01150 

47.521 

.420 

93.  The  Specific  Heat,  or  capacity  for  heat,  of  any  sub- 
stance is  the  ratio  of  the  quantity  of  heat  required  to  raise  the 
temperature  of  any  given  weight  one  degree,  under  specified 
conditions,  to  the  amount  demanded  to  raise  the  temperature 
of  an  equal  weight  of  water  one  degree  when  at  the  lower  of 
the  two  fixed  standards  of  temperature — usually  taken  as  that 
of  melting  ice,  or  the  "freezing-point."  The  specific  heat  of 
any  substance  thus  determines  what  rise  or  fall  of  temperature 
will  follow  the  introduction,  or  the  abstraction,  of  any  given 
amount  of  heat. 

Specific  heats  are  of  several  kinds.  The  real  specific  heat  of 
any  substance  measures  the  quantity  of  heat  producing  altera- 
tion of  temperature,  simply.  Apparent  specific  heat  measures 


THERMODYNAMICS  OF   THE  IDEAL  ENGINE.          337 

that  demanded  to  produce  variation  of  temperatures,  accom- 
panying other  physical  changes  involving  transformations  of 
heat-energy.  When  these  specific  heats  are  measured  in  me- 
chanical units  of  energy,  they  are  sometimes  called,  as  by  Ran- 
kine,  "dynamical  specific  heats"  real  or  apparent,  as  the  case  may 
be.  The  specific  heat  of  constant  volume  measures  the  quan- 
tity of  heat  required  to  produce  alteration  of  temperature 
without  variation  of  volume.  The  specific  heat  of  constant 
pressure  is  an  "  apparent  "  specific  heat,  and  determines  the 
amount  of  heat  demanded  to  cause  variation  of  temperature 
in  masses  of  fluid  under  invariable  pressure.  In  the  former  of 
these  two  cases  the  specific  heat  is  probably  always  identical 
with  the  real  specific  heat  ;  in  the  latter,  the  specific  heat,  which 
is  an  apparent  specific  heat,  and  the  heat  transferred,  includes 
a  part  which  does  not  affect  the  temperature  of  the  mass,  but 
is  essential  to  operations  involving  transformations  of  energy 
from  one  form  to  another. 

Either  form  of  specific  heat  may  be  taken  as  the  quantity 
of  heat,  in  thermal  units,  producing  a  variation  of  the  tempera- 
ture of  unity  in  weight,  of  the  given  substance,  one  degree, 
under  specified  conditions.  It  is  most  convenient  to  make  the 
temperature  of  maximum  density  of  water  (39°.  I  F.,  or  3°.9  C.) 
the  standard.  Rankine  gives*  the  following  expressions  for 
the  specific  heat  of  water  : 

c=  i  +  o.ooo  ooo  309  (/  —  39.1)';  (Fahr.)    .     .     (i) 
cm=  i  +  o.ooo  ooi  (t  —  3.94)*;  (Cent.).     ...    (2) 

The  total  heat,  in  thermal  units,  demanded  to  raise  the  tem- 
perature of  unity  of  weight  from  to  /  to  /,  is 

h  =ft-fiJr  0.000  ooo  103  [  (/,  -  39-1  >'  -  (/,  -  39-1)']  :   •  (3) 
£„=/,-*,  +0.000  ooo  33  [  (',  -  4)'  -  (>,  -  4)*].     ...     (4) 
The  specific  heat,  c,  as  determined  by  experiment  is  obvi- 
ously 

wt 


Steam-engine  ;  p.  246. 


338  A    MANUAL    OF    THE   STEAM-ENGINE. 

in  which  w  and  zvt  are  the  weights  of  the  given  substance,  and 
of  water,  or  other  standard,  used  in  the  experiment,  and  /  and  ^ 
are  the  ranges  of  temperature  where  cooling  is  performed  by 
the  immersion  of  the  given  body  in  that  weight  of  water. 

The  specific  heats  of  solids  and  liquids  are  usually  so  nearly 
the  same,  for  constant  volume  and  for  constant  pressure,  that 
the  figures  are  usually  given  for  their  capacity  for  heat  without 
reference  to  these  conditions ;  these  differences  are  rarely,  if 
ever,  measurable.* 

It  was  discovered  by  Dulong  and  Petit  that,  in  certain 
groups,  the  product  of  the  specific  heat  of  substances  and  the 
combining  weight  is  the  same  for  the  whole  group.  This 
product,  for  elementary  substances,  is  usually  not  far  from  6.5. 
Thus  we  have,  calling  the  real  specific  heat  c,, 


64  . 

c _  = : .~T~>  nearly. 

atomic  weight 


The  specific  heats  of  alloys  are  obtained  by  multiplying  the 
weight  of  each  constituent  by  its  percentage  in  the  alloy,  add 
these  products  and  divide  by  100.  Regnault  finds  that  the 
specific  heats  of  alloys  far  removed  from  their  fusing-points  are 
the  means  of  the  specific  heats  of  their  constituents. 

Dulong  and  Petit  found  the  specific  heat  of  iron  to  increase 
from  a  mean  of  0.1098  between  the  freezing  and  boiling  points 
of  water  and  0.1255  for  a  range  increasing  up  to  662°  F. 
(350°  C).  Copper  similarly  increased  from  0.0927  to  0.1013, 
and  zinc  from  0.0927  to  0.1015,  platinum  from  0.0335  to  0.0343 
and  to  0.03818  at  2192°  F.  (1400°  C.).  Holman,  finds  for  the 
latter,f 

c  =  0.03284-0.00000  3022  (/—  32)4-0.000000000009  (/— 32)"; 
=  0.0328  +  0.00000  544  /„,  4-  0.000000000016  /"  .     .     .     (5) 


*  See  Constants  of  Nature,  Part  II  ;  Clarke  ;  Government  Print, 
f  Journal  Franklin  Institute  ;  Aug.  1882. 


THERMODYNAMICS  OF   THE  IDEAL   ENGINE.  339 

for  the  Fahrenheit  and  Centigrade  scales,  respectively.     For 
iron  he  obtains 

c  —  0.10687  4-  0.0000304  (/  —  32)  -f-  0.0000000238  (/  —  32)*; 
=  0.10687  +  0.0000547  /  -|-  0.0000000428  /' (6) 

The  law  of  Dulong  and  Petit  is  equivalent  to  the  statement 
that  the  quantity  of  heat  demanded  to  raise  the  temperature 
of  an  atom  of  any  simple  substance,  in  the  solid  state,  one  de- 
gree is  the  same  for  all  such  elements ;  and  Neumann's  law 
asserts  that  all  compound  solid  substances  of  similar  chemical 
construction  require  the  same  quantity  of  heat  per  atom,  but 
that  this  amount  is  less  than  for  the  isolated  elements.  The 
specific  heat  of  elementary  solids  is  greater  than  that  of  com- 
pound solids.  Woestyn  and  Gamier  find  that  the  specific  heat 
of  molecules  is  equal  to  the  sum  of  the  specific  heats  of  their 
constituent  atoms,  a  conclusion  partly  confirmed  by  Keep. 
Marked  exceptions  are  noted,  however,  and  Thomson  and  Tait* 
enunciate  the  principle  that  if  a  system  of  material  points  are 
acted  upon  by  impulsive  forces,  more  kinetic  energy  is  gen- 
erated when  they  are  free  than  when  in  combination. 

The  following  table,  mainly  from  Dulong  and  Petit  and 
from  Pouillet,  gives  the  specific  heats  of  a  large  number  of 
solids  and  liquids. 

SPECIFIC  HEATS  OF  SOLIDS  AND  LIQUIDS. 

Alcohol  (liquid) 0.61500  J  Chalk 0.21485 

Charcoal 0.24150 

Chloride  of  barium 0.89570 

"         "     calcium  0.16420 

"     lead 006641 

'     magnesium 0.19460 

"         "     manganese  0.14250 

"        "    strontium 0.11990 

"         "    zinc 0.13618 

Cobalt 0.10696 

Copper o .  095 15 

Corundum 0.19762 


Aluminium 0.21430 

Ammonia  (a  vapor). 0.50830 

Anthracite  coal 0.20100 

Antimony 0.05077 

Arsenic 0.08140 

Benzine 0.45000 

Bismuth  (solid) 0.03084 

.0.03630 

Bituminous  coal 0.20085 

Brass      0.09391 

Bromine  (liquid) 0. 10700 


*  Nat.  Phil.;  §  315. 


340 


A    MANUAL    OF    THE    STEAM-ENGINE. 


Diamond o.  14687 

Ether  (liquid) 0.50342 

Galena 0.05088 

Glass o .  19766 

Gold 0.03244 

Graphite o.  20083 

Hydrochloric  acid o.  18450 

Ice 0.50400 

Iceland  spar o. 20850 

Iodide  of  mercury 0.04197 

"      "    potassium 0.08191 

"  "  silver 0.06159 

Iodine  (solid) 0.05412 

"  (liquid) o.  10822 

Iridium ..  .0.18870 

Iron 0.11379 

"  (cast)  ..0.12983 

Lead  (solid) 0.03065 

"  (liquid) 0.04020 

Magnesium 0.24990 

Manganese 0.12170 

Marble 0.20989 

Mercury  (liquid) 0.03332 

(solid) 0.03192 

Nickel o.  10863 

Nitrate  of  sodium 0.27821 

"  "  silver 0.14352 

Nitre o.  23875 


Oil  of  turpentine  (liquid) 0.46727 

Olive-oil 0.30960 

Oxygen 0.21750 

Palladium 0.05928 

Petroleum 0.46840 

Phosphorus 0.18870 

Platinum 0.03243 

Potassium o.  16956 

Salt 0.17295 

Sapphire 0.21737 

Selenium 0.07446 

Silica 0.19132 

Silicon o.  17740 

Silver 0.05701 

Sodium o.  29340 

Steel 0.11700 

Sulphide  of  zinc 0.12813 

Sulphur  (native) o.  17760 

"        (purified) 0.20259 

"         (liquid) 0.23400 

Sulphuric  acid 0.34300 

Tin  (solid) 0.05695 

"    (liquid) 0.06370 

Tungsten 0.03342 

Water i.ooooo 

Wood  spirit 0.64500 

Zinc 0.09555 


The  specific  heats  of  gases  differ  from  those  of  the  solids, 
not  only  in  magnitude,  but  also  in  method  of  variation.  The 
specific  heat  of  constant  volume,  which  may  be  considered  as 
the  true  measure  of  the  specific  heat  of  the  substance,  differs 
greatly  from  the  specific  heat  of  constant  pressure.  These  two 
specific  heats  are,  however,  constant  for  the  perfect  gas  and 
approximately  so  for  the,  so-called,  permanent  gases,  and  their 
ratio,  which  is  an  important  quantity  in  thermodynamic  inves- 
tigation, is  also  constant.  This  ratio  is  given,  for  air,  by  Rankine, 
by  calculation  from  the  experiments  of  Bravois  and  Martens, 
and  of  Moll  and  Van  Beek,  on  velocity  of  sound  in  air,  as 
y  =1.408,  by  Clausius  as  1.410,  by  Masson  as  1.419,  Weisbach 
1.4025,  Cazin  1.410,  Rontgen  1.4053,  and  by  Kayser  as  1.4106; 


THERMODYNAMICS  OF   THE  IDEAL  EXCISE.  34! 

it  is  usually  taken  as  1.41.  The  experiments  of  Dulong*  give 
closely  confirmatory  values,  thus  :  Air,  1.414  f  ;  ox>~gen,  1.413  ; 
h>*drogen,  1.409.  The  ratio  of  the  specific  heats  of  all  elemen- 
tary  gases  is  probably  the  same,  as  will  be  seen  later  (§  96,  Chap. 
IV).  The  greater  the  specific  heat  of  a  liquid,  evidently,  the 
greater  that  of  its  vapor.  For  all  the  familiar  gases,  at  tem- 
peratures far  removed  from  those  of  liquefaction,  these  quanti- 
ties may  be  assumed  to  be  sensibly  invariable.  It  is  hence 
inferred,  also,  that  the  zero  of  the  perfect  gas  thermometer  is 
an  absolute  zero  marking  the  absence  of  all  heat-energy,  or  mo- 
tion. Experiment  gives,  with  a  fair  degree  of  accuracy,  values 
of  the  specific  heat  of  constant  pressure  ;  but  it  has  not  directly 
determined  that  of  constant  volume. 

These  specific  heats  are  usually  distinguished  by  the  sym- 
bols cp  and  cf,  or  Kp  and  K,t  accordingly  as  they  are  measured 
by  thermal  or  mechanical  units,  and,  when  J  represents  Joule's 
*•  mechanical  equivalent," 


It  seems  probable  that  cr  and  K,  are  always  identical  with 
the  "  real  "  specific  heat  of  the  substance,  and  that  their  value 
is  invariable,  and  entirely  independent  of  physical  changes  of 
state.  These  specific  heats  relate  to  units  of  weight  of  the 
fluid,  and  measure,  in  thermal  units,  the  heat  required  to  raise 
its  temperature  one  degree. 

It  is  often  desirable,  however,  to  refer  to  another  specific 
heat  related  to  volume,  comparing  the  quantity  of  heat  required 
to  raise  unity  of  volume  one  degree  with  that  demanded  to 
raise  an  equal  volume  of  the  substance  taken  as  standard 

*  Annales  de  Chimie  et  de  Physique:  xti.  13. 

f  Corrected  by  later  determination  of  constants,  according  to  Watt. 


342 


A    MANUAL    OF    THE    STEAM-ENGINE. 


through  the  same  range.  The  standard  almost  invariably  taken, 
where  gases  and  vapors  are  compared,  is  atmospheric  air,  and 
specific  heats  are  given  in  the  tables  of  books  of  reference  for 
both  air  and  water  as  standards.  We  thus  have  for  gases  and 
vapors  two  specific  heats  at  constant  pressure  and  two  at 
constant  volume,  which  may  be  called  the  densimetric  and  the 
volumetric  specific  heats  of  constant  pressure  and  of  constant 
volume.  The  following  table  gives  a  number  of  their  values  as 
calculated,  by  Clausius*  mainly  from  Regnault's  data.  The 
specific  heat  of  air  at  constant  pressure  was  predicted  from  de- 
terminations theoretically  made  by  Rankine  before  experiment 
had  given  the  correct  value. 

SPECIFIC   HEATS   OF  GASES. 


S.  H 
Constant 

.of 

'ressure. 

S.  H 

Constant 

of 

Volume. 

Densi- 
metric. 

Volu- 
metric. 

Densi- 
metric. 

Volu- 
metric. 

Air 

I 

0.23/50 

o.  1684 

I 

o, 

I.  1056 

o.  21751 

.013 

o.  1551 

1  .018 

N2 

0.9713 

0.24380 

.9970 

o.  1727 

0.996 

Hydrogen  

Ha 

0.0692 

3  .  40900 

.9930 

2.4110 

0.990 

Chlorine 

Cla 

2    45O2 

O.  I2OIQ 

248 

0.0928 

I    TJO 

Br, 

5  .4772 

O.O5552 

.280 

0.0429 

I  •  ^Q5 

Nitric  Oxide  

NO 

I  .0384 

0.2317 

.013 

o.  1652 

I.OI8 

Carbonic  Oxide  
Hydrochloric  Acid.  .  . 
Carbonic  Acid  
Nitric  Acid  

CO 
HC1 
CO2 
NaO 

0.9673 
1.2596 
1.5201 
i  .  5241 

0.2450 
0.1852 
0.2869 
O.2262 

.998 
.982 
•39 

•45 

0.1736 
0.1304 

0.172 
0.181 

0.997 
0-975 
1-55 
1.64 

HSO 

o  4805 

26 

I  16 

Carbon  disulphide  
Car  buretted  H  ydrogen 

csa 

CH, 
CHCls 

2.6258 
0.5527 

0.1569 
0.5929 

•  74 

•  38 

0.131 
0.468 

2.04 
1.54 

Olefiant  Gas  

C,H4 
NH3 

0.9672 

0.4040 

•75 
26 

0-359 

2.06 

Alcohol 

C2H8O 

Ether  

C«Hi0O 

e    16 

6*87 

Hydrogen  is  seen  enormously  to  exceed  every  other  sub- 
stance in  the  value  of  its  specific  heat  as  measured  for  unity  of 
weight. 

Latent  Heat,  so  called,  is  not,  strictly  speaking,  heat ;    its 

*  Mechanical  Theory  of  Heat;  §  7;  1879. 


THERMODYNAMICS  OF  THE  IDEAL  ENGINE.          543 

measure  is  the  equivalent  of  the  quantity  of  heat  which,  in  cer- 
tain classes  of  operations,  is  expended  in  the  performance  of 
work,  internal,  or  external,  or  both ;  it  has  disappeared,  as  heat, 
by  transformation  into  mechanical  energies,  kinetic  or  poten- 
tial. Thus,  in  the  fusion  of  solids  and  in  the  vaporization  of 
liquids,  and  in  the  expansion  of  substances  with  rising  tem- 
perature, increase  of  volume  occurs,  in  all  cases,  against  resist- 
ances, either  external,  or  internal  and  molecular,  and  the  product 
of  the  mean  intensity,  /,  of  such  resistance,  into  that  change  of 
volume,  tfoj  gives  a  measure  of  an  amount  of  work 


which,  according  to  the  general  laws  of  energy,  can  only  be 
performed  by  the  expenditure  of  an  equivalent  amount  of  some 
form  of  energy  —  in  this  case  heat-energy.  Of  all  the  heat 
transferred  to  the  body,  a  portion,  //=  U\  must  be  transformed 
from  the  kinetic,  sensible,  form  ;  becoming  "  latent,"  in  the 
potential  forms  of  "  energy  of  position  "  of  the  separated  mole- 
cules, and  of  external  work  performed  during  their  displace- 
ment. It  is  common,  incorrectly,  to  state  that  a  body,  thus 
expanded  by  heat,  contains  a  certain  quantity  of  latent  heat  ; 
this  heat,  which  has  apparently  become  latent,  as  was  supposed 
by  its  discoverers,  Dr.  Black  and  James  Watt,  no  longer  exists 
as  heat.  It  is  this  so-called  latent  heat,  the  heat-energy  thus 
transformed,  which  produces  all  alterations  of  volume  and  all 
variations  of  internal  and  external  energy,  and  which,  alone. 
performs  work.  Its  measure  is  always 


(7) 


in  which  ft  is  the  intensity  of  the  sum  of  the  internal  and  ex- 
ternal resistances  to  increase  of  volume. 

The  reversal  of  such  processes  causes  the  restoration  of  this 
energy  to  the  form  of  sensible  heat  ;  the  quantity  so  restored 
also  has  the  measure  just  given.  Heat  which  has  been  appar- 


344  A    MANUAL    OF   THE   STEAM-ENGINE. 

ently  rendered  latent  is  thus  always  caused  to  reappear  by  such 
reversal. 

Clausius  calls  heat  thus  transformed  "  work-heat  /"  whether 
it  be  applied  to  the  performance  of  internal  or  of  external 
work. 

The  latent  heat  of  expansion  is  that  heat  which  disappears 
by  transformation  into  the  potential  energy  of  equivalent  work 
whenever  a  body  is  caused  to  expand  by  communication  to  it 
of  that  form  of  energy.  Thus,  if  unity  of  weight  of  air  is  caused 
to  expand  at  constant  pressure  in  such  manner  that  its  tem- 
perature rises  one  degree,  and  its  volume  increases  to  such  an 
extent  as  to  retain  its  pressure  unchanged,  its  rate  of  accept- 
ance of  heat  is  measured  by  its  specific  heat  of  constant  pres- 
sure, c  =  0.237 ;  while,  if  caused  similarly  to  increase  in  tem- 
perature, simply,  without  expansion,  the  heat  demanded  is 
proportional  to  cv  =  0.168  ;  the  difference  ct  —  cv  =  0.069,  by 
transformation,  has  disappeared  as  heat,  and  is  the  measure 
of  the  latent  heat  of  expansion  and  of. the  work  and  energy  de- 
manded to  produce  the  observed  expansion  of  volume  against 
resisting  forces — in  this  case,  mainly  external  work  against  ex- 
ternal pressure.  In  other  than  the  perfect  gases,  this  work  of 
expansion  consists  partly,  and  sometimes  principally,  of  inter- 
nal work  done  against  molecular  attractive  forces. 

The  difference,  cp  —  cv,  is  always  found  to  be  greatest  when 
the  mass  is  most  expansible  by  heat ;  and  the  part  c,,  which  is 
probably  constant  for  all  substances,. under  all  possible  condi- 
tions, is,  as  already  stated,  the  real  specific  heat,  while  the 
large  quantity,  cf,  is  the  real  specific  heat  increased  by  the 
quantity  demanded  as  latent  heat  of  expansion.  Values  of 
cp  —  cv  —  I  may  be  obtained  from  the  tables. 

The  Latent  Heat  of  Fusion  is  that  quantity  of  heat-energy 
demanded  to  perform  that  work  ©f  the  expansion  of  solids,  at 
constant  temperature  and  at  the  point  of  fusion,  which,  being 
done,  leaves  the  mass  so  far  expanded  that  the  mutual  direc- 
tional force  affecting  adjacent  molecules  becomes  inappreci- 
able, and,  stability  of  form  being  thus  lost,  the  body  becomes 
liquid.  The  latent  heat  of  fusion  thus  measures  the  work 


THERMODYNAMICS  OF   THE  IDEAL  ENGINE.          345 

done,  externally  and  internally,  in  producing  this  change  of 
volume  against  the  resisting  effort  of  molecular  forces  and  ex- 
ternal pressure ;  the  latter  is  usually  insignificant  in  amount  in 
comparison  with  the  former ;  the  work  is  principally  internal 
work. 

M.  Person  finds*  the  latent  heat  of  fusion  of  non-metallic 
substances  to  be  nearly 

/=(/  +  256fF.)fo-O, (8) 

in  which  /  is  the  temperature,  Fahrenheit,  and  c^  and  ct  are  the 
specific  heats  in  the  liquid  and  solid  states,  respectively. 

The  latent  heat  of  fusion  of  ice  is  found  by  experiment  to 
be  142.5  British  thermal  units,  nearly,  or,  on  the  metric  scale, 
about  79  calories.  During  fusion,  all  the  heat-energy  applied 
to  the  substance  is  expended  in  doing  the  work  of  expansion, 
and  none  is  effective  in  producing  increase  of  the  temperature, 
which  remains  constant  during  the  whole  period  of  fusion. 

The  introduction  and  transformation  of  heat-energy,  during 
the  process  of  fusion,  is  observed  to  occur  under  the  operation 
of  three  laws,  viz. : 

(1)  The  temperatures  of  fusion  and  of  solidification  are  the 
same,  and  are  definitely  fixed  for  each  substance  under  any 
given  pressure. 

(2)  This  temperature  remains  constant,  heat  being  slowly 
supplied,  during  the  whole  operation  of  change  of  state  of  the 
given  mass. 

(3)  Change  of  volume  always  occurs  during  this  change  of 
state,  and  is  the  greater  as  the  quantity  of  heat  so  supplied  and 
transformed  is  the  greater. 

The  temperature  of  fusion  is  raised,  as  a  rule,  by  pressure ; 
the  reverse  occurs  to  the  extent  of  O°.oi33  F.  (o°.oc>74  C.)  for 
each  atmosphere,  in  the  case  of  ice,  the  variation  being  gen- 
erally less  for  substances  of  high  cohesion,  and  fusing  points, 
and  greater  for  those  of  low  melting  points  and  little  strength. 

The  Latent  Heat  of  Ei'aporation  is  that  heat-energy  trans- 

*  Annales  de  Chimie  et  de  Physique;  Nov.  1849. 


346  A   MANUAL    OF   THE    STEAM-ENGINE. 

formed  into  potential  energy,  or  into  actual  energy  of  other 
form,  when  the  change  of  state  is  that  of  a  liquid  undergoing 
vaporization.  Its  amount  measures  the  energy  demanded  to 
remove  the  molecules  beyond  that  condition  of  equilibrium 
which  is  the  boundary  between  the  liquid  and  gaseous  states, 
and  at  which  stability  of  volume,  as  well  as  of  form,  disappears. 
As  will  be  seen  (§  112)  on  studying  the  thermodynamic  theory 
of  the  heat-engines,  the  magnitude  of  this  quantity  measures 
the  work  which  can  be  donejDer  unit  weight,  as  a  maximum 
by  the  substance,  if  used  as  a  working-fluid  in  heat-engines.  It 
does  not  at  all  affect  the  thermodynamic  efficiency  or  propor- 
tion of  heat  transformed  into  work  with  any  given  range  of 
temperature. 

The  three  laws  above  given  for  fusion  hold  equally  well  for 
this  change.  The  quantity  of  heat  transformed  is,  however, 
usually,  enormously  greater,  and  its  variation  with  the  tempera- 
ture and  the  pressure  due  the  boiling-point,  or  the  point  of 
liquefaction,  accordingly  as  the  change  is  produced  by  the 
communication  or  the  abstraction  of  heat,  is  very  considerable. 

Regnault  obtained  values  of  this  latent  heat,  for  water, 
which  are  very  exactly  expressed  by  one  of  his  formulas, 
slightly  modified  by  Rankine,  thus :  * 

/=  1091.7  -  0.695  (t  -  32°)  -  o.oooooo  103  (t  -  390-1)3:  (9) 

or,  similarly  applying  the  correction  indicated  by  the  last  term, 

lm  =  606.5  —  0.695  tm  —  o.ooo  ooo  333  (/„  —  4°)3;     .     .     (10) 

in  British  and  metric  units,  respectively.  For  the  former,  the 
following  nearly  equivalent  expressions  may  be  generally  used : 

/=  1091.7  -  0.695  (*- 32)      ) 
=  1114     -0.695   t  \.      .     .     .     (11) 

=    966.1  —  0.695  (/  —  212°)   ) 

*  Steam-engine;  p.  250.  See  Peabody's  Thermodynamics,  for  these  con- 
stants. 


THERMODYNAMICS  OF   THE  IDEAL  ENGINE.  347 

The  latent  heats  of  water  are  greater  than  those  of  any 
other  substance.  According  to  Andrews,  we  have  the  follow- 
ing, the  latent  heat  of  water  being  unity : 

Substance.  Latent  Heat.  Substance.  Latent  Heat. 

Water i  Bisulphide  of  carbon 0.162 

Wood-spirit 0.492  Oxalic  ether 0.136 

Alcohol.... ,..0.378  Bromine 0.085 

Ether 0.169  Peroxide  of  tin 0.059 

According  to  Mr.  H.  Whiting,*  the  application  of  the 
molecular  theory  of  gases  to  liquids,  in  combination  with  the 
magnetic  theory  of  cohesion,  requires  certain  numerical  rela- 
tions between  the  physical  constants  which  are  in  every  case 
obtained,  very  exactly,  by  experiment. 

The  most  important  are  the  following : 

(1)  "  The  product  of  the  latent  heat,  molecular  weights,  and 
coefficient  of  expansion  is  equal  to  8.4  for  liquids  at  tempera- 
ture zero,  expanding  by  ordinary  law." 

(2)  "The  product  in   metric  measures  of  the  mechanical 
equivalent  of  the  latent  heat  and  the  density  is  1.2  times  the 
product  of  the  coefficient  of  expansion,  the  resistance,  and  the 
absolute  temperature." 

The  Total  Heat  of  Evaporation  is  the  sum  of  the  sensible 
and  latent  heats,  measured  in  heat-units,  and  is  constant  at  any 
one  pressure,  but,  like  the  latent  heat  of  evaporation,  is  vari- 
able with  change  of  pressure,  and,  consequently,  of  the  boiling- 
point.  This  quantity  is  sometimes  called  the  "  total  heat  of 
vapor."  Its  amount  is  always  calculated  from  some  fixed  tern- 
perature,  and  is  defined  as  the  total  heat  from  that  fixed 
temperature,  and  at  the  given  temperature,  or  pressure,  of 
evaporation.  Thus,  water,  fed  to  a  steam-boiler  at  60°  F.,  and 
evaporated  at  70  pounds  pressure  according  to  the  steam- 
gauge,  is  said  to  be  evaporated  front  60°  F.  and  at  320°  F.,  the 
boiling-point  for  the  given  pressure. 

This  quantity  of  heat,  in  thermal  units,  is 

//  =  <(/.  -/.)  +  /,.     .     .     .     •     .     (12) 

*  Science  Bulletin;  1884. 


348  A   MANUAL   OF   THE   STEAM-ENGINE. 

in  which  c  is  the  specific  heat  of  the  liquid,  /,  —  /,  the  range  of 
temperature,  and  /  the  latent  heat  of  evaporation  at  the  boiL 
ing-point,  /a. 

For  water  we  have,  as  above,  according  to  Regnault,  when 
/,  =  32,  in  British  measures, 


b  =  i09i.7  +  o.305(/t-  32°), 
=  1082     +0.305*,,  V.  ...    (13) 

=  1146.6  +  0.305  (/,  -  212°); 

and  when  heated  from  any  higher  temperature  /„  deduct 
c  (tt  —  32),  c  being  the  mean  specific  heat  for  that  range  of 
temperature. 

Lm  =  606.5  +0.305*,  „,     .....    (14) 

in  metric  units,  the  heat  being  measured  from  the  freezing- 
point  ;  we  deduct  ct9  when  the  initial  temperature,  on  that 
scale,  is  tv 

The  efficiency  of  steam  generators  is  often  measured  by  the 
weight  of  water  evaporated  by  them  "  from  and  at  "  the  boiling- 
point  under  atmospheric  pressure.  Experiment  determines 
the  weight  evaporated  under  actual  conditions  ;  the  above  ex- 
pressions give  the  total  heat  required  per  pound,  and  this  quan- 
tity divided  by  the  latent  heat  under  the  standard  conditions, 
965.7  thermal  units  according  to  Regnault,  or  966.1  as  corrected 
by  Rankine,  gives  the  equivalent  weight  desired.  For  all  ordi- 
nary work  this  divisor  may  be  taken  as  966. 

The  Total  Heat  of  Gasification  is  always 


(15) 


in  which,  for  steam,  c  =  0.4805,  its  specific  heat  under  constant 
pressure,  as  a  gas,  and  /  has  very  exactly  that  value  found  at 
the  freezing-point  —  1091.7,  nearly,  for  British,  or  606.5  in  metric 
measures. 


THERMODYNAMICS  OF  THE  IDEAL  ENGINE.          34Q 

Supcrktated  steam,  or  "steam-gas.,"  requires  for  its  produc- 
tion by  the  change  of  the  liquid  into  the  vapor  under  a  stated 
pressure,  and  elevation  to  any  given  temperature,  a  quantity  of 
heat  and  energy  which  is  entirely  independent  of  the  pressure 
and  temperature  at  which  the  boiling-point  occurs.  The  pro- 
cess involves  two  distinct  operations:  (i)  the  raising  of  tem- 
perature, by  the  transfer  to  it  of  sensible  heat,  from  the  initial 
temperature  of  the  substance  to  its  final  temperature  ;  (2)  the 
performance  of  internal  work  by  the  conversion  of  sufficient 
heat  to  separate  the  molecules  from  that  proximity  which  char- 
acterizes the  liquid  state  to  their  final  relative  positions  in  the 
larger  volume  and  at  the  final  temperature  and  pressure  ;  which 
latter  quantities  are  fixed  for  the  unit  of  mass  by  the  equation 
fv  /  T  =  constant.  Hence,  starting  from  the  freezing-point, 


(16) 


where  H  is  the  total  heat,  ff0  the  latent  heat  at  Tv  and  K,  the 
dynamically  measured  specific  heat  of  the  gas  ;  its  real  dynamic 
specific  heat.  Rankine  takes  for  British  measures  :  * 

Jk0  =  842^72  foot-pounds, 

Kt  =  772  X  0475  =  366.7  foot-pounds; 


in  thermal  units, 


*=  1092, 
'  =  0-475- 


The  specific  heat  of  superheated  steam  is  found  by  Zeuner 
to  be  variable,  thus : 

/  in  Ibs.  per  sq.  in.        50  100  200 

C,  0.348        0.346        0.344 

P-«55- 


35O  A    MANUAL    OF    THE   STEAM-ENGINE. 

Hirn  finds  the  following  values  for  its  specific  volume : 

p  in  atmos.  1345 

t  Cent.  141°       200°        200°       200° 

Sp.  vol.,  cu.  in.      1.85      0.697      0.522      0.414 

It  can  be  readily  computed  if  necessary.* 
94.  The  Critical  State  is  a  condition,  intermediate  between 
the  liquid  and  gaseous  states,  which  is  sometimes  observed 
when  vaporization  occurs  under  very  high  pressures.     At  the 
"critical  temperature "  a   gaseous  body  may  be  liquefied  by 
pressure;    at  any  higher   temperature  such    liquefaction   has 
never  been  produced.     In  the  ordinary  process  of  vaporization 
the  mass  rises  in  temperature  with  but  slight,  and  often  no, 
observable,  change  of  volume,  until,  at  a  certain  temperature 
and  pressure,  fixed  for  each  fluid,  the  temperature  ceases  rising 
with  constant  volume,  and,  heat  being  still  introduced  at  a  uni- 
form  rate,  volume  increases,  with  temperature  constant,  and 
g<    ;  on  increasing  until  all  the  fluid  has,  molecule  by  molecule, 
been  transformed  into  the  state  of  vapor.    As  will  be  seen  later, 
in  the  first  part  of  the  process  the  heat  is  simply  transferred  as 
sensible  heat,  and  produces  rise  of  temperature ;  in  the  second 
period  heat  is  transformed,  and  an  equivalent  amount  of  work 
is  done  in  the  gradual  conversion  into  vapor  and  the  expansion 
of  the  mass,  during  the  continuous  process  of  change,  against 
internal  and  external  resistances.    When  the  pressures  resisting 
the  expansion  are  very  great,  this  variation  of  volume  is  greatly 
restricted,  and  a  point  may  finally  be  reached  at  which  no  such 
expansion  at  constant  temperature  can  take  place ;  the  sub- 
stance all  passes,  suddenly  and  completely,  into  the  vaporous 
condition.     The  temperature  at  which  this  occurs  is  the  "  crilx 
ical  temperature"  of  the  substance,  and  at  this  point  the  latent 
heat  of  evaporation  obviously  becomes  zero ;  the  two  states; 
the  liquid  and  the  gas,  at  this  point  have  a  common  limit.f 

*  Zeuner's  Warmeiheorie  ;  also  Peabody,  chap.  vii.  p.  125. 
f  This  has  been  experimentally  shown  by  Mathias;  Comptes  Rendus,  1889, 
p.  470;  and  Jour.  Franklin  Inst.,  Apr.  1890;  p.  297. 


THERMODYNAMICS  OF   THE  IDEAL   ENGINE.  351 

This  phenomenon  was  observed  by  M.  Cagniard  de  la  Tour 
in  the  case  of  water,  as  early  as  1822.  Dr.  Andrews  has  studied 
this  phenomenon  here  described  with  great  care.*  He  con- 
cludes the  two  fluids  to  be  merely  widely-separated  illustrations 
of  one  physical  state  ;  more  correctly,  the  two  states,  the  liquid 
and  the  vapor,  have  a  perfect  continuity.  The  critical  tempera- 
ture of  carbonic  acid  is  about  87°. 7  F.  (3O°.9  C.)  and  at  a  press- 
ure of  75  atmospheres;  that  of  ether  is  369°  F.  (187°  C.)  and 
at  37.5  atmospheres;  for  alcohol,  498°  F.  (258°  C.)  and  119  at- 
mospheres, according  to  M.  C.  de  la  Tour ;  for  carbon  disul- 
phide,  505°  F.(263°  C.)  and  66.5  atmospheres;  while  for  water 
the  temperature  rises  to  773°  F.  (410°  C),  and  the  pressure  is 
not  exactly  known,  probably  nearly  750  atmospheres,  as  calcu- 
lated by  the  Author.  At  the  latter  temperature  water  was 
found  to  dissolve  glass.  M.  Cailletet  reached  the  critical  tem- 
perature with  nitric  oxide  at  46°.4  F.  (8°  C.)  under  270  at- 
mospheres, marsh  gas  at  44°.6  F.  (7°  C.)  and  180  atmospheres, 
oxygen  and  carbonic  oxide  at  below  —  2O°.2  F.  (—  29°  C.)  and 
at  300  atmospheres, nitrogen  below  55°.4  F.(i3°  C.)  and  at  200 
atmospheres;  hydrogen  seemingly  approaches  this  state  at 
—  21°  F.  (—  29°  C.)  and  280  atmospheres.  The  so-called  per- 
manent  gases  may  all  be  reduced  to  the  liquid  state  by  pressure 
when  the  critical  temperature  is  reached,  and  have  been  so  con- 
densed by  M.  Cailletet  and  by  M.  Pictet,  the  pressures  applied 
reaching,  in  some  cases,  800  atmospheres  and  the  necessary  de- 
crease of  temperature  being  attained  by  expansion  at  initially 
low  temperatures  from  under  these  pressures. 

The  following  table  of  temperatures  of  physical  phenomena 
has  been  collated  by  Mr.  J.  J.  Coleman :  f 

PHYSICAL  CONDITIONS  AND  TEMPERATURE. 

De*.        Deg. 

Fahr.      Cent. 

+  698    +370    Critical  point  of  water =  195 . 5  atmos.  pressure. 

+  311    +155.4       "          "     "sulphurous  anhydride  =    78.9 

+  285   +141  "          "     "chlorine =    83.9      " 

*  Philosophical  Transactions;  1869. 

f  Trans.  Phil.  Soc.  Glasgow;  March  18,  1885. 


352                    A  MANUAL   OF   THE   STEAM-ENGINE. 

Deg.          Deg. 

Fahr.        Cent. 

+  266  +130  Critical  point  of  ammonia =  "5  atmos.   pressure. 

-f-212  -f-ioo.2  "          "     "  sulphuretted  hydrogen  =    92  " 

_j_   gg  _|_   37           "          "     "acetylene =    68  " 

_|_   95  _j_   35.4       "          "     "  nitrous  oxide =    75  " 

_j_   89  +    3I-9       "          "     "  carbonic  acid =    77  " 

4-    50  +    io.  I       "          "     "  ethylene =    51  "             " 


_|_  32  —  o  Nitrous  oxide  boils  at  32  atmos.  pressure Faraday. 

_^_  32  —      o  Carbonic  acid  boils  at  36       "  "        " 

-j-  14  —  io  Sulphurous  anhydride  boils " 

-j-  15  —  10.5  "     Bunsen. 

—  io  —  23  Methyl  chloride  boils Regnault. 

—  io  —  23  Carbonic  acid  boils  at  19.38  atmos.  pressure Faraday. 

—  20  —  29  Sulphurous  anhydride  boils  in  current  dry  air. Pictet. 

—  20  —  29  Carbonic  oxide  and  oxygen,  air  and  nitrogen,  com- 

pressed to  300  atmos.  in  glass  tubes,  and  suddenly 
expanded,  show  liquefaction Cailletet. 

—  26  —  32  Alcohol  containing  52  per  cent  water  freezes Pictet. 

—  29  _  33.6  Chlorine  boils Regnault. 

—  29  —  33.7  Ammonia  boils Bunsen. 

—  31  —  35  Commercial  paraffin  oil  (sp.  gr.  .810)  freezes Coleman. 

—  40  —  40  Nitrous  oxide  boils  at  8.71  atmos.  pressure Faraday. 

—  40  —  40  Carbonic  acid  boils  at  II  

—  40  —  40  Ethylene  boils  at  13.5  "         " 

—  53  —  47  Freezing  point  of  Hollands  gin  and  French  brandy.  Coleman. 

—  60  —  51  Nitrous  oxide  boils  at  5  atmos.  pressure Faraday. 

—  60  —  51  Carbonic  acid  boils  at  6.75  "  "       " 

—  60  —  51  Ethylene  boils  at  9  "  "        " 

—  62  —  52  American  petroleum  (sp.  gr.  790)  freezes Coleman. 

—  62  —  52  Freezing  point  of  extra  strong  whiskey  and  rum  . . . 

—  62  —  52  Alcohol  containing  40  per  cent  water  freezes " 

—  80  —  61.8  Sulphydric  acid  boils ....Regnault. 

—  80  —  62  Nitrous  oxide  boils  at  3  atmos.  pressure Faraday. 

—  80  —  62  Carbonic  acid  boils  at  3.75  "  "       " 

—  80  —  62  Ethylene  boils  at  6.5  "  "       " 

—  99  —  73  Critical  point  of  marsh  gas,  pressure  56  atmos.  Wroblewski. 
— 103  —  75  Liquefied  ammonia  freezes. 

— 103  —  75  Alcohol  containing  20  per  cent  water  freezes Coleman. 

— 108  —  78  Carbonic  acid  boils Faraday  and  Regnault. 

—  112  —  80  Solid  sulphurous  anhydride  melts Mitchell. 

—  123  —  86  Nitrous  oxide  boils Faraday. 

—  123  —  86  Marsh  gas  boils  at  40  atmos.  pressure Wroblewski. 

—  128  —  87.9  Liquid  nitrous  oxide  boils Regnault. 


THERMODYNAMICS  OF   THE  IDEAL  ENGINE. 


353 


SS. 


SSL 


—144     —     98  Marsh  gas  boils  at  25  aunos.  pressure WrtUewtK. 

52     —  102  Amyl  alcohol  an  oily  liquid Obemtti. 

52     —   102  Silicon  fluoride  a  white  mass " 

.2     —  102  Arseniurerted  hydrogen  liquid 

52     —  102  Hydrochloric  acid  boils " 

=2     —   102  Chlorine  orange  crystals " 

52     -  102  Eihylene  boils 

54     —   103  "  " 

•  66     —  no  Solid  carbonic  acid  and  ether  in  vacno Faradar. 

71     —  113  Critical  point  of  oxygen,  pressure  50  aunos WrtbUvesln. 

-i     —  113  Marsh  gas  boils  at  1 6  aunos.  pressure 

•5     —  115  Solid  carbonic  acid  in  vacuo,  25  mm.  pressure Deamr. 

75     —115  Hydrochloric  acid  gas  solid OhewskL 

—  116  Carbon  disulphide  solid. 

— 180     —  118  Arseninretted  hydrogen  white  crystals Okesoski. 

—  193     —   125  Nitrons  oxide  boils  in  vacuo Deseur. 

—200    —129  Ether  solidifies ObemsK. 

—202     —  130  Absolute  alcohol  solid. 

—209     —134  Amyl  alcohol  solid ObtmstL 

— 2i3     —  139  Eihylene  boils  in  vacno " 

—219     —  139.5  Critical  point  of  carbonic  oxide,  press.  55.5  aunos. .       " 

—220     —  140  "      "  air.  pressure  39.0  atmos " 

— 220     —  140  Calculated  temp,  of  carbonic  acid  snow  in  vacuo  (?). .  .PictcL 

—220     —  140  Hydrogen  compressed  to  650  atmos.  and  pressure 
released  produces  momentary  liquefaction  and 

solidification PicUt. 

— no    —  140  Oxygen  compressed  to  320  atmos.  and  pressure  re- 
leased produces  momentary  liquefaction Put  ft. 

—231     —  146  Critical  point  of  nitrogen,  35  atmos.  pressure ObraukL 

—238     —  150  Ethylene  boils  in  vacno •• 

—233     —   150  Carbonic  oxide  boils  at  20  atmos.  pressure " 

—242     —152  Atmospheric  air  boils  at  20     "  "      

-247     —  155  Marsh  gas  boils WrobU*ski. 

-—ago;    —  184  Oxygen  boils " 

—312     —  191.4  Airboils OttrmK. 

— 31*    —  191.2       "       "  WntlraHln. 

—315     —  193  Carbonic  oxide  boils 

—317     —  194  Nitrogen  boils Olte&ski. 

—337     —  205  Atmospheric  air  boils  in  vacno " 

—348     —  2ii  Carbonic  oxide  solidifies  in  vacuo " 

—351     —213  Nitrogen  boils  in  vacno " 

?  Hydrogen  at  100  to  200  atmos.  liquefies  to  colorless 
drops  (:n  glass  tubes  0.2  mm.  dia.  surrounded 

by  oxygen  boiling  in  vacuo) WnMcwsJd  amd  OhewtL 


354  A  MANUAL   OF    THE   STEAM-ENGINE. 

Deg.  Deg. 

Fahr.  Cent. 

-355  —  2I5         Calculated  boiling  point  of  hydrogen E.  J.  Mills. 

460  —  273        Absolute  zero. 

(The  critical  points  above  freezing  point  of  water  are  quoted  from  Professor  Dewar  ; 
Chemical  News,  Jan.  16,  1885.) 


95.  The  Definition  of  the  Perfect  Gas  has  been  seen  to  be 
capable  of  expression  by  statement  either  of  its  physical  consti- 
tution, of  its  physical  properties,  or  of  its  thermodynamic 
equation.  It  is  so  constituted  that  its  molecules  exert  no  in- 
herent cohesive  attractions,  or  mutual  repulsions,  and  it  can 
only  be  confined,  when  acted  upon  by  heat,  if  allowed  to  ex- 
pand within  a  defined  volume  by  the  application  of  external 
force  ;  and  hence  its  effort  to  expand — i.e.,  its  pressure,  tension, 
or  elasticity,  as  it  is  variously  called — is  supposed  to  be  due 
solely  to  that  energy  of  molecular  motion  which  we  call  heat. 
Its  distinguishing  physical  property  is  found  in  the  fact  that, 
when  reduced  to  any  given  volume,  and  confined  within  any 
given  space,  its  total  pressure  upon  the  confining-walls,  or  its 
total  tension,  is  precisely  equal  to  the  sum  of  the  pressures 
which  any  number  of  equal  parts  would  produce,  if  each  were 
separately  enclosed  in  an  equal  space.  This  is  equivalent  to 
saying  that,  the  temperature  being  constant,  the  tension  is  in- 
versely as  the  volume,  which  is  the  law  of  Boyle  and  of  Ma- 
riotte.  The  perfect  gas  is  also  found  to  vary  in  pressure,  or  in 
volume,  or  to  vary  in  product  of  pressure  and  volume,  both 
varying  together,  directly  as  the  temperature  measured  from 
the  "  absolute"  zero,  i.e.,  according  to  the  law  of  Charles  and  of 
Gay  Lussac. 

Experiment  thus  shows  that  the  more  nearly  a  gas  ap- 
proaches this  ideal  state,  the  more  perfectly  does  it  illustrate 
the  law  of  Boyle  and  Mariotte,  the  pressure  varying  inversely 
as  the  volume  ;  and  the  more  exactly  does  it  follow  the  law  of 
Charles  and  Gay  Lussac,  according  to  which  the  variation  of 
pressure  at  constant  volume,  or  of  volume  at  constant  pressure, 
or  of  the  product  of  pressure  and  volume,  varies  directly  as  the 
absolute  temperature. 


THERMODYNAMICS  OF   THE  IDEAL  ENGINE.  355 

TIu  Defining  Equation  of  the  Perfect  Gas  is,  therefore,  as 
already  seen, 


pv       T      po      pjp, 

.  • 


The  quantity  of  matter  considered  is  commonly  taken  as 
unity  of  weight,  and  v  is  here,  therefore,  the  "specific  volume," 
or  the  volume  of  unity  of  weight. 

The  value  of  R  is  thus  constant  for  any  one  gas,  and,  for 
different  gases,  will  vary  inversely  as  their  densities  at  stand- 
ard temperature  and  pressure.  Thus,  for  the  nearly  perfect 
gases,  oxygen,  hydrogen,  nitrogen,  and  for  the  mixture,  air,  the 
values  of  R  are,  respectively,  nearly  26.5,  42.3,  30,  and  29.3,  in 
metric  measures,  or  48,  70,  55,  and  53,  in  British  measures. 
Evidently, 


TD 


in  which  D  is  the  density  of  the  gas,  as  measured  by  the  weight 
of  unity  of  volume,  and  Tis  absolute  temperature. 

96.  The  Thermodynamics  of  the  Perfect  Gas  involves 
the  determination  of  the  methods  of  variation  of  temperature, 
pressure,  and  volume,  and  of  variations  of  quantities  of  heat 
and  work  consequent  upon  those  changes ;  in  such  manner  that 
the  General  Thermodynamic  Equation  may  be  applied  to  the 
case.  This  means  the  measurement  of  the  quantities  entering 
into  the  equation  and  ascertaining  their  physical  relations,  and 
thus  the  algebraic  relations  of  their  symbols ;  so  that  numerical 
values  may  be  substituted  and  the  equation  solved  for  any 
given  case. 

The  general  therm odynamic  equation  has  been  seen  to  be 
an  expression  in  which  the  change  of  heat-energy  is  measured 
in  terms  of  two  distinct  phenomena ;  the  application  of  heat  to 
alteration  of  temperature  in  any  "  working  fluid,"  the  transfer, 


3$6  A   MANUAL    OF   THE   STEAM-ENGINE. 

simply,  of  heat-energy  ;  and  that  producing  mechanical  energy, 
or  work.  We  now  see  that  the  first  of  these  quantities  is  meas- 
ured by  the  product  of  the  range  of  temperature  of  the  unit 
weight,  always  taken,  and  the  real  specific  heat  ;  while  the  sec- 
ond must  be  measured  by  the  product  of  the  intensity  of  the 
total  pressure  of  the  fluid  by  the  change  of  volume.  Hence 


dH=dS+dW; 


in  which  the  equation  may  be  solved  when,  in  the  second  term 
of  the  second  member,  the  relation  of/  to  v  is  known;  or,  when 
the  values  of  all  the  quantities  involved  can  be  directly  ob- 
tained by  observation  or  other  means. 

The  first  law  of  thermodynamics  and  the  experimental 
measure  of  the  mechanical  equivalent  of  heat  enable  us  to 
express  the  specific  heat,  Kv,  of  constant  volume,  the  "real  dy- 
namical specific  heat,"  in  terms  of  either  thermal  or  dynamical 
units.  The  second  law  of  thermodynamics  asserts  that  the 
value  of/  in  the  second  term  may  be  taken  as  proportional  to 
absolute  temperature  and,  hence,  the  value  of/,  at  any  instant, 
may  be  obtained  by  multiplying  the  rate  of  variation  of/  with 

T,  ->  by  T,  the  absolute  temperature  of  the  fluid  ;  and  hence 


f  =  T(jr): (»> 

and  we  have  simply  to  write 

then  to  obtain  values  of  the  several  symbols  ;  and  to  determine 
the  value  of  the  partial  differential  coefficient  H^J  ,  by  refer- 


THERMODYNAMICS  OF  THE  IDEAL  ENGIXTE.          357 

ence  to  the  algebraic  expression  of  the  laws  of  variation  of  the 
physic?!  characteristics  of  the  fluid. 

The  "Thermodjmamic  FiuKtum**  is  obtained  by  reference 
to  the  second  law,  also,  as  originally  shown  by  Rankine,  thus:* 

We  have  seen  that  the  second  law  asserts  that  any  effect  of 
heat,  being  proportional  to  the  quantity  of  heat  acting  in  its 
production,  is  proportional  to  the  absolute  temperature  of  the 
fluid,  and  is  measured  by  the  product  of  this  quantity  by  a 
"  thermodynamic  function/"  the  form  and  magnitude  of  which 
for  a  gas  will  be  presently  determined  ;  that  is: 


(4) 


when  $  represents  that  function. 

The  Thermodynaumc  Equations  for  Gases  are  thus  obtained 
by  inserting  in  the  general  fundamental  equations  the  values 
of  the  partial  differential  coefficients  obtained  from  the  charac- 
teristic equation  of  the  gas.  The  perfect  gas,  as  has  been  seen, 
is  defined  by  the  equation 


=  R=*,  a  constant, 

in  which  the  subscript,  0,  may  be  taken  to  indicate  the  state  of 
the  substance  at  a  standard  temperature,  as  at  the  melting. 
point  of  ice.  For  all  purposes  of  the  engineer,  and  for  nearly 
all  the  purposes  of  the  physicist,  the  permanent  gases,  so 
called,  may  be  taken  as  perfect.  The  values  of  the  coefficients 


The  general  equations  thus  become,  in  accordance  with 
these  two  laws, 

dH=  TdQ  = 


?   -":; 


358  A    MANUAL   OF   THE   STEAM-ENGINE. 


.........     (5) 

dH= 


Since  the  value  of  the  total  differential  dv  in  (5)  is 


and,  from  (6)  and  (7), 


(6) 


R  "T 

—  dp,     .....     (7) 


JJ.T 

-     =  Kt  •=•  Kv  -J-  R  ;    Kp  —  Kv  =  R  ;   .    .    .    (8) 


and  thus,  as  was  first  shown  by  Clausius,  both  specific  heats, 
that  of  constant  volume  and  that  of  constant  pressure,  and  their 
difference,  are  found,  by  thermodynamic  science,  as  well  as  by 
experiment,  to  be  constant. 
Since,  from  (7), 

,~_  vdp+pdv 
~~          ' 


(9) 


THERMODYNAMICS  OF   THE  IDEAL  ENGINE.          359 

But  since  the  specific  heat  at  constant  pressure,  Kp,  is  also 
fe) »  we  have 


We  may,  therefore,  unite  the  three  forms  of  the  equations 
for  perfect  gases  : 


dH  =  (Kt  - 

=  K/tT-  vdp 


(10) 


in  which  equation  the  specific  heat  at  constant  pressure  ap- 
pears instead  of  the  specific  heat  at  constant  volume  inserted 
in  (5). 

Introducing  both  specific   heats,   and   eliminating  R,  we 
obtain: 

dH  = 


When  a  perfect  gas  expands  at  constant  temperature,  ob- 
viously no  internal  work  can  be  done,  and  no  change  occurs  in 
the  amount  of  sensible  heat  present  in  the  mass. 

Hence,  under  the  laws  of  transference  of  energy,  if  no 
external  work  is  done,  a  constant  weight  of  such  gas,  freely  ex- 
panding at  constant  temperature,  requires  no  heat  from  exter- 
nal sources  to  keep  its  condition,  with  respect  to  heat  or  energy, 
unchanged. 


360  A  MANUAL    OF    THE    STEAM-ENGINE. 

This  conclusion,  based  upon  the  law  of  persistence  of 
energy,  has  been  confirmed  by  experiments  made  by  Joule  and 
Thomson  upon  the  permanent,  or  nearly  perfect,  gases.  In 
the  case  of  the  non-permanent  gases,  such  as  carbonic  acid,  it 
is  found  by  experiment,  as  by  theory,  that  this  conclusion  does 
not  hold.  In  the  latter,  as  in  any  case  in  which  internal  work 
is  done,  heat  must  be  introduced  during  expansion  to  perform 
that  internal  work,  if  the  temperature  is  to  be  kept  constant, 
and,  reversing  the  process,  heat  must  be  abstracted  during  com- 
pression at  constant  temperature. 

When  external  work  is  done  by  a  perfect  gas,  expanding  at 
constant  temperature,  it  is  obviously  necessary  to  supply  heat, 
to  do  that  work,  in  exactly  equivalent  amount,  and  the  heat 
absorbed  is  thus  a  measure  of  the  work  so  done. 

When  imperfect  gases  similarly  expand,  heat  is  added,  as 
before,  in  just  the  amount  demanded  for  conversion  into  work, 
and  its  measure  is  also  the  measure  of  the  total  work  done 
internally  and  externally. 

The  thermodynamic  function,  for  the  perfect  gas,  is  readily 
derived  from  the  general  equations. 

Since  this  function  is 

dH  — 
we  have 


Also,  L     .     .     .    (12) 


The  latter  may  be  deduced  directly  from  the  former,  by 
eliminating  dv  and  substituting  its  value  in  terms  of  dp.  We 
have 


THERMODYNAMICS  OF   THE  IDEAL  ENGINE.  361 

Substituting  in  (12), 


an  equation  which  is  perfectly  general. 
For  perfect  gases, 


T~   T0J  \dTh~  vT0  '  \dTlp 
and.  also,  when  */t>  =  o, 


—  —t-*L\      L  ^\  \   _  />\    (<\  fdv\ 

df~\df}P^~  \d~p)T\df}*  ~  °;     WrJ,  V^Jr  ™  ~  \df)i 

Substituting  in  (14), 

„  =  *,+'-*<-*#,.  .  .  (I5) 


which  is  the  second  equation  (12). 

Collecting  the  expressions  for  all,  we  have 


and  integrating, 

0  =  AT,  log,  T+  R  log,  v  +  C 
=  Kp\oge  T-Rlo&p+C 
=  (KV+R}  log,  T  -  R  log,  /  +  C 


362  A    MANUAL    OF    THE   STEAM-ENGINE. 

The  value  of  C,  the  constant  of  integration,  is  here  inde- 
terminable ;  but  this  is  a  matter  of  no  importance,  since  it  dis- 
appears in  application,  differences  in  values  of  thermodynamic 

functions,  only,  being  in  such  cases  considered. 

&>• 
Introducing  the  value  of  -j~  =  y,  and  observing  that 


_  i     7 


in  which  x  =  1.405,  nearly,  for  air,  and  is  usually  taken  as  1.41 
for  all  permanent  gases  ;*  ---  =  2.451  ;  _  =  3-451.  The 

value  of  ~^^,  for  air,  is  estimated  by  Rankine  at  53.15  foot- 

•*  o 

pounds  per  degree  Fahrenheit,  accepting  Regnault's  determi- 
nation of  the  value  of  pQv0  as  26,214  foot-pounds,  and  taking 
T0  at  493°.2  Fahr. 

The  applications  of  the  General  Equations  for  Perfect  Gases 
are  illustrated  by  the  following  cases  : 

(i)  Required  the  amount  of  heat  demanded  to  produce 
change  of  volume  at  constant  pressure. 

We  have 


*  Purely  theoretic   analysis  indicates  a  possibility  that  this  value  of  the 
perfect  gas  may  be  y  =  —  ^  =  1.405285.  —  Phil.  Mag.,  1885;  p.  520. 


THERMODYNAMICS  OF   THE  IDEAL  ENGINE.  363 

Since/  is  constant,  dp  —  o,  and 
dff  = 

whence,  integrating, 

H  =  £ 

(2)  The  gas  expands  or  contracts  at  constant  temperature. 
For  this  case  take 


But  T  is  constant  ;  dT  =  a 


(3)  Expansion  is  adiabatic  or  isentropic,  i.e.,  H  is  constant, 
dH  —  o.    Then 

dH  =K,dT  +  (K,  -  K^Td  =  o, 


rr 

Integrating  and  calling  -~  =  y, 

log,  T-\-  (y  —  i)  log,t/  =  constant, 


364  A   MANUAL   OF    THE    STEAM-ENGINE. 

Tvy~l  —  const.  =  7X*"1. 


•  •  7\  -  W 
Similarly,  from  the  equation 


dH  =  KtdT  -  (Kp  -  KJT      =  o 


we  obtain 


Combining  the  above,  we  get 


Or,  from 

dH  =  A^h  • 

we  have 

*/z>    ,  dp 

r-+f 

and,  as  before, 


and  /j^,v  =  pvy  =  constant. 

(4)  Required  an  expression  for  the  work  done  by  a  perfect 
gas  expanding  at  constant  temperature,  the  latent  heat  of  ex- 
pansion being  supplied  from  some  external  source  of  heat,  i.e., 
in  isothermal  expansion. 

We  have 

dH  =  pdv  ;    pv  =  constant  =  p^  , 
and  »  =  M. 


THERMODYNAMICS  OF   THE  IDEAL  ENGINE.  365 

.-.U= 


or,  if  the  ratio  of  expansion  is  r  =  -*, 


(5)  To  measure  the  work  done  during  adiabatic  expansion  : 
We  have 

pv1  =  constant  =  /,?,*. 


(6)  To  find  the  variation  of  temperature  when  a  gas  ex- 
pands adiabatically,  and  without  doing  work  ;  as  when  expand- 
ing from  one  given  volume  to  another  within  a  space  otherwise 
vacuous  : 

From  (i  i), 


v 
Since  the  work  done  by  the  gas  is  zero, 


=  KjlT\    dT=o;     T=  constant 

97.  The  Work  performed  and  Energy  expended,  by 
transfer  and  transformation  of  heat,  are  thus  readily  computed 
whenever  the  method  of  operation  is  known.  As  already 


3  A   MANUAL   OF   THE   STEAM-ENGINE. 

stated,  the  variation  of  pressure  with  change  of  volume  may 
usually  be  represented  by  some  curve  of  the  hyperbolic  class, 
and  by  algebraic  expressions  of  the  general  form, 

pvn  =  const.  —  pjv? (i) 

In  such  cases  the  work  done,  by  unity  of  weight,  is 


in  which  then 

and,  thence, 

<7_     vn    r*    -n  Pf>? 

=*-^T'> (4) 

whence,  for  gases, 


Hence,  the  work  done  during  expansion  along  a  line  of 
which  the  equation  is  pp?  =  pvn  is  proportional  to  the  differ- 
ence of  the  products  of  pressure  and  volume  at  the  initial  and 
terminal  portions  of  the  curve,  and,  in  the  case  of  gases,  to  the 
range  of  temperature  worked  through.  The  change  of  temper- 
ature is  thus,  in  all  such  cases,  directly  proportional  to  the 
quantity  of  work  performed  by  or  upon  the  expanding  or  con- 
tracting fluid. 

The  Heat  expended  is,  in  all  cases,  the  sum  of  the  amounts 
demanded  to  perform  internal  work,  to  do  the  external  work 
of  expansion,  and  to  produce  variation  of  sensible  heat.  In 
the  perfect  gases,  the  internal  work  is  zero ;  the  external  work 
is  measured  as  above;  and  the  variation  of  sensible  heat  is 
measured  by 

S=Kv(T,  -  TJ,       .     .     ;:  .,    .     .     (6) 
being  positive  for  compression  and  negative  for  expansion. 


THERMODYNAMICS  OF   THE  IDEAL  ENGINE.  367 

Hence,  the  total  heat  demanded  in  any  case  of  hyperbolic 
expansion,  such  as  the  above,  must  be  5+  U,  or 


Thus  it  is  found  that  the  total  amount  of  heat  emitted  or 
received  in  such  changes  is  directly  proportional  to  the  range 
of  temperature,  7\  —  Tt,  worked  through  during  such  expan- 
sion or  compression.  The  above  is  also  a  proof  that,  either 
specific  heat  being  found  constant  by  experiment,  the  other 
must  be  constant  as  well. 

For  the  case  of  common  hyperbolic  expansion,  in  which 
the  law  of  Boyle  and  Mariotte  is  followed,  n  =  I,  and  the  ex- 

pression for  work  done,  equation  (4),  becomes  H  —  —  ,  inde- 

terminate. 

In  this  case,  unity  of  weight  being  taken,  as  before, 
P*v*  =  P*V*  =  pv,  and 

C"*dv  v 

U  =  A",  /      —  =  A".  log,  -'  =  A",  log,  r,   .     .     (8) 

«/  vt  » 

in  which  r  is  the  ratio  of  expansion.  This  case  is  that  of 
isothermal  expansion  of  gases,  the  heat  transferred  to  or  from 
the  fluid  being  the  equivalent  of  the  work  done,  and  wholly 
transformed. 

When  n  exceeds  unity,  the  curve  falls  under;  and  when 
n  <  i,  the  line  lies  above  the  equilateral  hyperbola.  In  the 
first  case,  the  temperature  of  the  gas  must  obviously  fall  ;  in 
the  second  case,  it  must  as  evidently  rise,  as  expansion  pro- 
ceeds. 

Isothermal  changes  are,  by  definition,  those  occurring  at 
constant  temperature. 

Adiabatic  changes  are,  by  definition,  those  which  occur 
without  gain  or  loss  of  heat  by  transfer  to  or  from  the  enclosing 
vessel  ;  such  as  may  take  place  in  a  vessel  composed  of  a  non- 
conducting substance. 


368  A   MANUAL    OF    THE   STEAM-ENGINE. 

Isodynamic  changes  are,  by  definition,  those  taking  place 
without  variation  of  internal  energy. 

The  work  of  Isothermal  and  of  Adiabatic  Expansion  of  gas 
may  evidently  be  now  determined  by  assigning  to  n,  in  the  ex- 
pression PV*  =  constant,  proper  values,  and  the  quantity  of 
heat-energy  transformed  may  be  thus  ascertained. 

For  Isothermal  Expansion  of  gases,  as  already  seen,  n  =  i« 
and 

rdv  v 

—  =  A^  log,  -  =  A?,  log.  r  ;    .     .     (9) 
1 

which  measures  the  quantity  of  heat  transformed  into  external 
mechanical  work,  or  into  kinetic  energy.  Since  no  change  of 
temperature  takes  place,  no  heat  is  transferred  to  effect  such  a 
change ;  and,  since  no  intramolecular  forces  resist  or  aid  the 
change  of  volume,  no  heat  is  transformed  in  that  manner.  The 
quantity  £7thus  measures  the  total  amount  of  heat  transferred, 

which,  measured  in  thermal  units,  is,  calling  —  —  A, 


where  Q  is  the  quantity  of  heat,  in  thermal  units ;  /  =  - j  is 

A 

"  Joule's  equivalent." 

This  determination  may  be  effected,  also,  by  comparison  of 
the  thermodynamic  functions  for  the  initial  and  final  conditions 
of  the  fluid,  thus  : 

The  thermodynamic  function  at  the  beginning  of  expan- 
sion is 


and,  at  the  end  of  the  process, 

...     (12) 


THERMODYNAMICS  OF  THE   IDEAL  EXGIXE.          369 

Since  the  temperature  is  constant,  7~s  =  7^,  the  heat  ex- 
pended is 


(,3) 


as  before,  the  expanding  or  compressed  mass  weighing  unity. 
For  air,  adopting  T.  =  —  493°^  R,  R  =  53.15,  and 

U=  53.157;  log,r,   ......    (14) 

and,  in  metric  measures, 


Ft?r  Adiabatu  Expansion  of  gases,  there  are  two  equations 
of  condition  : 


The  work  done  during  expansion  is 


and  if  the  density  is  called  8  =  — 


37O  A   MANUAL    OF   THE   STEAM-ENGINE. 

Again, 

u=  rv.'-A^Y  r*v~*dv 

t/Z/j  I/ft 


For  compression,  the  work  is  similarly  measured  ;  its  value 
is  negative,  and  heat  is  produced  in  place  of  being  expended. 

The  variation  of  temperature  is  controlled  by  the  laws  ex- 
pressed in  the  equations 


whence 

~^  =Tl-r~\  .....    (20) 

r  being  the  "  ratio  of  expansion. 

The  Isothermal  and  the  Isodynamic  Lines  on  a  diagram  of 
heat-energy  in  cases  of  the  expansion  of  gas  are  identical  in 
form  and  location.  As  has  been  seen,  the  whole  internal 
energy  of  the  perfect  gas,  and,  approximately,  all  that  of  the 
permanent  gases,  is  the  energy  of  heat-motion,  and  is  mani- 
fested as  sensible  heat,  its  total  amount  being  proportional  to 
the  absolute  temperature  of  the  fluid.  A  line  of  invariable 
internal  energy,  or  the  isodynamic  line,  is  therefore,  for  gas,  a 
line  of  uniform  temperature. 

The  equation  of  this  line  is  obtained  directly  from  the  de- 
fining equation  of  the  gas,  thus  : 

T—  constant;     ......     (21) 

pv  —  RT=  constant  .....     (22) 

Calling  abscissa  and  ordinate  x  and  y,  v  =  ax,  p  =  by,  and 
pv      RT 


THERMODYNAMICS  OF   THE  IDEAL  EXGIXE. 


371 


a  and  b  being  assigned  values  to  be  determined  by  the  scale 
on  which  the  curve  is  drawn.  The  isothermal  and  isodynamic 
lines,  for  gases,  are  thus  again  seen  to  be  alike  hyperbolic. 

Since  heat  must  be  converted  into  mechanical  energy,  when 
the  fluid  expands  isothermally  behind  a  piston,  it  is  again  evi- 
dent that  an  amount  of  heat  must  be  supplied,  during  such  ex- 
pansion, precisely  equal  to  the  external  work  done,  in  order 
that  the  temperature  of  the  gas  shall  not  vary ;  and  that  dur- 
ing compression,  heat  must  be  abstracted  to  a  similar  extent. 

The  Adiabatu  or  Istntropic  Lint,  also,  represents  the 
method  of  variation  of  pressures  and  volumes  when  the  ~  en- 
tropy" of  the  fluid  is  constant,  Le.,  when  no  heat  is  communi- 
cated to,  or  emitted  from,  the  gas,  all  change  of  temperature  of 
the  fluid  being  due  to  transformation  of  energy.  Since  all 
energy  expended  upon  external  bodies  must,  in  this  case,  be 
produced  by  conversion  of  heat  into  mechanical  energy,  and 
all  heat  gained  by  the  substance  must  be  due  to  the  reverse 
transformation,  it  is  evident  that  the  fluid  must  cool  during 
expansion,  and  become  heated  by  compression,  when  it  is  en- 
closed in  a  non-conducting  envelope  of  variable  volume.  It 
thus  follows,  also,  that  the  expanding  fluid  will  give  an  adia- 
batic  line  which  will  fall  more  rapidly  from  the  same  initial 
state  i^an  its  own  isothermal,  the  adiabatic  curve  thus  lying 
under  the  isothermal,  on  the  diagram  of  energy.  When  com- 
pression occurs  from  the 
same  initial  state,  the  adia- 
batic line  lies  above  the  iso- 
thermal. 

The  relations  of  the  two 
lines  are  shown  in  Fig.  130, 
in  which  T,  T,  Tlt  Tt,  are 
isothennals.  and £lt£t,£2t 
EIt  are  adiabatics.  The  in- 
tersections of  the  latter  with 
the  former  being  considered  as  marking  initial  conditions,  the 
curves  are  seen  to  separate,  in  the  manner  just  indicated, 
with  change  of  volume  in  either  direction,  as  explained  in  §  81. 


372  A    MANUAL    OF   THE   STEAM-ENGINE. 

The  equation  of  the  adiabatic  line  is  readily  obtained  from 
the  characteristic  equation  of  the  gas,  combined  with  the  special 
defining  conditions  of  the  assumed  change,  thus  : 

Since  no  heat-energy  is  absorbed  by,  or  emitted  from,  the 
fluid,  in  this  case,  during  change  of  volume, 

0  =  constant  ;     dH  =  Td(f>  =  o  ;     d<f>  =  o. 
Then 

d*  =  K  *±+%*,      .....     (24) 

dT     p0v0dv 
=  Kv-f+-f--;  .....     (25) 

0  =  Kv  log,  T  +  K,  (y  —  i)  log,  v.     (26) 
Then 

(f) 
-g  =  log,  T-\-(y  —  i)  log,  v 

=  log,(rFY-');       .....     (27) 
and,  since  <p  —  const, 

T  ± 

Tvy    *  .=  —-pv1  —  eKv  =  constant  ;  .     .     (28) 

Po^o 

and  the  equation  of  the  adiabatic  line  is 

yx1  •=.  pvy  =  constant  =  pj)?  ; 
•*£ 
in  which  v  —  -£  =  1.41,  nearly. 

&T, 

The  expressions,  derivable  as  above, 


are  statements  of  Poisson's  law  relating  pressures  to  volumes 
and  specific  heat  ratios  ;  the  heat  being  constant,  none  being 
supplied  or  abstracted  from  the  fluid,  and  expansion  being 
adiabatic. 


THERMODYNAMICS  OF   THE  IDEAL  ENGINE.          373 

As,  in  isothermal  expansion,  the  sole  equation  of  condition 
is 

T  =  const.;    .......     (29) 

so,  in  adiabatic  expansion,  the  equation  of  condition  is 

0  =  const  ........     (30) 

98.  The  Thermodynamics  of  the  Vapors  and  imperfect 
gases  may  be  considered  as  precisely  the  same,  in  essence,  as 
for  the  permanent  and  the  perfect  gases  ;  which  for  the  pur- 
poses of  the  engineer  are  taken  to  be  physically  identical,  as 
well  as  thermodynamically.  The  total  change  of  energy,  in 
any  operation  in  which  changes  of  pressure,  volume,  heat,  and 
temperature  occur  in  the  vapors,  as  working  fluids  in  heat- 
engines,  is  always  capable  of  representation  on  a  balance-sheet, 
the  gain  or  loss  of  energy  as  heat  being  equal  to  the  sum  of 
the  quantities  producing  variation  of  temperature  and  acting 
to  produce  loss  or  gain  of  work  or  mechanical  energy. 

The  general  thermodynamic  equation  remains,  as  before, 


but,  in  this  case,  while  the  first  term  of  the  second  member  is 
as  easily  determined  and  measured  as  in  the  case  of  the  gas, 
this  is  by  no  means  the  fact  as  regards  the  second  term.  In 
this  case,  internal  as  well  as  external  work  is  done,  and  a 
difficulty  at  once  presents  itself  in  the  attempt  to  measure  the 
former  component,  and  hence  the  total  work.  We  have  no 
instrumental  means  of  directly  measuring  the  internal  pressure, 
pi  ,  and  work,  p^dv  ;  which,  with  the  external  pressure,  pt  ,  — 
which  we  easily  measure,  in  all  cases,  by  means  of  pressure- 
gauges,  —  and  work,  p/lv,  make  the  total  work,  pdv,  of  the 
equation.  Then  we  have,  as  before, 


374  A   MANUAL    OF   THE   STEAM-ENGINE. 

Yet  the  computation  of  internal  forces  and  work,  and  of 
external  work,  are  readily  effected.  Notwithstanding  the  fact, 
as  just  stated,  that  the  molecular  forces,  and  the  work  per- 
formed by  or  against  them,  are  beyond  the  reach  of  any 
physical  apparatus  and  are  incapable  of  direct  measurement,  it 
becomes  easy  to  calculate  both  force  and  work  from  measura- 
ble data  by  application  of  the  second  law  of  thermodynamics. 

The  rate  of  variation  of  external  pressure  and  work,  with 
temperature,  at  constant  volume,  may  be  determined  easily  by 
experiment ;  this  rate,  according  to  the  second  law,  is  constant 
for  all  temperatures,  and  hence,  being  multiplied  by  the  abso- 
lute temperature  at  which  the  total  pressure  or  the  work  is  to 
be  determined,  the  product  measures  that  total  pressure  or 
work.  In  symbols,  let  p,  w,  and  T  represent  the  total  pressure 
and  work,  and  the  absolute  temperature ;  then  the  rates  of  va- 

dp    dw 
riation  -7^,,  -7™,  with  temperature,  may  be  ascertained  by,  for 

example,  noting  the  change  of  external  pressure,  as  measured 
by  the  steam-gauge,  for  a  change  of  one  degree  or  other  small 
but  exactly  measurable  range,and  taking  this  ratio  of  differences, 

Ap  dp  dpe 

~p,  as  sensibly  equal  to  -7=.     The  value  of  -r=  is  identical, 

evidently,  at   any  given   point  on  the   scale,  with  -7™;    as  is 

dw  dw 

-j=  with  -p=,.     The  work-ratio  is  obtained  by  multiplying  the 

Ap  by  the  volume  and  taking  this  product,  Ap .  v  =  Aw,  as  the 

Aw      dw 

numerator  in  —^  =  -7=,.     Then  the  total  pressure,  internal  and 
AT      dT 

external,  must  be  measured  by 

and  the  total  work  of  expansion  from  zero 

W=T^T=T^ & 


THERMODYNAMICS  OF   THE  IDEAL  EXGIXE.          375 

It  thus  becomes  possible  readily  to  determine  the  internal 
and  external  pressures,  the  internal  and  external  work,  and  the 
latent  heats  of  the  vapors,  or  of  any  other  imperfectly  gaseous 
or  non-gaseous  substance. 

Since  the  heat  rendered  latent,  in  any  case,  is  the  equivalent 
of  the  work  performed  by  it,  the  latent  heat  of  vaporization 
must  be  exactly  equal,  dynamically,  to  the  work  just  measured  ; 
and  if  it  be  called  H  for  unity  of  weight, 


when  Av  is  the  increase  of  volume  taking  place  during  the 
change  of  physical  state.  If  its  value  is  made  known,  as  is 
usual,  by  experiment,  and  dr  is  observed,  it  becomes  easy  to 


dT~  Tfa-r/f 


(4) 


dp 
The  value  of  -?=.  is  sometimes  found  to  be  negative,  e^j.,  in 

the  case  of  ice.     Professor  James  Thomson  found 

dp 
—  ~fr=  o°jOi33  Fahr.  =  o3.ooj4  Cent. 

as  the  amount  by  which  the  melting-point  of  ice  is  lowered  by 
every  increase  of  one  atmosphere  of  pressure.  The  latent  heat 
of  fusion  is  similarly  measured.  The  total  heat  of  vaporization, 
as  it  is  called,  from  a  temperature  7*,  and  at  a  temperature  Ts . 
is  the  sum  of  the  latent  heat  converted  into  work,  as  just  meas- 
ured, and  the  sensible  heat  demanded  to  raise  the  temperature 
from  T;  to  Tf 

The  latent  heat  of  vaporization  per  unit  of  volume  is  obvi- 
ously measured  by 


3?6  A    MANUAL    OF    THE  STEAM-ENGINE. 

and  this  permits  the  ready  computation  of  the  heat  demanded  in 
supplying  any  steam,  or  other  vapor,  engine  with  the  quantity 
of  fluid  required  to  do  any  given  amount  of  work,  or  to  drive 
its  piston  through  any  given  space,  and  this  without  knowing 
the  density  of  the  fluid. 

99.  The  Thermodynamics  of  Steam  may  thus  be  brought 
under  the  general  rules  of  the  science.  The  rate  of  variation 
of  the  external,  or  gauge,  pressure  of  the  vapor  in  contact  with 
the  liquid  from  which  it  is  produced,  or  at  the  boiling-point, 
with  temperature,  may  be  obtained  from  the  tables,  or  from 
formulas  such  as  have  been  given  for  steam  by  Regnault,  and 
for  that  and  other  vapors  by  Rankine.*  The  latter  are  the  most 
general  and  usually  the  most  exact  ;  they  have  the  form,  as 
already  seen  (§  90), 


/?        f* 
com.  logp  =  A-,-~-,  .....    (i) 


whence 


106  .a.    .    .    (2) 


The  density  of  vapor  may  thus  be  readily  computed  from 
the  known  value  of  its  latent  heat,  and  much  more  satisfactorily 
and  exactly  than  it  can  be  derived  by  any  known  method  of 
experimental  determination.  The  increase  of  volume  of  unity 
of  weight  must  always  be 


(3) 


in  which,  practically,  the  values  of  vl  may  usually  be  neglected. 
Then  the  densityt  is 


(4) 


*  Steam-engine;  §  206,  Div.  III. 

f  Tables  thus  calculated  for  steam  and  for  ether  and  other  fluids  are  given  by 
Rankine  in  his  Miscellaneous  Papers  and  in  his  treatise  on  the  Steam-engine. 


THERMODYNAMICS  OF   THE  IDEAL  ENGINE.  377 

The  specific  volume,  the  volume  of  a  pound  of  water,  at 
customary  modern  working  pressures  and  temperatures  is  not 
far  from  0.017  cubic  foot.  The  external  work  of  formation  of 
steam  is  thus 

U  =  pl(y,  —  0.017),  nearly;  .....     (5) 

the  latent  heat  is  H  foot-pounds  ;  and  the  variation  in  internal 
work,  during  evaporation,  its  increase,  is 

AH=H-p&,  -0.017);  .....     (6) 

which  quantity  measures  its  total  energy,  T.  The  heat  ab- 
sorbed in  any  purely  thermodynamic  operation  is  the  sum  of 
the  accessions  of  internal  energy  and  external  work,  i.e.,  of 
sensible  and  internal  latent  heat  and  external  work. 

When  steam  is  wet,  if  x  represents  its  quality,  as  measured 
by  the  fraction  of  dry  steam,  the  latent  heat  is 

H'  =  xH\ 
and  its  total  heat  is 


where  5  is  the  total  sensible  heat  of  the  water.     The  specific 
volume  is 

F'  =  ;rF+(i  -;r)o.Ol7:   .....     (8) 

V  being  the  specific  volume  of  pure  dry  saturated  steam  ;  and 
this  is 

F'  =  *F,  nearly  .......     (9) 

Temperature,  Pressures,  and  Volumes  of  Steam  are  related  by 
natural  law  quite  as  definitely  as  those  governing  these  relations 
for  the  gases  ;  but  algebraic  expressions  of  those  laws  are  not 
yet  obtained,  except  empirically.  There  have  been  numerous 
formulas  proposed  of  the  latter  class,  some  of  which  are  remark- 
ably exact  within  a  moderate  range.  The  most  accurate  are 


3/8  A   MANUAL    OF   THE    STEAM-ENGINE. 

probably  those  of  Rankine,*  already  given  (§§  90,  99)  for  vapors 
generally,  taking/  as  the  symbol  of  gauge-pressure: 

T)  /" 

com.  logp  =  A  —       —       ;      .     .    .     .    (10) 


in  which,  for  steam, 


D 
-4=8.2591;  =.=  0.003441; 


log  B  =  343642  ; 

r>? 

log  C  =5-59873;         -,  =  0.00001184; 


pressures  being  taken  in  pounds  on  the  square  foot,  and  tem- 
perature in  degrees  Fahrenheit  on  the  absolute  scale.  The  ex- 
periments of  Regnault  and  of  Fairbairn  and  Tate  have  furnished 
the  generally  accepted  values. 

Unwin  has  proposed  f  a  simpler  formula  than  Rankine's, 
which,  while  not  quite  as  exact,  gives  more  manageable  expres- 

sions for  -££  and  its  functions  ;  thus,  for  vapors  generally  : 

«-;     .......    (12) 


*  Steam-engine;  p.  237,  §  206.     Ibid.;  pp.  559-564. 
f  Phil.  Mag.;  April  1886. 


THERMODYNAMICS  OF   THE  IDEAL  ENGINE.  379 

I  dp  nb 

--=2.3025^ 

(a  —  log  ^"pT 

=  2.3025«V  --  |^—  ;.      .      .      (I4) 

b* 
t  dp  nb 

(15) 


--  =  2.3025- 


For  steam,  these  formulas  become  : 

log  p  =  7.5030  -y;  .    .    .    .    .    (16) 

r-(  _  7579        Y-\ 
~  V7.5030  -  log//    ' 

i  *#      21815 


(7- 5Q30-  log  ff*  ,,,, 

441-3 

T  dp       21815 


=  2.8782(7.5030  -log/);     .     .    (19) 

which  expressions  give  remarkably  exact  results.    Metric  meas- 
ures are  used  throughout. 

Many  simple  expressions  have  been  proposed  for  the  rela- 
tions of  pressure  and  temperature  of  saturated  steam.  These, 
in  their  simplest  forms,  are  usually  of  the  type  : 


in  which,  for  British  measures,  as  the  Fahrenheit  scale  and  ab- 
solute pressures  in  pounds  on  the  square  inch,  values  are  very 


38o 


A    MANUAL    OF   THE   STEAM-ENGINE. 


nearly  a  =  0.0085  5  *  =  °-22-  Thus  Mr.  Estler  makes  a  = 
0.008484,  i  =  0.222,  for  all  customary  working  pressures,  and 
obtained  a  sufficiently  close  approximation  for  any  ordinary 
work  of  the  engineer. 

Internal  pressure  and  work  are  computed  by  deducting 
external  pressure  and  work  from  the  totals.  Clausius  thus 
obtained  the  following  values  of  p  for  steam  of  the  pressures 
given,  all  in  millimetres  of  mercury,  of  which  760  measure  one 
atmosphere  of  pressure: 

TOTAL   PRESSURES  OF   STEAM. 


Centigrade. 

External  Pressure. 

Ratio 
dp 

Total   Pressure 
dp 

Ratio 

P 

/. 

T. 

A- 

At. 

Tr- 

*-Tir- 

A' 

IOO° 

374° 

760 

t 

27  •  200 

10146 

13-3 

I2O 

394 

1520 

2 

48.595 

19150 

12.6 

134 

408 

2280 

3 

67.020 

27277 

ii.  g 

144 

418 

3040 

4 

84-345 

35172 

«.  5 

152 

426 

3800 

5 

100.375 

42659 

II.  2 

159 

433 

4560 

6 

116.085 

50149 

II.  O 

1  66 

440 

5320 

7 

133-445 

58502 

10.8 

171 

445 

6080 

8 

146.910 

65228 

10.7 

176 

450 

6840 

9 

161.27 

72410 

10.6 

180 

454 

7600 

10 

173-425 

78561 

10.4 

199 

473 

11400 

15 

239.57 

113077 

9-9 

It  is  seen  that  the  rate  of  variation  of  pressure  with  the 
temperature  of  steam  continually  increases  as  pressures  and 
temperatures  rise,  and  that  the  proportion  of  internal  to  ex- 
ternal work  and  pressure  continually  diminishes;  but  that  the 
latter  ratio  is  large,  about  ten  to  one,  for  the  whole  range  of 
pressures  familiar  in  standard  practice. 

The  specific  volume  of  steam,  or  the  volume  of  unity  of 
weight,  and  its  reciprocal,  the  density,  have  been  seen  to  be 
capable  of  easy  computation  when  the  latent  heat  of  vaporiza- 
tion at  the  given  temperature  is  known  ;  since  this  latent  heat 
measures  the  work  done  while  the  force  resisting  it  is  calculable 
as  above.  From  the  expressions  (3)  already  given,  §  98, 
r*P  *.  H  dp 


we  thus  obtain  very  exact  values. 


THERMODYNAMICS   OF   THE  IDEAL   E  \GI.\E.  381 

Clausius  thus  obtains  the  following  values,  and  compares 
them  with  the  somewhat  uncertain  figures  of  Fairbairn  and 
Tate,  derived  experimentally.  Metric  measures  are  employed. 

SPECIFIC  VOLUMES   OF  STEAM. 


'•                               r-               •       Calculated. 

By  Experiment. 

117.17                 :  .:  .  :- 
124.17                398.17 
125.41                402.41 
137.46        1     -  411.46 
144-74                 413-74 

0-947 
0.769 
0.651 
0.530 
0-437 

0.941 
0.758 
0.645 
0.514 

•-:- 

Adopting  his  nomenclature,  let  s  and  <r  represent  the  spe- 
cific volumes  of  vapor  and  liquid  ;  then  the  change  of  volume 
in  evaporation  is 

;/  =  s  —  cr, 

and  the  external  and  internal  work  are,  respectively, 


when  r  is  the  total  heat,  in  thermal  measure. 

The  heat  which  has  been  absorbed  by  one  pound  of  water 
to  convert  it  into  a  pound  of  steam  at  atmospheric  pressure 
is  sufficient  to  have  melted  three  pounds  of  steel  or  thirteen 
pounds  of  gold.  This  has  been  transformed  into  something 
besides  heat  ;  stored  up  to  reappear  as  heat  when  the  process  is 
reversed.  That  condition  is  what  we  are  pleased  to  call  latent 
heat,  and  in  it  resides  mainly  the  ability  of  the  steam  to  do 
work. 

The  diagram,  Fig.  131,  for  which  we  are  indebted  to  Mr. 
Babcock,  shows  graphically  the  relation  of  heat  to  temperature. 
the  horizontal  scale  being  quantity  of  heat  in  British  thermal 
units,  and  the  vertical  temperature  in  Fahrenheit  degrees,  both 
reckoned  from  absolute  zero  and  by  the  usual  scale.  The  dotted 
lines  for  ice  and  water  show  the  temperature  which  would 


382 


A  MANUAL    OF    THE    STEAM-ENGINE. 


have  been  obtained  if  the  conditions  had  not  changed.  The 
processes  represented  by  our  equations  are  here  exhibited  very 
clearly. 

The  ordinates  of  the  diagram  represent  the  temperatures 
of  the  substance  as  heat  is  applied,  measured  from  absolute 
zero ;  and  the  abscissas  measured  heat  supplied,  in  thermal 
units  per  pound  of  fluid,  to  effect  the  alteration  of  temperature 
and  change  of  physical  state.  Every  step  in  the  process  is 
readily  traced  and  is  clearly  seen. 


FIG.  131.— THERMODYNAMICS  OF  STEAM. 

Factors  of  Evaporation  measure  the  relative  amount  of  heat 
demanded  to  effect  the  heating  of  water  from  a  given  tempera- 
ture, /t ,  and  its  vaporization  at  a  higher  temperature,  t2 ,  and  to 
simply  produce  vaporization  at  the  boiling-point  under  atmos- 
pheric pressure,  which  latter  is  now  usually  taken  as  a  stand- 
ard. The  value  of  this  factor  of  evaporation  is  evidently 


/=!+- 


-212°)  +  (212°  - 

"966.1 


2 

nearly. 


(i) 


THERMODYNAMICS  OF   THE  IDEAL  ENGINE. 


383 


The    following   are  values  of  such   factors,  calculated    as 
above : 

TABLE  OF  FACTORS  OF  EVAPORATION. 


Boiling-point,  7"lt 
Fahr. 

Initial  Temperature  of  Feed-water,  7",. 

32° 

5°° 

:;87 

— 
11 

86" 

1.13 
1.14 

:- 

I.I 
I.I 

•  : 

122° 

140° 
1.  08 

158° 
1.06 

176" 

194° 

212* 

1.  00 
1.  01 

212° 

2S 

266 

284 
303 
320 
338 
356 

374 
392 

410 
428 

.19 

.20 

3 

I.  10 

1.04 

.21 

.22 
-23 

.20 

.21 
.21 

- 

- 
- 

I. 

:• 

- 

: 

I. 
I. 

: 
5 

3 

4 

a 

1 

••- 

-°7 

.07 
.08 

.05 

% 

.06 

1.03 
i  03 
1.04 
1.04 

-- 

•24 
•25 
-25 

•23 
•23 
•24 

I. 

) 

K 

I. 

- 

: 
: 

5 

:- 
' 

3 

4 
4 

i 

.09 
.11 

-°7 
.08 
.09 

1.0* 
i.o6 
1.07 

A  vastly  more  convenient  form  of  table  is  that  in  which  the 
pressures  at  which  evaporation  takes  place  are  given ;  such  as 
may  be  found  in  the  Appendix,  Table  XIII. 

It  is  seen  that  the  relative  cost  of  using  feed-water  at  any 
one  temperature  as  compared  with  the  use  of  water  at  any 
other  temperature  is  as  the  reciprocal  of  their  factors  of  vapo- 
rization. Thus  if  feed-water  can  be  supplied,  by  means  of  a 
heater,  at  210°  F.,  where  previously  drawn  from  the  mains  at 
50°,  the  relative  cost  of  making  steam  will  be,  at  100  pounds 
pressure,  by  gauge,  -}f£f  =  0.86,  and  a  gain  of  fourteen  per 
cent  will  be  effected.  These  tables  are  very  useful  in  reducing 
the  data  obtained  in  trials  of  steam-boilers  to  standard  condi- 
tions. 

100.  Regnault's  Researches  and  Methods  have  furnished 
all  the  essential  data  relating  to  the  production  of  steam  in  the 
boiler  and  the  supply  of  stored  heat-energy  to  the  engine. 

The  memoir  of  M.  Henri  Victor  Regnault  on  "The  Elastic 
Forces  of  Aqueous  Vapors,"*  in  which  he  described  his  re- 
searches, is  a  most  magnificent  exposition  of  a  still  more  re- 
markable series  of  investigations.  He  repeated  the  methods 


*  Ann.  de  Chimie  et  de  Physique,  July  1844  ;  Mem.  de  Tlnsfitut,  tome  x». 
p.  465  (1847)  ;  M6m.  de  I'Aeademi'e  dcs  Sciences,  xxi,  xxvi. 


384  A   MANUAL   OF    THE   STEAM-ENGINE. 

and  experiments  of  earlier  physicists,  invented  new  ways,  and 
finally  obtained  a  set  of  data  of  unexampled  extent  and  accu- 
racy.* Regnault  found  that  the  density  of  aqueous  vapor  in 
vacua  and  under  feeble  pressure  may  be  calculated  according  to 
the  law  of  Boyle  and  Mariotte  when  the  fraction  of  saturation 
is  less  than  0.8,  while  the  density  becomes  sensibly  greater 
when  approaching  saturation.  He  further  found  that  the  den- 
sity of  vapor  in  air,  in  a  state  of  saturation,  may  be  similarly 
calculated,  and  the  ratio  of  weight  of  equal  volumes  of  vapor 
and  air  is  a  trifle  less  than  that  obtained  theoretically. 

The  data  obtained  by  Regnault  were  carefully  tabulated, 
and  curves  were  constructed  exhibiting  the  variation  of  pres- 
sure with  temperature  for  saturated  steam  for  the  whole  range 
covered  by  his  experiments.  Three  formulas  of  interpolation 
were  used  for  three  different  parts  of  the  scale  of  temperatures ; 
for  that  part  below  the  freezing-point  he  adopted  the  formula 

F=a  +  bor, (i) 

in  which  Fis  the  pressure,  a  and  b  constants,  and  aT  a  function 
of  r  =  t  -\-  32°,  t  being  the  temperature  corresponding  to  F. 

Between  the  freezing  and  boiling  points  Regnault  used 
Biot's  formula, 

\ogF=a  +  bot  —  cp\ (2) 

and  above  the  boiling-point, 

log  F  =  a  —  bo*  —  c/3T  ; (3) 

in  which  r  =  t  -j-  20.  This  last  answers  well,  also,  for  the 
whole  range.  In  it  a  =  6.2640348  ;  log  b  =  0.1397743  ;  log  c 
=  0.6924351 ;  log  or  =  1.994049292  ;  log  /3  =  1.998343862,  as 
given  by  Regnault ;  or,  according  to  Dixon, 

a  =  6.263  5°9  686  5 
log  a  =  1.998  343  377  8 
log/?  =  1.994  048  173  7 
log  b  =  0.692  450  419  2 
log  c  =  0.139  553  958  4 


*  Vide  Dixon  on  Heat;  vol.  i.  §  724. 


THERMODYNAMICS  OF   THE  IDEAL  ENGINE.          385 

For  British  measures, 

a  =  4.859  984  524  7 
log  a  =1.999  079  751  3 
log  ft  =  1.996  693  778  3 
log  b  =  0.659  317  975  2 
log  f  =  0.020  517  432  4 

A  break  was  observed  by  Regnault,  and  is  exhibited  by  the 
curves  and  the  formulas,  at  the  freezing-point,  which  had  been 
attributed  to  error,  the  two  curves  cutting  each  other  at  a  very 
small  but  appreciable  angle;  but  Professor  James  Thomson 
has  supposed  such  a  break  to  have  a  real  existence,  and  to  be 
produced  by  the  physical  change  marking  the  freezing-point. 

141.  Regnault's  Tables  have  been  reproduced  in  many 
forms,  usually  with  additions.  The  Appendix,  among  other 
tables,  contains  the  data  obtained  by  Regnault,  and  these 
values  are  accepted  as  standard  universally.  The  table  here 
given  exhibits  the  temperatures  and  corresponding  pressures 
of  saturated  steam  throughout  the  full  range  now  used  in 
steam-boilers  and  far  beyond ;  the  quantity  of  heat,  sensible 
and  latent,  in  unity  of  weight :  the  total  heat  of  evaporation, 
and  the  density  of  the  steam.  Reference  to  these  tables  is 
vastly  more  convenient  than  calculation.  Should  it  be  neces- 
sary, or  desirable,  however,  to  make  such  calculations,  the  for- 
mulas already  given  will  furnish  the  means.  They  also  permit 
the  calculation  of  data  beyond  the  limits  of  Regnault's  experi 
ment,  and  are  probably  practically  correct  far  beyond  any  pres- 
sure likely  to  become  familiar  in  the  operation  of  steam-boilers. 
Regnault's  limit  was  at  230°  C.  (446°  F.).  Rankine's  formula 
has  been  used  beyond  it.* 

The  formulas  used  in  these  calculations  are  also  given. 
Table  XXII,  for  convenience  of  reference.  British  measures 
are  used  throughout. 

*  The  tables  of  Professor  Peabody.  which  are  more  recent,  may  be  obtained 
separately  published.  These  tables,  and  those  here  given  by  the  Author,  and 
those  reduced  by  Xystrom,  win  be  found  in  close  accordance. 


386  A    MANUAL   OF   THE   STEAM-ENGINE. 

The  stored  energy  in  steam  at  any  pressure  and  temperature 
is  now  easily  ascertained  by  calculation,  in  accordance  with  the 
first  law  of  thermodynamics. 

The  first  attempt  to  calculate  the  amount  of  energy  latent 
in  the  water  contained  in  steam-boilers,  and  capable  of  greater 
or  less  utilization  in  expansion  by  explosion,  was  made  by  Mr. 
George  Biddle  Airy,*  the  Astronomer  Royal  of  Great  Britain, 
in  the  year  1863,  and  by  the  late  Professor  Rankinef  at  about 
the  same  time. 

Approximate  empirical  expressions  are  given  by  the  latter 
for  the  calculation  of  the  energy  and  of  the  ultimate  volumes 
assumed  by  unit  weight  of  water  during  expansion,  as  follows, 
in  British  and  in  metric  measures  : 

772(7*-  2  12)*  _423.55(:T-  IPO)- 

' 


=  2.29(7-  IPO) 


+  1134.4 

These  formulas  give  the  energy  in  foot  pounds  and  kilo- 
grammetres,  and  the  volumes  in  cubic  feet  and  cubic  metres. 
They  may  be  used  for  temperatures  not  found  in  the  tables  to 
be  given,  but,  in  view  of  the  completeness  of  the  latter,  it  will 
probably  be  seldom  necessary  for  the  engineer  to  resort  to 
them. 

The  quantity  of  work  and  of  energy  which  may  be  liberated 
by  the  explosion,  or  utilized  by  the  expansion,  of  a  mass  of 
mingled  steam  and  water  has  been  shown  by  Rankine  and  by 
Clausius,  who  determined  this  quantity  almost  simultaneously, 
to  be  easily  expressed  in  terms  of  the  two  temperatures  be- 
tween which  the  expansion  takes  place. 

When  a  mass  of  steam,  originally  dry,  but  saturated,  so 
expands  from  an  initial  absolute  temperature,  7*,,  to  a  final 
absolute  temperature,  T2,  if  /  is  the  mechanical  equivalent  of 


*  "  Numerical  Expression  of  the  Destructive  Energy  in  the  Explosions  of 
Steam-boilers." 

f  "  On  the  Expansive  Energy  of  Heated  Water." 


THERMODYNAMICS  OF   THE  IDEAL   ENGINE.  387 

the  unit  of  heat,  and  H  is  the  measure,  in  the  same  units,  of 
the  latent  heat  per  unit  of  weight  of  steam,  the  total  quantity 
of  energy  exerted  against  the  piston  of  a  non-condensing  en- 
gine, by  unity  of  weight  of  the  expanding  mass,  is,  as  a  maxi- 
mum, §  101, 


U  =  JT        -  i  -  hyp  log        +     ~H. 

This  equation  was  published  by  Rankine  a  generation  ago.* 

When  a  mingled  mass  of  steam  and  water  similarly  ex- 

pands, if  M  represents  the  weight  of  the  total  mass  and  in  is 

the  weight  of  steam  alone,  the  work  done  by  such  expansion 

will  be  measured  by  the  expression 


U=  MJT        -  i  -  hyp  log         +  m     -=       H. 

This  equation  was  published  by  Clausius  in  substantially 
this  form,  f 

It  is  evident  that  the  latent  heat  of  the  quantity  m,  which 
is  represented  by  mfft  becomes  zero  when  the  mass  consists 
solely  of  water,  and  that  the  first  term  of  the  second  member  of 
the  equation  measures  the  amount  of  energy  of  heated  water 
which  may  be  set  free,  or  converted  into  mechanical  energy 
by  explosion.  The  available  energy  of  heated  water,  when 
explosion  occurs,  is  thus  easily  measurable. 

The  computers  of  the  tables  given  in  the  Appendix  were 
Messrs.  Ernest  H.  Foster  and  Kenneth  Torrance.  The  tables 
range  from  20  pounds  per  square  inch  (1.4  kgs.  per  sq.  cm.)  up 
to  100,000  pounds  per  square  inch  (7030.83  kgs.  per  sq.  cm.),  a 
maximum  probably  falling  far  beyond  the  range  of  possible 
application,  its  temperature  exceeding  that  at  which  the  metals 
retain  their  tenacity,  and  in  some  cases  exceeding  their  melting- 
points.  These  high  figures  are  not  to  be  taken  as  exact. 
The  relation  of  temperature  to  pressure  is  obtained  by  the 
use  of  Rankine's  equation,  of  which  it  can  only  be  said  that  it 

*  Steam-engine  and  Prime  Mover*;  p.  387. 

t  Mechanical  Theory  of  Heat;  Browne's  translation,  p.  283. 


388  A    MANUAL    OF   THE   STEAM-ENGINE. 

is  wonderfully  exact  throughout  the  range  of  pressures  within 
which  experiment  has  extended,  and  within  which  it  can  be 
verified.  The  values  estimated  and  tabulated  are  probably 
quite  exact  enough  for  the  present  purposes  of  even  the  mili- 
tary engineer  and  ordnance  officer. 

The  table  presents  the  values  of  the  pressures  in  pounds 
per  square  inch  above  a  vacuum,  the  corresponding  reading  of 
the  steam-gauge  (allowing  a  barometric  pressure  of  14.7  pounds 
per  square  inch),  the  same  pressures  reckoned  in  atmospheres, 
the  corresponding  temperatures  as  given  by  the  Centigrade 
and  the  Fahrenheit  thermometers,  and  as  reckoned  both  from 
the  usual  and  the  absolute  zeros.  The  amount  of  the  available 
stored  energy  of  a  unit  weight  of  water,  of  the  latent  heat  in  a 
unit  weight  of  steam,  and  the  total  available  heat-energy  of 
the  steam,  are  given  for  each  of  the  stated  temperatures  and 
pressures  throughout  the  whole  range  in  British  measures, 
atmospheric  pressures  being  assumed  to  limit  expansion.  The 
values  of  the  latent  heats  are  taken  from  Regnault,  for  mod- 
erate pressures,  and  are  calculated  for  the  higher  pressures,  be- 
yond the  range  of  experiment,  by  the  use  of  Rankine's  modifi- 
cation of  Regnault's  formula.* 

The  energy  of  gunpowder  is  somewhat  variable  with  com- 
position and  perfection  of  manufacture,  and  is  very  variable  in 
actual  use,  in  consequence  of  the  losses  in  ordnance  due  to 
leakage,  failure  of  combustion,  or  retarded  combustion  in  the 
gun.  Taking  its  value  at  what  the  Author  would  consider  a 
fair  figure,  250,000  foot-pounds  per  pound,  it  is  seen  that,  as 
found  by  Airy,  a  cubic  foot  of  heated  water,  under  a  pressure 
of  60  or  70  pounds  per  square  inch,  has  about  the  same  energy 
as  one  pound  of  gunpowder.  The  gunpowder  exploded  has 
energy  sufficient  to  raise  its  own  weight  to  a  height  of  nearly 
50  miles,  while  the  water  has  enough  to  raise  its  weight  about 
one  sixtieth  that  height.  At  a  low  red  heat  water  has  about 
40  times  this  latter  amount  of  energy  in  a  form  to  be  so  ex- 

*  It  is  seen  that,  could  we  reduce  steam,  at  atmospheric  pressure,  to  water, 
without  loss  of  heat,  the  energy  thus  stored  would  raise  the  water  to  the  red 
heat;  and  if  to  a  solid,  would  become  hotter  than  molten  steel. 


THERMODYNAMICS  OF   THE  IDEAL  EXGIXE.          389 

pended.     One  pound  of  steam,  at  60  pounds   pressure,  has 
about  one  third  the  energy  of  a  pound  of  gunpowder.* 

101.  The  General  Thermodynamic  Equation  for  Vapors 
must  thus  evidently  have  the  same  general  form  as  that  appli- 
cable to  gases.  The  heat-energy,  dH,  demanded  for  any  ele- 
mentary change  is,  as  in  all  other  cases,  composed  of  two 
portions  : 

(1)  That,  KdTy  required  to  effect  change  of  temperature 
and  of  sensible  heat,  simply  ; 

(2)  That   transformed    in    the   performance  of   equivalent 

dp 
work,  T-j~  du  ;  the  volume  //  being  that  measuring  the  expan- 

sion of  the  fluid  ;  which  is  not,  in  this  case,  equal  to  v  ,  the 
volume  of  unity  of  weight  in  the  gaseous  state. 

When  this  equation  is  applied  to  the  change  by  which 
water  is  converted  into  steam,  it  is  observed  that  the  tempera- 
ture remains  constant,  during  vaporization  at  constant  pressure, 
and  the  heat  expended  is  simply 


when  vt,  i\,  and  u  are,  respectively,  the  volume  of  the  liquid, 
that  of  its  vapor,  and  the  total  change  of  volume,  under  the 

pressure/,,  and  at  the  temperature  7*,.     The  value  of  -~  may 

be  obtained  either  by  reference  to  experimental  data  or  by  dif- 
ferentiating the  algebraic  expression  already  given  (§  99)  for 
the  relation  of/  to  T. 

The  transformed  equation 


dT 


*  See  Manual  of  Steam-boilers,  §  143,  p.  289,  for  a  more  complete  discussion 
of  this  interesting  subject. 


39°  A    MANUAL   OF   THE   STEAM-ENGINE. 

has  been   used  to  determine,   from   experimentally  obtained 

values  of  H  and  of  \^ff\  >  the  density  of  steam  ;  the  results 

according  very  perfectly  with  those  obtained  in  the  researches 
of  Messrs.  Fairbairn  and  Tate.* 

The  general  equation  for  steam  and  vapors  thus  becomes, 
since  Kv  =  /,  as  before, 


}- (3) 

.  dp 

dT 
The  thermodynamic  function  for  vapor  is,  as  before,  in  form, 


...     (4) 


and  is  similar  in  form  to  that  obtained  for  gases.  For  steam, 
the  value  of  Kv  is  the  dynamically  expressed  measure  of  the 
specific  heat  of  water,  or  "  Joule's  equivalent."  Thus,  the  ex- 
pression for  this  function  becomes,  for  any  other  fluid  than 
steam,  of  which  the  specific  heat  in  the  liquid  state  is  C, 


(5) 


Professor  Unwin  adopts  an  empirical  expression  for  the 
relations  of  external  pressure  and  the  temperature  of  saturated 
vapors,  having  the  form,f 

log/  =  a  —  bT~n-, 

and 

(6) 

y-1 


Rankine;  Miscellaneous  Papers,  p.  423. 
London  Engineer;  April  g,  1886;  p.  277. 


THERMODYNAMICS  OF   THE  IDEAL  ENGINE. 


391 


in  which,  when/  is  the  pressure  in  pounds  on  the  square  inch, 
T'the  absolute  temperature  reckoned  from  —  461°  F.,  and,  for 
steam,  a  =  5.8031 ;  b  =  15,900;  n  =  1.25,  common  logarithms 
being  used. 

This  expression  gives  values  agreeing  with  those  obtained 
by  Regnault,  to  within  0.007,  throughout  a  range  extending  up 
to  about  25  atmospheres. 

From  the  above  equation  we  obtain 


I     dp  nb 

-.  —  =  2.3026^- 

45765. 

/«5     ' 

t     dp  ,nb 

--        =  2.3026     .; 


_  457^5. 

=  2.8783(5-8031- log/);  J 


(7) 


(8) 


which  gives  the  numerical  values  which  follow. 

The  ratio  of  total  pressure,  internal  and  external,  7*-j~,  to 

external  pressure,  /,  and  of  latent  heat  of  vaporization  to  heat 
transformed  into  external  work,  is  as  below : 


/      dp 

p'dT 

p 

Eq.  8 

Rankine 

Diff. 

5 

14.69 

14.79 

—  .10 

10 

13.83 

13.88 

-  .05 

20 

12.96 

12.98 

—  .02 

40 

12.09 

12.08 

+  .01 

70 

n-39 

11.36 

+  .03 

140 

10.53 

10.49 

+  -04 

200 

10.08 

10.03 

+  .05 

250 

9.80 

9-75 

+  .05 

392  A  MANUAL   OF   THE   STEAM-ENGINE. 

The  ratio  of  internal  pressure,  T  '-r—r  —  p,  or  of  the  pressure 
due  internal  work,  to  the  external  and  observed  pressure,  p,  is 


(9) 


45765 


=  2.8783(5.8031  -log/)-  i  J 


The  specific  volume  of  steam,  v  —  s,  the  difference  in  vol- 
ume of  a  pound  of  steam  and  of  the  .water  from  which  it  is 
made,  at  any  given  pressure,  /,  is,  as  has  been  seen,  a  factor 

by   which   the   total   pressure,    T -j~ ,   being   multiplied,    the 

product  measures  the  work  expended  in  its  evaporation,  or  its 
equivalent,  the  latent  heat,  H,  of  vaporization  at  that  pressure. 
Thus 

/  j*  \ 

'  =  //;     ....    (10) 

Jt  •      (M) 


and  p  being  expressed  in  pounds  on  the  square  foot,  and  s  taken 
as  0.016, 

1.8626? 


An  approximate  expression  for  /  is,  for  British  units, 

/=  1443  —  ojiT 

1632 


03) 


The  following  are  a  few  calculated  values  of  latent  heats 
and  of  specific  volume  : 


THERMODYNAMICS  OF  THE  IDEAL  ENGINE.          393 


p 

/ 

r  —  j 

D-- 

5 

1000.8 

73-03 

0.0137 

10 

978.8 

37-96 

0.0263 

20 

954-0 

1973 

O.O5O6 

40 

926.2 

IO.27 

0.0972 

70 

900.9 

6.056 

0-1647 

140 

865.4 

3-149 

0.3160 

200 

845.0 

2^48 

0.4417 

250 

831-4 

1.820 

0-5447 

The  external  work  of  evaporation  \sf(v  —  s\  or 

268.2/ 


59.28 
The  internal  work  is 


_log/> 

(14) 


The  following  table  gives  the  value  of  T  and  of  /,  actual 
and  as  computed  by  the  approximate  equation.  /  is  here 
given  in  pounds  on  the  square  inch. 


/^Fahr. 

T 

A::-i. 

Computed 

100 

56l 

0.942 

0-953 

150 

611 

3-707 

3.706 

212 

673 

14-70 

14.62 

250 

711 

29-88 

29.67 

300 

761 

67.22 

66.82 

350 

811 

I35-U 

134-62 

400 

861 

247-75 

247.70 

432 

893 

350-73 

351-50 

394  A    MANUAL    OF   THE   STEAM-ENGINE. 

102.  The  Thermal  Lines,  for  Vapors,  differ  somewhat  in 
form  from  those  found  for  gases.  The  exact  equations  of  the 
expansion  lines  become,  however,  so  difficult  of  application, 
in  the  theory  of  the  heat-engines,  that  it  has  been  found 
advisable  to  substitute  for  them  approximate  expressions  of 
simple  form,  which  may  be  more  conveniently  applied. 

These  approximate  formulas  are  usually  equations  of 
hyperbolas,  of  the  form 

pif1  =  constant (i) 

The  value  of  the  index  n  varies  from  o  for  isothermal  and 
isopiestic  expansion  of  moist  saturated  vapors,  to  unity,  as 
in  the  isothermal  expansion  of  gases,  and  to  1.333  f°r  tne 
adiabatic  expansion  of  steam-gas. 

"  The  Curve  of  Saturation  "  and  constant  weight  is  that 
thermal  line,  on  a  diagram  of  energy,  which  exhibits  the  rela- 
tions of  pressure  and  volume  (usually  of  unity  of  weight)  of 
the  fluid  when  expanding,  and  kept  constantly  in  the  saturated 
state.  In  the  case  of  initially  dry,  saturated,  steam,  at  all 
ordinary  pressures  and  temperatures,  it  would  be  necessary  to 
supply  heat  during  expansion,  and  to  abstract  it  during  com- 
pression, in  order  that  the  vapor  should  be  kept  "  dry  and 
saturated  ;"  i.e.,  on  the  point  of  condensation.  The  relations 
of  simultaneous  pressures,  temperatures,  and  volumes  of  steam 
are  given  elsewhere.  It  will  be  seen  that  they  are  so  com- 
plicated that  the  true  equation  of  this  curve  becomes  too  cum- 
bersome for  convenient  use.  Comparison  of  numerical  results 
has  shown,  however,  that  the  curve  may  be  very  closely  repre- 
sented by  equation  (i),  making  n  =  -fj,  according  to  Rankine, 
or,  a  little  more  nearly,  by  1.0646,  as  given  by  Zeuner,  i.e., 

pv&  =  const. ;     or,    /z/1-0646  =  const. ;       .     .     (2) 

p  and  v  being  the  pressure  and  specific  volume  of  the  vapor. 
The  value  of  this  constant,  in  British  measures,  is  475,  nearly; 
in  metric  measures,  1.7.  An  equivalent  expression  to  the 
above  is  p° m  v  =  const. 


THERMODYNAMICS  OF   THE  IDEAL  ENGINE.  395 

The  Specific  Heat  of  Saturated  Steam  is  that  quantity 
demanded,  during  rise  of  temperature,  to  keep  unity  of  weight 
in  the  saturated  condition,  and  is  measured  by 

dQ       dh        I  I 


in  which  the  coefficient  0.305,  representing  the  increment  of 
total  heat  per  unit  rise  of  temperature,  is  obtained  from  data 
given  by  Regnault's  experiments.  Applying  the  formula  to 
any  familiar  pressure  and  temperature  of  saturated  steam,  it  is 

dQ 
found  that   -^=,  is   negative   in   all  ordinary  cases,  and  that, 

consequently,  it  is  necessary  to  add  heat  to  a  mass  of  expand- 
ing steam  to  keep  it  dry  and  saturated,  notwithstanding  the 
fact  that  it  continuously  falls  in  temperature  as  well  as  in 
pressure.  Should  not  heat  be  so  supplied,  the  steam  would 
become  a  mixture  of  steam  and  water,  the  proportion  of  steam 
decreasing  with  progressing  expansion.  The  negative  value 
of  the  specific  heat  of  saturated  steam  and  its  consequence, 
partial  condensation,  were  discovered  in  1850,  independently, 
by  Rankine  and  Clausius.  It  has  some  importance  in  the 
theory  of  the  steam-engine. 

The  Isothermal  Line  for  Saturated  Steam,  or  any  other 
vapor,  expanding  in  presence  of  the  liquid  from  which  it  is 
formed,  or  containing,  as  is  usually  the  case,  in  practice,  more 
or  less  mist,  is  an  isopiestic  line,  a  line  of  constant  pressure. 

The  pressure  of  saturated  steam  is  a  function  of  tempera- 
ture, only,  and  remains  constant  and  invariable  so  long  as  the 
temperature  of  the  liquid  and  its  vapor  remains  unchanged. 
The  equations  for  isothermal  expansion  of  steam,  or  other 
vapor,  are  therefore 

n  =  o  ;        p  —  const.  =/(/);     .     .     .     .     (4) 
»  =  *;/*•  =  $  .........    (5) 

The  line  is  rectilinear,  parallel  to  the  axis  measuring  vol- 
umes, and  at  a  greater  or  less  height  accordingly  as  the  tem- 
perature is  higher  or  lower. 


39^  A   MANUAL   OF    THE   STEAM-ENGINE. 

The  Hyperbolic  Expansion  of  Steam,  or  other  vapor,  is  not 
isothermal.  The  tendency  of  such  expansion,  when  produced, 
as  it  possibly  may  be,  at  times,  is  to  dry  moist  vapor,  and  to 
superheat  that  already  dry;  the  temperature  falling  at  a  lower 
rate  than  in  expansion  either  adiabatically  or  as  saturated 
vapor.  This  case  thus  differs  greatly  from  that  of  the  hyper- 
bolic expansion  of  the  perfect  gas  ;  which  has  been  seen  to  be 
perfectly  isothermal.  In  the  latter  case,  the  supply  of  heat 
must  be  precisely  equivalent  to  the  work  done  ;  in  the  former, 
heat  must  be  supplied  considerably  in  excess  of  the  equivalent 
of  the  external  work  performed. 

Hyperbolic  expansion  of  steam,  or  other  vapor,  is  never 
met  with  in  practice,  except  by  probably  the  rarest  accident. 
The  assumption  made,  usually,  however,  in  computing  the 
power  of  the  steam-engine,  that  the  steam  expands  in  this 
manner,  is  often  sufficiently  correct  for  ordinary  work,  in  prac- 
tice. The  differences  between  the  several  curves,  as  shown 
by  the  steam-engine  indicator,  are,  in  good  practice,  seldom 
important  or  noticeable. 

The  Adiabatic  Line  of  expanding  steam  may  be  obtained 
by  making  the  thermodynamic  function  constant,  thus  : 


0  =/  log,  T+u  j   =  const.,     ...     (6) 

and 

^0  =  o  ..............     (7) 

When,  in  such  case,  steam,  initially  dry  but  saturated,  ex- 
pands from  the  temperature,  pressure,  and  volume  7^  ,  /,  ,  z>,  , 
to  any  other  state,  T,  p,  v,  the  value  of  <p  remains  unchanged, 
and 


Siog.T+u(-jfr)  =  7  log.  7;  +  *,  ^).   .   (8) 

Then 


dT. 


THERMODYNAMICS  OF    THE  IDEAL  ENGINE.  397 

which  represents  the  volume  of  unity  of  weight  of  wet 
steam,  expanding  from  the  dry  and  saturated  state  in  which 
its  condition  is/,,  •vl ,  7*,,  to  the  state/,  v,  T;  the  proportion 
of  water  present,  and  due  to  expansion,  as  will  be  presently 
seen,  increasing  as  expansion  progresses.  The  value  of 


be  obtained  by  differentiating  the  expressions  in 
which  /  is  given  as  a  function  of   T,  or  by  taking  it  from  the 

(dp  \ 
"  steam-tables,"  \~^p)  being  the  change  of  pressure  due  to  a 

change,  unity,  of  temperature,  and  -7-  being  the  change  of  tem- 

df 

perature  for  a  variation,  unity,  of  pressure.* 

The  ratio  of  expansion  is  evidently  r  =  — ,  and,  since  the 


latent  heat  is  H=  T\-^s 


uf~  T' 

in  which  L  is  the  latent  heat  when  u  becomes  unity,  or  the 
latent  heat  per  cubic  foot,  or  per  cubic  metre, 


.,'•••    (IO) 

when  D  =  -,  the  density  of  the  fluid. 
v 

Comparing  the  values  of  u  as  expansion  progresses,  with 
those  of  v  for  saturated  steam  of  the  same  temperature,  Ran- 

*  Care  must  be  taken,  obviously,  to  use  correct  units;  e.g.,  in  British  measures 
pounds  on  the  square  foot,  in  metric  measures  kilogrammes  on  the  square 
metre,  as  commonly  adopted  in  engineering,  the  units  of  volume  being,  respec- 
tively, cubic  feet  and  cubic  metres,  and  of  weight,  the  pound  and  the  kilogramme. 


398  A    MANUAL    OF   THE    STEAM-ENGINE. 

kine  found  that  the  former  quantity  is  the  greater  in  all  familiar 
cases;  and  it  thus  follows,  as  he  first  showed,*  that  the  fluid 
must  partially  condense  when  expanding  adiabatically.  The 
higher  the  pressure,  /, ,  and  temperature,  Tl  ,  of  the  initially 
saturated  steam,  the  less  this  condensation  ;  until  a  point  is 
reached — probably  at  about  the  bright  red  heat  of  solids  f — at 
which  condensation  ceases  to  be  a  consequence  of  adiabatic 
expansion  of  saturated  steam,  and  beyond  which  adiabatic  ex- 
pansion may  produce  superheating. 

The  value  of  H  for  steam  may  be  obtained  from  the  em- 
pirical formula 

H=a-bT-t (11) 

in  which,  in  British  measures,  and  for  steam, 
a  =1,109,550;     £=540.4. 

For  Mixtures  of  Steam  and  Water,  in  the  approximate  ex- 
pression for  the  adiabatic  curve,  in  which,  for  steam  initially 
dry  and  saturated,  or  on  the  point  of  condensation,  n  =  1.135, 
the  equation  being 

Pv^  =  475,  nearly,      |  , 

fmVn™  =  1.704,  nearly,  ( 

for  British  and  metric  measures,  respectively.  The  value  of  the 
exponent,  n,  depends  upon  the  initial  condition  of  the  steam, 
and  Zeuner  proposes  the  expression  $ 

«=  1.035  +  0.1*; (13) 

in  which  x  is  the  proportion  of  vapor  initially  existing  in  the 
mixture.  When  x  <  0.7  the  expression  becomes  less  exact. 
Rankine  takes  n  —  ^°-  =  i.m,  in  his  treatment  of  the  steam- 
engine,  which  corresponds  to  x  =  0.8,  nearly,  the  mixture  con- 
taining 20  per  cent  water.  The  value  of  n  is  also  affected 

*  Steam-engine;  p.  384. 

f  Rankine  ;  Miscellaneous  Papers  ;   p.  398. 

+  Warmetheorie. 


THERMODYNAMICS  OF   THE  IDEAL   ENGINE.          399 

by  variations  of  pressure,  slightly  increasing  as  pressures  rise, 
the  mean  value  being  similarly  affected,  also,  by  decreasing  the 
value  of  r. 

When  the  value  of  x  is  less  than  about  one  half,  evaporation, 
instead  of  condensation,  goes  on  in  the  mixture. 

Comparing  the  curve  of  saturation  with  the  adiabatic  curve, 
as  represented  by  their  equations,  it  is  seen  that  the  former 
has  the  lower  value  of  it,  and  hence  that  the  curve  falls  less 
rapidly  than  the  adiabatic.  But  it  has  been  seen  that,  in  the 
case  of  the  saturation  curve,  heat  must  be  added  to  preserve 
the  steam  in  the  saturated  state :  it  thus  again  follows  that,  in 
the  case  of  adiabatic  expansion,  in  which  no  heat  can  be  thus 
supplied,  a  part  of  the  steam  must  condense ;  the  volume  of 
unity  of  weight  being  less  than  when  dry  and  saturated. 

The  adiabatic,  the  hyperbolic,  and  the  saturation  curves  of 
steam  have,  respectively,  for  the  approximate  values  of  », 
K  =  1.135,  «=!,»=  1.0646;  the  first  is  therefore  a  curve  of 
more  rapid  fall  in  pressure,  with  any  given  rate  of  expansion, 
than  either  of  the  others :  while  the  saturation  curve  lies  be- 
tween the  other  two. 

The  fact  independently  discovered  by  Rankine  and  Clausius, 
in  1850,  and  exhibited  above,  that,  when  steam  expands  adia- 
batically,  a  portion  must  be  liquefied,  yielding  its  latent  heat  to 
assist  in  producing  the  expansion  of  the  remainder,  is  impor- 
tant in  its  relation  to  the  thermodynamics  of  vapors,  and  was  at 
first  supposed  to  have  great  importance  in  the  operation  of  the 
steam-engine.  This  is  not  usually  the  case,  however.  The 
condensation  observed  in  steam-engine  cylinders  is  mainly  due 
to  the  conductivity  and  storing  capacity  of  the  material  of 
which  they  are  composed,  and  in  but  a  comparativel}*  slight 
degree  to  this  cause. 

Hirn,  in  1853,  confirmed  by  experiment  this  discover}'.  It 
is  found,  by  experimental  investigation,  that  vapors  differ  in 
this  respect,  and  that  while  many,  like  steam,  partially  condense 
\vhile  expanding  and  doing  work,  some,  as  ether,  superheat. 
In  other  words,  their  specific  heat,  under  similar  conditions,  is 
positive,  while,  in  the  case  of  steam,  it  is  negative ;  steam  requir- 


4OO  A   MANUAL   OF   THE   STEAM-ENGINE. 

ing  to  be  supplied  with  heat,  as  its  temperature  and  pressure 
fall,  if  it  is  to  retain  the  dry  and  saturated  condition. 

103.  The  Construction  of  Thermal  Lines  and  of  Dia- 
grams of  Energy  illustrating  the  behavior  of  vapors  acting  as 
working  substances  in  the  transformation  of  heat  into  work  is 
a  subject  of  still  greater  importance  and  interest  than  in  the 
working  of  gases.  The  diagram  of  energy,  representing  the 
cycle  of  operations  occurring  in  the  steam-engine,  or  other 
machine  in  which  a  vapor  is  employed  as  the  working  fluid,  is 
composed  of  thermal  lines  the  character  and  dimensions  of 
which  are  determined  by  the  construction  and  method  of 
operation  of  the  engine.  Such  lines  may  usually  be  referred 
to  one  or  another  of  the  classes  already  described,  and  the  con- 
struction of  the  diagram,  once  its  general  form  is  so  deter- 
mined, becomes  easy  when  the  methods  of  laying  down  the 
principal  thermal  lines  are  understood. 

In  all  cases  these  lines  may  be  represented  by  algebraic 
expressions  the  forms  of  which  have  been  given.  These  equa- 
tions express  the  relations  of  magnitude  of  the  simultaneous 
pressures  and  volumes  of  the  working  fluid  when  undergoing 
expansion  or  compression  under  definitely  prescribed  conditions. 
These  conditions  being  settled  by  the  method  of  operation,  in 
any  given  case,  the  corresponding  thermal  line  is  identified  for 
any  step  in  the  operation,  and  the  numerical  relations  given  by 
the  equation  of  the  line  permit  the  laying  down  of  the  ordinate 
representing  the  pressure  corresponding  to  each  successive 
magnitude  taken  for  the  volume  of  the  working  fluid,  as  the 
piston  of  the  engine  traverses  its  cylinder.  Thus,  for  the  line 
of  equal  pressure  produced  during  the  entrance  of  steam  from 
the  boiler  into  the  steam-engine,  pl  is  fixed,  and  /  =/,  through- 
out, its  whole  extent.  When  the  supply  of  steam  is  interrupted 
by  the  closing  of  the  induction-valve,  adiabatic  expansion  oc- 
curs, in  the  ideal  engine,  and 

/,«/,*  =  pvn  =  Rs , 

and  the  initial  state  being  known,  and  /,  and  z>,  thus  given, 
pvn  becomes  known  as  the  value  of  the  constant  quantity  Ri} 


THERMODYNAMICS  OF  THE  IDEAL  ENGINE.          4OI 

and  it  becomes  easy  to  calculate  the  value  of  /  corresponding 
to  any  value  of  v. 

In  illustration,  for  one  pound  of  initially  dry  steam,  ex- 
panded adiabatically, 

ppf>*>  =jrs-*x  =  475,  nearly, 

and  we  obtain  for  successive  values  of  p  =    /^5  to  the  nearest 

unit,  volumes  in  cubic  feet,  and  pressures  in  pounds  on  the 
square  foot : 

v  p  *  P  v  P 

1  475  6         61  15        22 

2  216  8         45  20        16 
4           97               10         35  25         13 

These  figures  measuring  the  co-ordinates  of  the  curve,  it 
may  be  laid  down  to  any  desired  scale.  The  existence  of 
sensible  error  in  any  figure  is  shown  by  the  point  so  erroneously 
fixed  falling  outside  the  smooth  curve  passing  through  the 
other  points.  The  graphical  construction  is  thus  a  reliable 
check  upon  the  computation. 

The  geometrical  construction  of  curves  of  the  class,  pvu 
=  const.,  is  very  easy  and  often  preferred  to  construction  by 
the  preceding  method.  When  n  =  i,  the  curve  becomes  the 
equilateral  hyperbola  and  may  be  laid  down  by  the  following 
methods : 

There  are  several  methods  of  constructing  this  curve,  of 
which  the  simplest  are,  perhaps,  the  following,  as  applied  to 
produce  the  equilateral  hyperbola,  the  curve  of  Mariotte,  to 
which  the  expansion-line,  in  the  best  classes  of  engine,  very 
closely  approximates,  and  which  is  commonly  taken  as  the 
standard. 

Let  XX,  YY  be  given  asymptotes  (i.e.,  the  clearance  and 
true  vacuum-lines  of  the  indicator-card),  and  x  any  given  point, 
and  let  xx,  xy  be  its  co-ordinates. 

Extend  YO  until  OY'  =  YO  and  draw  AP,  making  Y'P 
equal  to  xY  and  parallel  to  XX. 


402 


A    MANUAL    OF    THE   STEAM-ENGINE. 


Divide  YO  and  OY'  into  similar  divisions. 

Assume  an  ordinate  Om  of  a  point  to  be  found,  and  draw 
mx"  parallel  to  XX. 

At  Y'  erect  Y'n  =  Om,  and  draw  Pnx" ;  the  point  x"  of 
intersection  with  x"n  is  the  required  point. 


FIG.  132.— THE  HYPERBOLA. 


For  in  the  triangles  n/  P,  nmx"  we  shall  have 


nY'  :  Y'P::  mn  :  x"m  =        =  x" ; 

i.e.,       y"  \x\\y\x".     Q.  E.  D. 

When  the  expansion-line  is  true  to  the  hyperbolic  curve,  it 
becomes  possible  to  obtain  a  fairly  approximate  measure  from 
the  diagram  of  the  clearance-space  ;  or,  the  latter  being  known, 
to  determine  the  real  locus  of  the  hyperbolic  expansion-curve, 
as  follows : 

Let  S',  E,  E',  V,  S  represent  an  indicator-card  ;  let  OX  be  the 
line  of  perfect  vacuum  ;  OY  the  line  at  end  of  cylinder  plus  the 
clearance;  then  OX  and  OYwill  be  asymptotes  of  the  hyper- 
bola E,  A,  A',  E',  the  curve  of  expansion. 


THERMODYNAMICS  OF   THE  IDEAL  ENGINE. 


403 


Take  two  points  on  the  curve  A  A',  and  AK,  AC,  A'B,  and 
A'ff  will  be  their  co-ordinates. 

Draw  AAt  and  from  Ct  the  line  CB  parallel  to  A  A'  ;  the 
point  B,  where  it  intersects  A'B,  will  be  a  point  in  the  line  OY. 

Or,  draw  HK  parallel  to  A  A ',  and  AT,  the  intersection  with 
AKt  will  be  such  a  point. 


For  by  Mariotte's    law  and  from  the   properties   of  the 
hyperbola,  xy  =  m ;  x'y'  =  m ;  .-.  jry  =  J^X- 


or, 


A'D'.BD-AD'.DC. 


And,  from  similar  triangles  (by  construction), 

A'D\  BD  \\AD\  DC.    Q.  E.  D. 

Conversely,  having  given  the  clearance  and  the  scale  of  the 
indicator,  with  point  of  cut-off,  to  find  the  expansion4ine. 

In  proportion  y  — y1 '  '.  y  ::  x"  —  x  :  x,  assume  x'  and  find 
values  of  y  by  constructing  the  triangle  KPH,  similar  to  ADA '. 

Taking  the  point  of  release  as  a  point  in  the  hyperbolic 
curve,  and  laying  down  that  curve  on  the  diagram,  it  will  be 
found,  not  only  that  the  curve  and  the  expansion-line  of  the 
diagram  do  not  coincide,  but  that  the  latter  falls  above  the 


404  A    MANUAL   OF   THE    STEAM-ENGINE. 

former  throughout  its  length,  in  nearly  all  cases,  indicating, 
usually,  initial  condensation  and  later  re-evaporation,  but  some- 
times indicating  some  leakage  as  well.  If  the  weight  of  steam 
actually  drawn  from  the  boiler  be  taken  as  the  basis  of  a  dia- 
gram, using  its  volume  as  the  initial  ordinate  of  the  hyperbolic 
curve,  it  becomes  easy  to  trace  the  variations  of  the  whole 
actual  diagram  from  the  ideal  indicator-card,  as  here  shown. 

In  any  case  in  which  the  curve  represented  by  the  expan- 
sion-line is  of  the  class  of  which  the  equation  is 


the  co-ordinates  sought,  any  one  point,  /,$;,  or  pjj^  being  given, 
may  be  found,  and  any  new  point  in  the  ideal  curve  determined 
by  computation,  thus  :  From  the  above  expression, 

n  log  v  +  log/  =  n  log  vl  +  log/,  ; 

and  if/,  and  vr  are  known,  for  any  assumed  volume  v,  the  log- 
arithm of  the  corresponding  new  pressure  must  be 

log/  =  n  log  vl  -\-  log/,  —  n  log  v  ; 

which  expression  being  used  to  determine  several  points,  the 
curve  may  be  drawn  through  them. 

The  values  of  n  have  been  seen  to  be  as  follow  : 

Equilateral  hyperbola,     .     .     .     .  I 

Curve  of  steam  ;  saturation  -£-£,  or  1.0646 

Adiabatic  curve,  steam,  ....  1.035  ~(-  o.i^r 

"        gas,       ....  1.408 

Isothermal    "         "     .....  i.o 

The  variation  of  the  actual  ratios  of  expansion  from  their 
apparent  values,  in  engines  having  large  clearance-spaces,  is 
very  considerable  at  high  ratios  of  expansion  and  in  short- 
stroke  engines. 

The  close  approximation  of  the  three  principal  steam-ex- 
pansion lines  is  well  shown  by  the  accompanying  diagram,  a 


THERMODYNAMICS  OF   THE  IDEAL  EXGIKE.          405 

set  of  curves  shown  in  various  publications,  but  probably  first 
laid  down  in  this  form  by  Mr.  Porter.*  AB  exhibits  the 
initial  volume,  as  does  also  CD ;  AD  and  BC  represent  the 
initial  pressure ;  EF  is  an  ordinate,  taken  at  convenience ;  and 
the  terminal  ordinates  are  GH,  7J/,  and  LK.  OR  is  taken 
at  half-stroke ;  while  CN  is  the  axis  of  the  equilateral  hyper- 
bola, AOGt  the  upper  curve,  of  which  CB  and  CH  are 
asymptotes.  Ordinates  measure  absolute  pressures  in  pounds 


FIG.  i34--TH«  TMBI  FII     1111   mil 

per  square  inch  :  abscissas  represent  volumes  of  unity  of  weight 
(i  lb.lt  Thus  BA  is  the  volume  (4.73  cu.  ft.)  of  one  pound 
of  steam  at  a  total  pressure  of  90  pounds  per  square  inch; 
ABCD  is  the  external  work  done  in  its  production.  It  is  this 
curve  which  is  commonly  assumed  to  be  that  of  the  expansion 
of  steam. 

The  curve  AOI  is  the  curve  of  dry  and  saturated  steam, 
its  co-ordinates  representing  the  simultaneous  pressure  and 
volume  of  the  fluid  when  in  contact  with  the  mass  of  water 
from  which  it  is  produced.  The  expansion  is  less,  and  the 
rate  of  fall  of  pressure  greater,  than  if  it  were  to  follow  the  law 

*  Steam-engine  Indicator;  p.  1*3. 


406  A  MANUAL    OF   THE   STEAM-ENGINE. 

of  Mariotte.  It  is  this  curve  which  is  assumed  to  be  described 
when  steam  expands  in  well-jacketed  engines. 

The  lower  line,  AOL,  is  the  adiabatic  curve,  assumed  to 
be  obtainable  in  engines  with  non-conducting  cylinders  and 
approximately  in  "  high-speed  engines."  The  area  under  this, 
as  under  the  other  curves,  represents  the  work  done  as  the 
steam  expands,  and  exhibits  the  gain  obtainable  by  expansion, 
in  each  case.  In  all  real  engines,  however,  the  expansion-line 
falls  at  first  more  rapidly,  and  finally  more  slowly,  than  either 
of  these  curves.  As  elsewhere  seen,  this  variation  from  the 
ideal  curve  is  often  very  observable. 

Cylinder  Condensation  and  Leakage  produce  variations  in  the 
diagram,  as  obtained,  which  differently  affect  the  different 
parts  of  the  curve.  Leakage  can  usually  be  eliminated,  and 
always  should  be  before  the  engine  is  set  at  work  regu- 
larly. The  first-named  waste  is  usually  irremediable.  Its 
character,  laws  of  variation,  and  magnitude  will  be  studied  in 
detail  in  the  succeeding  chapter.  When  the  exact  measure  of 
the  quantity  of  steam  expended  is  obtained  by  a  boiler-trial,  it 
is  easy  to  trace  these  variations,  as  in  the  indicator-diagram, 
Fig.  135,  taken  from  the  engine  and  worked  up  by  the  late 
Professor  C.  A.  Smith,  in  which  illustration  the  diagram  which 
should  have  been  produced  by  the  same  steam,  had  there  been 
no  initial  condensation,  is  shown  with  the  real  diagram.* 

This  indicator-diagram  is  an  unusually  good  sample,  as  to 
form,  and  was  taken  from  the  St.  Louis  high-service  pumping- 
engine,  a  machine  of  705  I.  H.  P.,  85  inches  diameter  of  cylin- 
der and  10  feet  stroke  of  piston,  making  1 1£  revolutions  per 
minute.  Taking  measures  of  the  abscissas  of  the  two  dia- 
grams, it  is  seen  that  the  condensation  amounts  to  from  about 
30  per  cent  as  a  minimum  to  50  per  cent  as  a  maximum,  so 
far  as  measurable,  the  actual  card  illustrating  the  expansion  in 
a  metallic  cylinder  of  the  steam,  which  would  have  given  the 
larger  diagram  in  an  ideal  engine  with  its  non-conducting 
cylinder.  The  complete  ideal  diagram  would  extend  propor- 

*  Steam-making;  p.  91. 


THERMODYNAMICS  OF   THE  IDEAL  ENGINE.          407 

tionally  farther  toward  the  right  and  beyond  the  limits  of  the 
actual  figure.  When  the  two  lines  continue  so  far  separated, 
it  is  an  indication  of  large  initial  condensation,  and  correspond- 
ingly great  re-evaporation  after  the  exhaust-valve  opens  ;  as  the 
initial  condensation  is  due  to,  and  is  proportional  to,  the  re- 
evaporation.  In  most  cases,  however,  the  engineer,  unable  to 
determine  these  data,  assumes  the  point  of  release,  or  the 
point  of  intersection  of  the  expansion-line  prolonged  with  the 
ordinate  at  the  extreme  end  of  the  diagram,  as  that  of  coinci- 


80- 


FIG.  133. — THE  REAL  AND  THE  IDEAL  CARD. 

dence  of  the  ideal  and  the  real  curve,  and  draws  the  hyperbolic 
curve  backward  from  that  as  a  given  point,  in  the  manner 
already  described.  A  comparison  of  the  ideal  diagram  thus 
formed  with  the  actual  indicator-card  will  give  a  means  of 
judging  of  the  character  of  the  engine  studied  as  a  thermo- 
dynamic  machine. 

Rankine's  construction  will  enable  the  engineer  conveniently 
to  find  the  absolute  mean  pressure  in  the  steam-cylinder  and 
the  final  pressure.*  Thus,  in  Fig.  136,  draw  AB  and  AG ;  take 
AC  equal  to  one  fourth  AB ;  from  C  as  a  centre,  strike  the  arc 
BFG\  and  AG  then  measures  the  stroke  of  piston  plus  clear- 
ance. Take  CD  proportional,  on  the  adopted  scale,  to  the 
clearance ;  AD  then  measures  the  stroke.  Make  AE  the  dis- 


•Hutton's  Handbook;  p.  380. 


4o8 


A  MANUAL    OF    THE    STEAM-ENGINE. 


tance  to  the  point  of  cut-off,  and  draw  the  perpendicular  EF, 
which  will  measure,  very  closely,  the  absolute  mean  pressure ; 


FIG.  136.— MEAN  PRESSURES. 

while  EH,  measured  to  the  intersection  with  the  line  BG,  will 
be  approximately  the  final  pressure.* 

EF       I  +  log,  r       pm 
Then  -j-^  = =  — ,  nearly,  the  quantity  EF  being 

slightly  large  for  large  values  of  r,  small  for  small  values,  and 
exact  for  r  =  3.5,  nearly. 

The  curve  pvn  =  C  may  be  constructed  approximately  by 
the  following  general  method  (see  Fig.  137).*  Starting  from 
L,  draw  any  horizontal  line,  QC,  at  a  small  distance  below  L, 
then  the  question  is  to  find  S,  the  point  on  the  curve  which 
lies  on  QC.  For  this  purpose,  set  downwards 


and 


and  complete  the  rectangle  NT  as  shown  in  the  figure ;  also 
draw  the  horizontal  line  RF  to  meet  the  ordinate  LNH  in  F, 
as  shown  in  the  figure.  Then  bisect  DQ  in  Z,  join  ZF,  and 
prolong  it  to  meet  the  horizontal  through  T  in  E :  a  vertical 


Rankine's  Ship-building. 


f  Cotterill;  ist  ed.,  p.  340. 


THERMODYNAMICS  OF    THE   IDEAL    ENGINE. 


409 


through  E  will  be  the  new  ordinate  very  approximately,  and  by 
its  intersection  with  QC  will  determine  5. 

For,  completing  the  rectangle  TS',  as  shown  by  the  dotted 
lines   in   the    figure,  the    rectangles   ZH,  ZG   are   equal,  for 


ZT  ~  RG' 


<  RG  =  FR,  and  ZN  is  common. 

.-.  OH—  OG  +  NS'\ 
that  is  to  say, 

Rectangle  NS'  =  Rectangle  OH  —  Rectangle  OG. 


H      E 


FIG.  137.— CONSTRUCTION  or  PARABOLAS. 

Now  if  the  points  LS  be  taken  near  enough  together,  the 
area  of  the  rectangle  NSf  may  be  made  to  differ  as  little  as  we 


410  A   MANUAL    OF    THE   STEAM-ENGINE. 

please  from  the  area  of  the  strip  of  the  curve  LSN,  and  the 
rectangles  OH,  OG  are  equal  to  P,  Vl ,  P,Vt,  respectively, 
divided  by  n  —  I ;  hence,  referring  to  the  formula  for  the  area 
given  above,  it  is  clear  that  we  have  determined  S,  so  that  it 
lies  on  the  curve  PVn  =  constant  very  approximately. 

The  thermal  lines  being  thus  constructed,  their  combina- 
tion in  diagrams  of  energy  representing  the  cycles  of  operation 
of  any  heat-engine  becomes  practicable  when  the  construction 
and  method  of  operation  of  the  engine  are  given,  and  the 
graphical  solution  of  problems  relating  to  work  and  efficiency 
may  thus  be  effected. 

The  lines  observed  in  real  engines  are  so  different  from 
those  of  the  ideal  engine,  in  nearly  all  cases,  that  it  is  not  worth 
while  ordinarily  to  use  the  complicated  exact  expressions 
found  for  the  latter.  The  simpler  curves  above  described  give 
quite  as  satisfactory  approximations  to  the  actual  forms.  The 
expansion  line,  usually,  in  real  engines,  falls,  at  the  beginning, 
more  rapidly  than  the  common  hyperbola,  and  at  the  end  less 
rapidly,  thus  giving  a  curve  of  a  different  class. 

104.  Cyclical  Thermodynamic  Operations  are  such  as 
consist  of  a  series  of  thermodynamic  changes,  in  such  order 
and  of  such  character  that,  at  the  termination  of  the  cyclical 
period,  the  initial  physical  conditions  are  precisely  reproduced. 
Such  cycles  were  first  defined  by  Carnot,  and  he  was  also  the 
first  to  call  attention  to  the  obvious  fact  that,  in  such  opera- 
tions, the  internal  structure  and  internal  variations  of  energy 
might  be  ignored  ;  since,  at  the  end  of  each  cycle,  the  working 
fluid,  whatever  its  nature,  "returns  to  precisely  its  original 
state ;  that  is,  to  that  state  considered  in  respect  to  density,  to 
temperature,  to  mode  of  aggregation."  * 

In  such  operations,  therefore,  it  is  a  matter  of  no  importance 
whether  internal  forces  are  known  or  unknown,  large  01  3mall, 
measurable  or  indeterminate;  whether  the  fluid  be  a  gas,  a 
vapor,  a  liquid,  or  a  solid.  The  changes  of  internal  work  and 

*  Reflections  on  the  Motive  Power  of  Heat;   edited  by  R.  H.  Thurston; 
N.  Y.,  J.Wiley  &  Sons;  1890;  p.  67,  foot-note. 


THERMODYNAMICS  OF  THE  IDEAL  EJTGIA'E.         411 

energy,  positive  and  negative,  must  balance;  and  their  sum 
must  be  zero  for  the  cycle.  It  thus  becomes  easy,  in  such 
cases,  as  shown  by  Carnot,  to  determine  the  useful  effect,  the 
wastes,  and  the  efficiency  of  any  cyclical  thermodynamic 
changes  irrespective  of  the  character  of  the  working  fluid. 

Such  cycles  are  illustrated  in  the  well-known  "Carnot 
cycle;"  in  which  the  fluid  expands  (i)  isothermally,  (21  adia- 
batically ;  (3)  is  compressed  isothermally,  and  (4)  adiabaticaliy ; 
the  latter  period  being  so  adjusted  as  to  finally,  at  its  close  and 
at  the  termination  of  the  cycle,  bring  the  fluid  back  precisely 
to  its  initial  temperature,  pressure,  and  volume.  Here  the 
work  of  adiabatic  expansion  balanced  that  of  adiabatic  com- 
pression; while  those  quantities  performed  during  the  iso- 
thermal changes,  positively  and  negatively,  are  in  exact  propor- 
tion to  the  constant  absolute  temperatures  at  which  the  two 
steps  occur.  Thus  this  cycle  results  in  the  performance  of 
work  by  transformation  of  a  proportion  of  the  total  heat- 
energy,  *  T — -,  into  mechanical  energy  and  the  waste  of  the 

•*! 

proportion,  ~t  as  rejected,  untransformed,  heat.     This,  as  was 

shown  by  Carnot,  also,  is  the  maximum  possible  efficiency  of 
any  system  whatever,  and  with  whatever  working  fluid  the 
work  may  be  done. 

It  is  evident  that,  with  the  steam-engine,  the  same  principles 
and  conclusions  apply,  and  the  study  of  the  engineer  is  to 
endeavor  to  approach  this  fraction  of  efficiency  in  practice  as 
closely  as  possible;  while  also  making  its  absolute  value  as 
high  as  possible  by  making  Tt  —  Tt  a  maximum. 

In  order  to  solve  many  problems  in  the  thermodynamics  of 
the  steam-engine,  as  of  other  heat-engines,  it  is  necessary  to 
study  the  methods  of  expenditure  of  heat  and  of  performance 
of  external  work,  step  by  step,  through  a  cycle,  and  thus  to 
ascertain  the  extent  and  character  of  those  variations  from 
Caraot's  ideal  cycle  of  maximum  efficiency  which  result  in 
loss  of  heat  and  dynamical  effect. 

Fig.   138   illustrates  the   more   regular   forms  of  thermo- 


412 


A  MANUAL   OF   THE   STEAM-ENGINE. 


dynamic  cycle  met  with  in  the  operation  of  heat-engines.  A  B 
and  CD  are  two  isothermal  lines  crossed  by  two  adiabatics, 
EFand  G H.  The  perfect  engine  cycle  of  Carnot  \sabcd; 
the  same  with  the  adiabatic  lines  replaced  by  lines  of  constant 
volume,  which  are  here  those  of  a  regenerative  action,  is  seen 
in  a  b  n  m.  Others  are  formed,  as  e  f  g  k,  and  fijA,  by  lines 
of  constant  pressure  crossing  the  two  pairs  of  curves,  and  by 
lines  of  constant  volume  crossing  them,  as  in  a  bum  and  o  pqr. 
Many  other  cycles  are  formed  by  other  combinations.  That 

A    C  E    G 


FIG.  138.— THE  THERMODYNAMIC  CYCLE. 

seen  in  w  s  t  u  v  is  the  ideal  steam-engine  cycle  modified  by  the 
usual  exhaust  line,  and  drop  of  pressure  at  constant  volume  at 
t  u.  //"/is  taken  as  the  "atmospheric"  line.  Here  the  iso- 
thermal, w  s,  corresponds  to  that  portion  of  A  B  or  C  D  at  the 
extreme  right ;  where  it  becomes  asymptotic  with  O  X.  The 
cycle  of  Carnot,  abed,  is  illustrated  in  the  action  of  the  now 
well-known  type  of  air-engine  of  Stirling ;  in  which  a  mass 
of  air  is  permanently  enclosed  in  a  working  cylinder,  in  which 
its  variations  of  pressure,  temperature,  and  volume  are  pre- 
cisely such  as  are  above  described.  It  represents  the  most 
efficient  of  all  known  types  of  hot-air  engine. 


THERMOD  YXA  MfCS  OF   THE  IDEAL  ENGIXE.          413 

The  closed  cycle,  w  s  t  u  p,  is  also  well  illustrated  in  the 
most  effective  types  of  modern  steam-engine.  In  the  marine 
steam-engine,  for  example,  the  feed-water  is  taken  from  the 
hot- well  or  the  discharge  of  the  surface-condenser,  with  which 
such  engines  are  now  always  fitted ;  is  forced  into  the  boiler 
by  the  feed-pump  ;  is  there  converted  into  steam  by  accession 
of  heat  from  the  fuel,  with  consequent  expansion  into  the  va- 
porous state;  is  next  transferred  to  the  working  cylinder; 
where  its  expansion  results  in  the  conversion  of  a  certain  pro- 
portion of  its  heat  into  mechanical  energy,  by  a  process  similar 
to  that  just  described  as  in  the  cycle  of  Carnot.  It  first  drives 
the  piston  at  constant  pressure  and  temperature,  as  is  required 
in  a  cycle  of  this  form ;  next  it  expands  adiabatically.  to  a 
minimum  temperature  and  pressure  and  a  maximum  volume, 
precisely  as  in  that  cycle ;  then  it  is  compressed,  at  this  mini- 
mum pressure,  into  the  condenser,  which  removes  the  heat  of 
compression  and  preserves  its  pressure  and  temperature  con- 
stant, so  as  to  give  an  isothermal  change ;  and,  finally,  being 
thus  reduced  to  the  liquid  state,  once  more,  it  is  once  again 
forced  into  the  boiler,  to  enter  upon  another  similar  cycle  to 
that  now  completed.  The  last  step,  compression  as  liquid,  into 
the  boiler,  and  its  increase  of  temperature  to  that  of  the  steam 
into  which  it  is  presently  converted,  corresponds  to  the  period 
of  adiabatic  expansion  at  the  other  side  of  the  cycle.  To  make 
it  exact,  however,  it  is  evident  that  the  last  step  should  be  the 
compression  of  the  vapor  into  liquid,  at  the  higher  temperature 
and  pressure,  by  a  purely  mechanical  action  ;  instead  of  its  in- 
troduction, cold,  into  the  boiler,  and  its  elevation,  there,  to  the 
maximum  temperature  by  heat  directly  applied. 

The  action  of  the  non-condensing  engine  is,  in  essence,  the 
same  as  that  just  traced.  The  steam  enters  the  engine  at  a 
maximum  temperature  and  pressure ;  drives  the  piston,  up  to 
the  point  of  cut-off,  by  an  isothermal  expansion ;  is  then  ex- 
panded to  the  back-pressure  and  corresponding  temperature  by 
an  adiabatic  process,  as  nearly  as  the  nature  of  the  case  will 
permit;  is  then  rejected  into  the  atmosphere — an  isothermal 
process, — where  it  is  condensed,  the  atmosphere  being  here  the 


414  A    MANUAL    OF   THE  STEAM-ENGINE. 

condenser  ;  and  it  finally  reappears  as  feed-water  to  be  once 
more  passed  through  the  same  cycle  again.  Thus  each  revolu- 
tion of  the  engine  illustrates  a  cycle,  in  duplicate,  one  on  each 
side  the  piston. 

In  the  trials  of  engines,  it  is  necessary,  to  secure  a  satisfac- 
tory result,  that  the  engine  should  be  operated  steadily  until 
its  "  regime  '"  is  fully  established,  and  until  it  is  making  cycle 
after  cycle,  precisely  under  the  same  conditions,  before  the  trial 
is  commenced.  This  is  here  especially  important  because  of 
the  facts,  to  be  more  fully  discussed  later,  that  the  reactions 
between  the  steam  and  the  cylinder-surfaces  are  of  real  impor- 
tance in  the  economics  of  the  machine,  and  that  it  takes  some 
time  to  establish  uniform  action  in  this  respect. 

Steam  and  Air  being  compared,  as  representative  of  two  ex- 
treme types  of  working  fluid,  it  will  be  found,  as  indicated  by 
our  formulas,  which  show  maximum  efficiency  of  fluid  to  be 
dependent  upon  temperature  solely,  that  the  one  must  be  just 
as  efficient  as  the  other  as  a  medium  of  transformation  of  heat 
into  mechanical  energy,  provided  the  fluids  are  worked  be- 
tween the  same  initial  and  terminal  temperatures.  The  formulas 
already  given  enable  this  comparison  to  be  readily  made. 
Both  fluids  may  be  assumed  to  work  in  the  Carnot  cycle. 

Such  a  comparison  was  made  by  Rankine  as  early  as  1867,* 
the  data  and  results  being,  in  British  units,  as  follow  : 

DATA. 


T  —  T 

E  =      '         '  =  0.2228. 
*  i 

U  (assumed)  —  68,420  ft.-lbs. 
Pressure  of  steam  ...................  pl  =  5652  ;     Pl  =  39.25 

Pressure  of  air  ......................  ./>,  =  5050  ;     P,  =  35.  1 

*  The  Engineer  ;  Aug.  2,  1867. 


THERMODYNAMICS  OF   THE  IDEAL  ENGINE.          4! 5 

Volume  of  steam,  initial,  vt i.oo  cu.  ft. 

Weight  of  steam 0.0956  Ibs. 

Weight  of  air 1.6113  Ibs. 

Volume  of  air,  initial,  t/, 9.81  cu.  ft. 

Volume  of  air,  atmospheric 22.87  cu.  ft. 

RESULTS. 

St. -engine.  Air-engine.  Diff. 

Heat  expended,  ft.-lbs 68,420  68,420  o 

Heat  rejected,        "       53,i?6  53,176  o 

Heat    transformed    into   work, 

ft.-lbs 15,244  15,244  o 

Work  of  expansion,  ft.-lbs 16,690  68420  5 1,730 

Work  of  compression,  ft.-lbs 1446  53,176  5i,73O 

Work  per  indicator,  net 15,244  15,244  o 

Efficiency 0.2228  0.2228  o 

An  enormously  greater  amount  of  work  is  thus  seen  to  have 
been  done  during  the  forward  stroke  of  the  air-engine  than  in 
the  case  of  the  steam-engine ;  but  this  is  balanced  by  a  pre- 
cisely equal  excess  in  compression  during  the  return-stroke ; 
the  heat  of  such  compression  being  necessarily  wasted.  Both 
engines  thus  do  exactly  the  same  net  amount  of  work  during 
each  cycle,  expending  the  same  quantities  of  heat  and  exhibit- 
ing  the  same  efficiencies  of  fluid.  But  it  is  seen  that  the  air- 
engine  must  have  much  the  greater  bulk,  and,  consequently,  in 
nearly  the  same  ratio,  the  greater  weight ;  and  this  fact  makes 
the  comparison  of  efficiencies  of  engine,  including  both  efficiency 
of  fluid  and  that  of  mechanism,  result  much  more  favorably  to 
the  steam-engine.  This  advantage  of  the  steam-engine  be- 
comes greater  at  high  pressures,  and  is  a  vital  one  under  its 
usual  working  conditions. 

In  all  cases  of  adiabatic  change  of  volume  under  pressure, 
doing  external  work,  we  shall  have  for  the  thermal  change,  in 
dynamic  units, 


416  A   MANUAL    OF   THE   STEAM-ENGINE. 

where  x  and  /  represent  the  proportion  of  fluid  in  the  vaporous 
state  in  the  mixture  and  the  corresponding  latent  heat.  In 
gases  x  —  x'  =  I,  and  /  =  /'  =  o;  and  we  have 


When  the  work  is  that  of  expansion,  t  —  t'  is  positive  ;  the 
difference  of  latent  heats  may  be  either  positive  or  negative. 
In  compression  these  signs  are  reversed.  The  former  case  is 
illustrated  in  heat-engines  ;  the  latter  in  refrigerating  ma- 
chinery. In  the  former,  efficiency  is  promoted  by  a  wide  range 
of  expansion  to  a  minimum  temperature  ;  in  the  latter,  by  a 
narrow  range  at  maximum  temperature  ;  the  measure  being,  for 
the  first, 

T,    a  -  & 


E= 


and,  for  the  second, 


JQ_F 
- 


T,  -  T,  -  <2,  - 


The  choice  of  a  working  fluid,  in  both  cases,  is  purely  a  mat- 
ter of  extra-thermodynamic  consideration,  all  working  fluids 
having  identical  thermodynamic  efficiency. 

Conclusions  of  interest  and  importance  relative  to  the  ther- 
modynamic properties  of  the  several  vapors  practically  most 
available  for  the  operation  of  heat-engines,  as  ether,  chloroform, 
alcohol,  carbon  disulphide,  water,  may  be  deduced  from  sim- 
ilar comparisons,  thus  :* 

Where  the  several  fluids  are  worked  between  the  same 
temperature-limits,  and  consequently  have  the  same  thermody- 
namic efficiency,  considerable  differences  are  to  be  observed  in 
their  tensions,  at  both  initial  and  terminal  temperature,  ether 
exhibiting  highest,  and  steam  the  lowest,  pressures  ;  the  one 
having  nearly  four  times  the  tension  of  the  other.  It  is  ob- 

*  Efficiency  of  Fluid  in  Vapor-engines;  Van  Nostrand's  Magazine;  1884. 
Wood's  Thermodynamics;  1889. 


THERMODYNAMICS  OF  THE  IDEAL  ENGINE.          417 

served  that  a  high  tension  is  accompanied  by  a  small  value  of 
the  potential  energy  of  latent  heat :  while  great  elasticity  is 
generally  an  accompaniment,  also,  of  high  density ;  although 
no  direct  relation  is  yet  determined. 

Most  interesting  differences  are  seen  in  the  magnitudes  of 
work,  of  compression  and  expansion.  The  net  effective  work 
being  the  same,  those  vapors  with  which  the  work  of  expan- 
sion is  greatest  also  demand  the  expenditure  of  most  energy 
in  their  compression  ;  the  difference  in  energy  exerted  and  en- 
ergy received  being  constant  throughout  the  list. 

The  variation  of  the  ratio  of  expansion  among  the  various 
working  fluids  is,  in  such  cases,  very  noticeable ;  and  the  in- 
fluence of  this  ratio,  and  of  the  magnitude  of  the  final  volumes 
of  the  several  fluids,  upon  the  size  of  working  cylinder  required 
is  an  important  practical  consideration,  which  is  well  illustrated 
by  the  comparison  of  these  quantities  in  the  steam-  and  the 
air-engines.  The  fact  that  the  familiar  limiting  conditions  of 
operation  of  real  engines  may  produce  important  practical  re- 
sults in  the  modification  of  efficiency  of  fluid  and  of  economy 
of  working  is  forcibly  shown  by  the  results  obtained  in  the 
other  cases  of  comparison  of  vapors. 

On  the  whole,  it  will  be  found  that,  if  we  make  our  com- 
parisons within  those  limits  of  pressure  found  practicable  with 
the  steam-engine,  the  vapor  of  water  is  the  most  efficient  of  all 
available  fluids  under  the  conditions  of  use  in  real  engines, 
and,  since  all  the  apparent  advantages  of  the  non-aqueous 
vapors  may  be  gained  by  increasing  pressures  and,  especially, 
of  temperatures  of  steam,  it  seems  probable  that  none  of  those 
fluids  will  ultimately  successfully  compete  with  steam.  It  is 
further  evident  that  the  use  of  air  and  other  gases,  now  giving 
large  thermodynamic  efficiency,  must  involve  comparatively 
low  efficiency  of  mechanism,  and  that  this  latter  disadvantage 
may  be  lessened  by  working  a  larger  weight  of  fluid  within  a 
given  volume :  i.e.,  by  working  the  fluid  at  initially  greater 
density. 

Collating  expressions  used  in  the  preceding  study  of  the 
thermodynamics  of  the  ideal  engine,  their  tabulation  in  compact 


41 8  A  MANUAL    OF   THE   STEAM-ENGINE. 

form  will  be  found  very  convenient  for  reference  and  in  doing 
work.     The  following  table  is  thus  obtained  : 


WORKING   FORMULAS   OF  THERMODYNAMICS. 

(I)  dH  =  Qd<j>. 
.  (2)  dH  =  Td$. 


(C)dH=dE 
§  90-  (3)  log/  =  a  -  bo?  -  eft*. 


,    x    Si«i         So"o         ^vj_-' 

(4)       A^T~       ~T~' 


ioo 

=  274  Centigrade 


(or  493°  F.). 


§93- 


dU  =  pdv, 


THERMODYNAMICS  OF   THE  IDEAL  EXGINE.          419 

pv        T 
§95.  (i)  ~—  =  j^  =  constant  =  R,  for  a  perfect  gas. 


(3)  dff= 


(5)        =  KJT+fdv. 


(6)        = 


(7)  dH= 


(15)    <t>= 


42O  A   MANUAL    OF   THE   STEAM-ENGINE. 

When  gas  expands  or  contracts  at  constant  temperature 
§ 96.        H=RTl  log,  ^  =  A"i  log, ^  =  A",  log. r- 

Adiabatic  expansion  : 
§96.        dH  = 


r, 


Work  of  perfect  gas  at  constant  temperature: 

/Vj  A*?  j 

fc/f,  J  i>\  >l  l 

U  =  plvl  \oger. 
Work  of  adiabatic  expansion': 


CHAPTER  V. 

THERMODYNAMICS  OF  THE  STEAM-ENGINE.    WASTES  OF 
ENERGY;    EFFICIENCY. 

105.  The  Thermodynamics  of  the  Real  Engine  involves 
the  application  of  the  principles  of  science  to  the  determina- 
tion of  the  quantities  of  thermal  converted  into  mechanical 
energy,  the  proportion  wasted,  the  efficiency  of  steam  as  the 
working  fluid  in  the  machine,  and  the  weight  of  steam,  and — 
where  the  data  permit — that  of  the  fuel  demanded  per  horse- 
power and  per  hour,  or  other  unit  of  power  or  of  time,  in  effect- 
ing such  transformation  in  an  ideal,  purely  thermodynamic,  en- 
gine. 

Since  no  other  than  thermal  and  the  equivalent  mechanical 
energies  are  taken  cognizance  of  by  this  science,  and  no  physi- 
cal changes  or  transfers  are  considered,  all  those  circumstances 
and  conditions  which  distinguish  the  real  from  the  ideal  case, 
in  energy-transforming  machinery,  in  the  case,  for  example,  of 
the  heat-engines,  must  be  treated  by  extra-therm odynamic 
methods.  The  study  of  the  thermodynamics  of  the  steam- 
engine  comprehends,  simply,  the  investigation  of  the  machine 
so  far  as  it  is  an  ideal  heat-engine,  subject  to  no  other  than  the 
inevitable  thermodynamic  wastes. 

The  study  of  actual  engines,  however,  involves  the  exami- 
nation of  both  physics  and  dynamics  in  their  applications  in 
such  machines,  and  the  problem  is  thus  rendered  a  much  more 
complicated  one  than  that  in  thermodynamics  and  far  less  easy 
of  exact  solution. 

It  is  still  generally  admitted  by  writers  on  the  steam-engine 
that,  as  stated  by  Him,  it  is  impossible  to  construct  a  theory 
that  shall  be  scientifically  exact,  and  will  accord  perfectly  with 


422  A   MANUAL   OF   THE   STEAM-ENGINE, 

practical  experience  in  even  the  best  practice.*  Nevertheless, 
designers  and  builders  are  required  to  use  methods  and  formu- 
las in  their  preliminary  computations  and  in  preparation  of 
their  plans,  not  only  for  the  computation  of  dimensions  and 
proportions  of  parts,  but  also  to  obtain  approximate  estimates 
of  the  quantity  and  the  cost  of  the  work  to  be  performed  and 
of  the  heat,  the  steam,  and  the  fuel  to  be  demanded  for  its 
performance.  In  the  following  pages  so  much  of  applied  theory 
and  approximate  methods  as  may  be  considered  as  practically 
useful,  to-day,  will  be  exhibited  and  illustrated.  In  all  cases, 
however,  the  engineer  is  guided  largely  by,  and  his  computa- 
tions are  checked  by  reference  to,  experience  with  as  nearly 
as  may  be  similar  practice. 

106.  The  Steam-engine  as  a  Heat-engine  is  a  machine 
in  which  heat-energy  stored  in  steam  is  converted  into  the 
dynamical  form  and  applied  to  the  purposes  for  which  the  en- 
gine has  been  designed.  In  this  process,  the  steam,  produced 
in  the  steam-boiler,  is  supplied  to  the  engine  at  such  a  pres- 
sure and  temperature  as  will  permit  a  considerable  range  of 
adiabatic,  or  approximately  adiabatic,  expansion,  and  the  con- 
sequent transformation  of  a  considerable  fraction  of  its  thermal 
energy. 

This  energy  exists,  initially,  in  the  steam,  in  the  form  of 
sensible  and  latent  heat,  and  is  in  larger  proportion  sensible,  as 
has  been  seen,  as  the  temperature  and  the  pressure  are  more 
elevated.  Were  it  practicable  to  use  the  fluid  at  the  tempera- 
ture and  pressure  of  its  "  critical  state,"  all  heat-energy  would 
be  in  the  sensible  form.  In  any  case,  a  fraction  of  the  heat 
supplied  is  converted,  by  the  cyclical  action  of  the  machine, 
into  work  ;  while  the  other  portion,  usually  large,  is  necessarily 
rejected  at  the  minimum  temperature  reached.  The  larger 
the  fraction  transformed  into  mechanical  power,  the  larger  the 
efficiency  of  the  machinery  ;  and  its  maximum  possible  effect 
is  measured  by  the  proportion, 


_    , 


Him:  Thermodynamique;  1876.     Sinigaglia:  Machines  a  Vapeur;  1890. 


THERMODYNAMICS  OF   THE   STEAM-ENGIXE.          423 

of  total  heat-energy  stored  in  the  fluid  at  its  entrance  into  the 
engine. 

As  elsewhere  shown  (§93,  §  112),  the  quantity  of  work  per- 
formed per  unit  weight  of  working  fluid  is  determined  by  the 
quantity  of  energy  that  may  be  stored  as  latent  heat  of  expan- 
sion and  vaporization.  In  this  respect,  steam  is  superior  to 
other  available  working  substances  ;  and  the  engine  in  which 
it  is  employed  can  be  given  smaller  volume  and  weight  than 
any  other,  the  air-engine  for  example,  in  which  this  latent  heat 
is  less. 

107.  The  Real  and  the  Ideal  Engines  are  so  radically 
different  in  their  conditions  of  action  and  in  the  nature  and 
magnitudes  of  their  wastes  of  energy  that  the  engineer  distin- 
guishes carefully  between  the  two  cases. 

The  ideal  engine  presents  a  purely  thermodynamic  prob- 
lem, capable  of  exact  and  unqualified  solution.  It  illustrates 
simply  the  transformation  of  thermal  into  dynamic  energy, 
with  no  other  loss  than  that  unavoidable  waste  due  to  the 
operation  of  the  second  law  of  thermodynamics,  the  magnitude 
of  which  is  easily  and  precisely  computed  as  soon  as  the  con- 
ditions of  the  problem  are  definitely  given.  This  process  of 
computation  has  been  fully  described  and  its  application  illus- 
trated. 

The  real  engine  is  a  piece  of  mechanism  composed  of  sub- 
stance incapable  of  retaining  heat  and  permitting  free  transfer 
to  and  from  the  working  fluid,  wasting  large  quantities  exter- 
nally by  conduction  and  radiation,  and  internally  by  alternate 
storage  in  its  own  substance  and  restoration  to  the  working 
fluid  in  such  manner  that  transfer  occurs  without  transforma- 
tion, in  large  proportion.  It  also  wastes  a  large  amount  of  the 
mechanical  energy  produced  by  transformation  in  the  work  of 
moving  its  own  cumbersome  parts. 

The  Real  and  the  Ideal  Engines  in  their  operation  are 
thus  distinguished  by  a  very  wide  difference  of  efficiency, 
resulting  from  the  correspondingly  enormous  differences  of 
physical  working  conditions  arising  out  of  the  thermal  and 


424  A    MANUAL    OF    THE   STEAM-ENGINE. 

mechanical  operations  unavoidably  accompanying  the  thermo- 
dynamic  phenomena. 

In  all  real  engines  the  departure  from  the  ideal  conditions 
assumed  is  very  great,  not  only  in  steam-,  but  even  in  gas-  and 
air-engines,  and  so  great  as,  in  most  cases,  to  lead  to  radically 
different  results  from  those  attained  in  the  ideal  case. 

Explosive  and  other  gas  engines  are  impelled  by  a  mixture 
of  hot  gaseous  and  vaporous  products  of  combustion,  of  which 
the  latter  portion  is,  like  the  working  fluid  in  the  steam-  and 
other  vapor-engines,  subject  to  rapid  and  considerable  changes 
of  thermal  state.  Enclosed,  usually,  in  a  chamber  the  sides  of 
which  are  kept  cool  by  a  water-jacket,  enormous  quantities  of 
heat  are  lost  as  expansion  proceeds,  and  the  efficiency  of  the 
machine  is  correspondingly  diminished,  and  both  the  efficiency 
and  the  most  economical  ratio  of  expansion  are  altered  by  the 
increased  losses  which  accompany  the  higher  ratios. 

Steam  always  condenses  in  the  steam-cylinder  in  conse- 
quence of  the  conversion  of  a  part  of  its  heat  into  work,  even 
though  the  expansion  be  perfectly  adiabatic ;  and,  in  the 
actual  engine,  this  occurs  to  a  much  greater  extent,  unless, 
by  superheating  or  by  the  use  of  an  efficient  jacket,  consid- 
erable heat  is  supplied  it  before  or  during  expansion.  The 
first  quantity  is,  however,  insignificant  in  comparison  with 
direct  losses  of  heat ;  it  probably  seldom  approaches  ten  per 
cent  of  the  heat  supplied,  and  is,  usually,  a  very  much  smaller 
figure. 

Initial  condensation  and  later  re-evaporation  of  steam  in 
the  steam-engine,  and  initial  cooling  without  subsequent  re- 
heating, in  gas-engines,  are  the  greatest  sources  of  waste 
of  heat,  and  give  rise  to  losses  that  are  both  absolutely  and 
relatively  very  great  wherever  the  range  of  temperature  during 
expansion  is  very  considerable,  and  especially  with  low  back- 
pressure. 

The  steam  passing  out  of  the  exhaust-ports  to  the  con- 
denser or  into  the  atmosphere  is  moist  and  heavy  with  the 
water  of  condensation,  and  is  a  good  conductor  of  heat 
as  well  as  a  very  greedy  absorbent.  It  sweeps  out  of  the 


THERMODYNAMICS  OF   THE   STEAM-ENGINE.          425 

cylinder  large  quantities  of  heat  abstracted  from  its  inner 
surfaces,  leaving  those  surfaces  comparatively  cold  and  wet 
with  a  chilling  dew.  The  entering  steam  meets  these  cold 
metallic  and  liquid  masses  and  is  condensed  in  sufficient  quan- 
tity to  reheat  them  to  the  temperature  of  prime  steam.  As 
the  piston  moves  forward  it  uncovers  new  surfaces,  and  con- 
densation continues  until,  sometimes,  a  large  fraction  of  the 
steam  supplied  lies  in  the  cylinder  or  floats  in  the  uncondensed 
steam  as  water  and  mist.  Toward  the  end  of  expansion,  and 
especially  during  exhaust,  re-evaporation  occurs,  from  the  ex- 
posed surfaces  and  in  the  midst  of  the  mixture  of  water  and 
steam,  at  lower  pressures  and  to  a  similarly  serious  extent. 
Thus  heat  is  constantly  transferred  from  the  steam  to  the 
exhaust  side,  and,  doing  little  or  no  work,  is  wasted,  and  the 
efficiency  of  the  engine  and  the  cost  of  fuel  are  greatly 
affected. 

This  loss  may  be  greatly  reduced  by  superheating  and 
steam-jacketing.  Loss  from  this  cause  has  been  found  to  be 
so  great,  and  to  increase  so  rapidly  with  increased  expansion, 
that  it  practically  often  sets  an  early  limit  to  the  economical 
increase  of  the  ratio  of  expansion. 

It  is  thus  seen  that  several  directions  of  distribution  and 
waste  of  energy  are  found  in  the  real  engine  which  do  not 
exist  in  the  ideal  case,  and  which  constitute  characteristic  dis- 
tinctions between  the  two.  The  engineer  thus  observes  the 
following  facts,  and  bases  upon  them  his  nomenclature  of  the 
various  "  powers"  and  "  efficiencies." 

When  steam  enters  the  engine  from  the  boiler,  it  is  made 
the  vehicle  of  heat-transfer  and  the  medium  of  transformation 
of  thermal  into  mechanical  energy.  The  work  performed  in 
the  cylinder  and  the  power  developed  are  called  the  "indi- 
cated work  and  power" 

The  ratio  of  this  work  to  the  mechanical  equivalent  of  heat 
required  in  a  non-conducting  cylinder  for  the  same  operation 
is  the  measure  of  thermodynamic  efficiency.  The  ratio  of  this 
latter  quantity  to  the  actual  efficiency,  as  measured  by  the  ratio 
of  mechanical  energy  to  the  total  actual  heat  used,  including 


426  A   MANUAL    OF   THE    STEAM-ENGINE. 

heat-wastes  in  the  metallic  cylinder,  may  be  called  the  efficiency 
of  the  working  substance ;  its  efficiency  for  use  as  a  medium  of 
energy  transfer  and  transformation. 

When  the  energy  applied  to  the  piston,  as  measured  by  the 
indicator,  is  carried  onward  through  the  machine,  and  finally 
given  out  at  the  shaft  to  the  driven  machinery,  it  loses  an 
amount  measured  by  the  friction  of  the  engine,  and,  this  lost 
work  being  taken  out  of  the  indicated  work,  we  have  the  work 
usefully  given  out  as  measured  by  the  dynamometer.  This  is 
called  the  dynamometric  power.  Its  ratio  to  the  indicated 
power  is  the  efficiency  of  the  machine. 

Engineers  usually  express  the  quantities  of  power  in  horse- 
power and,  in  symbols,  as  /.  H.  P.  and  D.  H.  P. 

108.  The  Wastes  of  the  Steam-engine  are  comprised  in 
three  distinct  classes:  (i)  the  thermodynamic  waste;  (2)  the 
physical,  thermal,  waste ;  (3)  the  friction-wastes,  and  other 
dynamic,  or  mechanical,  losses.  Of  these,  the  first  is  easily 
computed  when  the  thermodynamic  cycle  of  the  machine  is 
known,  and  can  be  determined  with  precision.  The  second 
is  divided  into  two  parts :  the  waste  of  heat  directly  by  im- 
mediate conduction  and  radiation,  the  heat  so  wasted  stream- 
ing steadily  out  to  surrounding,  cooler,  bodies  ;  and  the  waste 
caused  by  the  process  described  in  the  preceding  article,  that 
due  to  alternate  storage  of  heat,  without  transformation,  in  the 
metal  of  the  working  cylinder,  and,  later,  with  little  or  no  util- 
ization, discharged  from  the  engine.  The  third  kind  is  that 
produced  by  waste  of  energy  previously  transformed,  by  the 
thermodynamic  operation,  from  the  thermal  to  the  dynamic 
form,  and  expended  in  overcoming  back-pressure  and  the 
friction  of  rubbing  parts. 

The  sum  of  these  wastes  being  deducted  from  the  total 
energy  supplied  as  heat,  the  remainder  measures  the  heat- 
energy  utilized  by  the  engine,  and  delivered  to  the  user  in  the 
form  of  available  mechanical  power. 

The  efficiency,  as  already  seen,  of  any  purely  thermody- 
namic engine  depends  solely  on  the  method  of  heat-supply  and 
rejection,  and  in  no  respect  upon  the  nature  of  the  working 


THERMODYNAMICS  OF  THE   STEAM-ENGINE.          427 

substance,  or  the   structural    details  or   arrangement   of    the 
machine. 

The  heat-wastes  of  the  real  steam-engine,  in  the  usual  order 
of  magnitude  and  importance,  may  thus  be  considered  as  fol- 
lows: 

(1)  Thermodynamic  loss. 

(2)  Internal  condensation. 

(3)  Conduction  and  radiation. 
In  detail,  wastes  are  due  to 

(1)  Exhaust-wastes  by  action  of  the  metal  of  the  cylinder. 

(2)  Incomplete  expansion. 

(3)  Back-pressure. 

(4)  Clearance  and  restricted  steam-passages. 

(5)  Exhaust- waste,  from  the  expansion  period  on. 

(6)  Transmission  of  heat,  externally. 
To  which  may  be  added, 

(7)  Boiler  and  feed-water  heat  and  other  wastes. 

The  character  and  the  method  of  these  various  wastes  of 
energy  in  the  real  engine  remain  to  be  studied,  and  their  mag- 
nitudes to  be  determined  by  experimental  investigation.  . 

As  was  probably  first  noted  by  Cotterill,  the  wastes  by  the 
exhaust  include  both  that  due  **  cylinder-condensation,"  initially, 
and  that  produced  by  condensation  during  expansion.  The 
latter  occurs,  with  production  of  a  suspended  mist,  within  the 
whole  expanding  mass,  and  its  effect  in  robbing  the  metal  of 
the  cylinder  of  its  heat  is  little  or  nothing ;  while  the  former 
measures  the  loss  by  alternate  storage  and  restoration  of  heat 
by  exchanges  between  the  steam  and  the  metal.  There  is 
always,  as  shown  by  Him,  a  balance,  in  this  case,  of  heat  stored 
and  heat  restored,  of  heat-waste  to  the  condenser  and  heat 
taken  out  of  the  entering  charge. 

Exact  computations  would  always  require  correction  of 
estimates  of  energies  transferred  by  consideration  of  the  work 
of  air-pump  in  condensing  engines,  and  of  the  feed-pump  in  all 
forms ;  although  the  latter  is  too  small  a  quantity  to  assume 
importance  in  ordinary  work. 

109.  The  Thermodynamic  Wastes  include  only  that  pro- 


428  A    MANUAL    OF   THE   STEAM-ENGINE. 

portion  of  the  heat  supplied  to  the  machine  which  is  computed 
as  waste  in  the  ideal  case ;  and  which  is  necessarily  rejected 
from  the  machine  at  the  lower  limit  of  temperature  and  press- 
ure, during  the  return-stroke  of  the  piston.  In  the  case  of 
those  engines  in  which  the  working  fluid  is  retained,  this 
wasted  energy  is  rejected  as  heat,  by  transfer  to  some  other, 
cooling,  substance ;  the  work  of  the  engine  being  effected  by 
changes  of  volume,  temperature,  pressure,  and  heat-content 
of  the  same  unchanging  mass  of  molecules.  In  other  engines, 
the  heat  is  rejected  with  the  discharged  working  fluid,  during 
the  exhaust-period.  The  Sterling  air-engine  and  the  non-con- 
densing steam-engine  are  examples  of  the  two  classes  of 
engine  and  the  two  methods  of  rejection. 

In  the  case  of  the  perfect,  ideal,  engine  working  in  the  cycle 
of  Carnot,  the  proportions  of  heat  constituting  these  thermo- 
dynamic  utilizations  and  wastes  have  been  seen  to  be,  invariably, 


and 


T 

=    r  //, ;      Ha  -f-  Hb  = 


when  Ha,  ffb,  and  //,  are  the  quantities  of  heat  utilized  and 
wasted,  and  that  initially  supplied.  In  all  other  cases  the 
quantity  wasted  is  larger,  as  the  working  cycle  departs  more 
and  more  from  that  of  Carnot ;  as,  for  example,  by  incomplete 
expansion.  It  can  always  be  computed,  however,  when  the 
cycle  is  known,  either  by  tracing  the  complete  cycle,  noting 
the  quantities  of  work  done  positively  and  negatively,  taking 
the  algebraic  sum  as  the  measure  of  heat  transformed,  and  the 
remainder  as  that  wasted ;  or  by  simply  measuring  up  the 
curve  of  energy,  the  "  indicator-diagram  "  for  the  cycle,  and 
taking  it  as  the  mechanical  equivalent  of  the  heat  utilized  by 
transformation,  and  the  difference,  between  this  quantity  and 
the  total  supplied,  as  the  waste. 


THERMODYNAMICS  OF   THE  STEAM-ENGINE.          429 

HO.  The  Physical  Wastes,  externally,  the  purely  thermal 
external  losses,  due  to  conduction  and  radiation  to  adjacent 
bodies,  are  not  usually  very  large  in  amount  in  the  real  engine: 
while  they  have  no  existence  in  the  ideal  case.  In  small  gas- 
engines,  the  Author  has  found  this  loss  to  amount  to,  in  some 
cases,  ten  or  even  fifteen  per  cent  of  the  heat  supplied :  with 
single-cylinder  steam-engines  of  100  I.  H.  P.,  and  upward,  this 
ought  not,  with  good  coverings  on  external  surfaces,  to  exceed 
about  5  per  cent ;  the  compound  engine  is  naturally  subject 
to  greater  loss.  The  amount  can  be  easily  computed  wherever 
the  area  of  exposed  surfaces,  their  character,  their  tempera- 
tures, and  the  nature  of  the  covering  are  known.  The  larger 
the  machine  for  a  given  power,  the  higher  the  steam-pressures, 
and  the  less  effective  the  clothing  and  lagging  of  the  cylinders, 
the  greater  this  loss.  It  is  also  exaggerated  by  roughness  of 
exposed  surfaces,  as  of  cylinder-heads,  or  of  piston-rods  and 
valve-rods. 

The  internal  wastes,  t/iose  due  to  "  cylinder-condensation"  on 
the  other  hand,  are  often  simply  enormous,  as  has  already 
been  stated,  and  are  extremely  variable  with  all  the  changing 
conditions  of  the  every-day  operation  of  the  engine.  It  is  well 
known  that  the  magnitude  of  this  loss  is  greater  as  the  range 
of  temperature  during  expansion  is  greater ;  it  is  increased  by 
slow  speed  of  engine,  by  reduction  of  the  back-pressure,  by  in- 
crease in  size  of  engine  for  a  given  amount  of  work  done,  by 
increase  in  conductivity  of  the  surfaces  of  the  \vorking  cylinder, 
and,  within  certain  limits,  probably,  by  wetness  of  steam.  It 
is  reduced  by  low  ratios  of  expansion,  by  increasing  back- 
pressures, by  reducing  initial  pressures,  by  increasing  speed  of 
engine,  and  by  special  expedients,  as  steam-jacketing,  super- 
heating, and  the  division  of  the  expansion  between  two  or 
more  cylinders,  as  in  "  compound  "  or  multiple-cylinder  engines. 
Even  increasing  compression  may  reduce  this  loss  and  thus 
give  a  higher  steam-line  and  an  altered  expansion-line.  The 
waste  becomes  the  less,  when  the  sides  of  cylinders  only  are 
jacketed,  the  smaller  their  diameter  ;  it  is  lessened,  when  both 


43O  A    MANUAL   OF    THE   STEAM-ENGINE. 

heads  and  sides  are  jacketed,  by  increasing  diameters,  volumes 
being  in  both  cases  equal. 

The  difference  in  back-pressure  between  non-condensing 
and  condensing  engines  is  productive  of  such  a  wide  difference 
in  the  range  of  temperatures  worked  through  in  usual  cases, 
that  the  Author  has  been  accustomed  to  consider  the  compen- 
sation so  complete  as  to  justify  the  assumption  that  the  value 
of  this  waste,  its  equivalent  pressure  being  taken  as  a  "  virtual 
back-pressure,"  may  be  assumed  to  be  independent  of  the  mag- 
nitude of  the  actual  back-pressure,  and  to  be  determined  solely 
by  other  conditions  above  noted. 

This  waste  is  found  to  be  reduced  most  effectively  by  super- 
heating, and  somewhat  by  the  admixture  of  air  with  the  steam, 
or  by  the  free  use  of  oil  in  the  cylinder,  as  well  as  by  any  ex- 
pedient, in  fact,  which  will  reduce  the  facility  of  exchange  of 
heat  between  the  steam  and  the  metal  of  the  cylinder,  whether 
by  decreasing  the  condensing  and  heat-transferring  power  of 
the  former,  or  the  receiving  and  storing  power  of  the  latter. 

This  internal  condensation  is  an  exceedingly  rapid  process ; 
being  precisely  like  that  occurring  on  the  tubes  of  the  surface- 
condenser,  except  that,  instead  of  the  difference  of  tempera- 
ture, or  head  producing  heat-flow,  being  constant,  the  condens- 
ing surface  immediately  rises  in  temperature,  and  presently 
reduces  the  condensation  to  that  rate  at  which  the  heat  re- 
ceived and  thus  stored  can  be  transmitted  into  the  mass  of 
metal  behind.  In  Emery's  experiments  on  the  Bache  and  the 
Dallas,  this  rate  exceeded  100  pounds  per  square  foot  per 
hour,  and  is  often  in  excess  of  even  that  rate.  It  is  thus  found 
that  the  rate  of  condensation  exceeds  that  of  ordinary  surface- 
condensation  very  greatly  ;  this  greater  activity  of  heat-transfer 
being  very  possibly  due  to  the  fact  that  the  deposited  water  of 
condensation,  which,  unless  artificially  swept  off,  impedes  this 
action  greatly,  in  the  engine  is  re-evaporated,  at  each  exhaust ; 
thus,  perhaps,  giving  clean  surfaces  at  the  time  of  initial  con- 
densation. 

in.  The  Mechanical  Wastes  in  the  real  engine  are  com- 
monly somewhat  greater  than  the  thermal  wastes,  externally ; 


THERMODYNAMICS  OF   THE  STEAM-ENGINE.          43! 

but  are  not  necessarily  so  ;  they  have  been  reduced,  in  some 
instances,  at  least,  in  non-condensing  engines,  to  as  low  as  five 
per  cent  of  the  total  power  of  the  engine,  and,  in  condensing 
engines,  below  ten  per  cent.  Probably  usual  values  are  a  half 
higher.  This  loss  is  measured  by  the  difference  between  the 
power  shown  on  the  indicator-diagram  and  that  measured  at 
the  same  time  by  the  Prony  brake,  the  absorption-dynamom- 
eter. Its  magnitude  depends  on  the  size  and  proportions  of  the 
engine,  and  especially  of  its  rubbing  surfaces,  and  upon  the 
character  of  the  lubrication.  Journals  of  sufficient  size  to  pre- 
vent danger  of  overheating,  and  the  most  liberal  possible  con- 
tinuous supply  of  the  best  lubricants,  are  the  means  to  be 
adopted  in  the  reduction  of  this  waste  to  a  minimum.  Flooded 
journals  and  a  system  of  recovery  and  re-use  of  oil  will  be  proba- 
bly always  found  advisable. 

The  effects  of  clearances  and  of  back-pressure  will  be  studied 
later  (Chap.  VI). 

112.  Transformations  in  the  Ideal  Case,  those  of  Ex- 
ternal Work,  Energy,  and  of  Heat,  by  the  expansibn  of  steam, 
or  any  other  vapor,  are  easily  determined  oy  the  thermody- 
namic  processes  already  enunciated  and  illustrated. 

The  external  work  done  during  isothermal  expansion  of 
vapors  containing,  or  in  contact  with,  their  liquids,  since  their 
isothermal  line  is  a  line  of  constant  pressure,  is  evidently, 
measuring  from  the  zero  line, 


and  this  amount  of  work  demands  an  equivalent  quantity  of 
heat-energy  for  transformation  into  the  mechanical  form.  A 
certain  additional  amount  of  heat  must  also,  in  all  cyclical 
operations,  always  be  transferred,  without  transformation,  and, 
at  the  same  time,  "  degraded  "  in  intensity,  i.e.,  in  temperature. 
This  latter  quantity  is  determined  by  the  character  of  the 
operation  of  which  the  cycle  is  representative. 

Still  another  quantity  of  heat  will  be  required,  for  trans- 
formation in  performing  the  internal  work   of  separation  of 


432  A    MANUAL    OF   THE   STEAM-ENGINE. 

molecules — the  latent  heat  of  expansion, — the  method  of  com- 
putation of  which  quantity  has  already  been  considered  As 
has  been  seen,  the  amount  of  this  heat  and  internal  work  is 
unimportant  in  cyclical  operations;  since  equal  amounts  are 
always  stored  and  restored  during  the  cycle.* 

In  isometric  changes  in  vapors,  as  with  gases,  no  work  is 
done,  and  no  heat  is  transferred,  except  in  the  production  of 
changes  of  temperature ;  for  no  space  is  traversed  against  re- 
sistances only  to  be  overcome  by  transformed  energy. 

In  cases  of  expansion  in  real  engines,  in  which  the  curve 
may  be  fairly  represented  by  the  equation  pv*  =  constant, 
the  amount  of  external  work  done,  and  the  equivalent  heat 
transformed,  is  thus  found  : 


When  the  external  -work  of  isothermal  expansion,  plvl ,  is 
added,  as  in  the  measurement  of  the  total  work  done  during 
the  forward  stroke  of  the  steam-engine, 


*  Precisely  as  if  molecule  were  connected  to  molecule  by  a  system  of  coiled 
springs  of  such  tension  and  range  as  would  produce  the  observed  effects. 


THERMODYNAMICS  OF   THE  STEAM-ENGINE.          433 

where  r  is  the  ratio  of  expansion,  and  pm  the  mean  total  abso- 
lute pressure.     Then,  for  the  forward  stroke, 


(3) 


When  n  =  I,  the   expressions   just   given    for  U,  for   the 
external   work,   become    indeterminate  ;    but,    for    this    case, 

=  r  ;     pv=v  =         ;     and 


/1W2  (*r-*dv 

U  =  JPl  Pdv  =  P*vJVl  —  =  A*.  l°8<  r-      -     -     (4) 


The  form  of  the  expression  shows,  and  calculation  verifies 
the  conclusion,  that,  as  the  value  of  —  =  r  increases  in  geo- 
metrical ratio,  the  work  of  hyperbolic  expansion  increases  in 
an  arithmetical  progression. 

r  =  2,     U=  1.693  /,?,;  r=    8,     U  =  3.078  /,*;,; 

r  =  4,     U—  2.386 /,v,;  r=i6,     ^7=  3-773  A^i» 


Thus,  we  have  a  constant  difference  of  0.693  plvl  . 
Then,  as  before,  for  the  forward  stroke, 


(5) 


The  heat  demanded  for  transformation  into  external  work 
will  be  the  thermal  equivalent  of  these  measures  of  that  work, 
and  all  heat  supplied  in  excess  of  these  amounts  is  waste.  We 
now  have  two  typical  cases  to  examine  : 

The  exact  expression  for  the  work  thus  done^by  saturated 
steam  in  the  steam-engine  is  obtained  thus  : 

(i)  The  work  of  one  stroke  of  the  piston  of  the  engine  is 


434 


A    MANUAL    OF   THE   STEAM-ENGINE. 


measured  on  the  diagram  of  energy  by  a  a'  b'  x'  O  a,  the  work 
of  isothermal  expansion  being  a  a'  x  O  a,  and  that  of  adiabatic 


expansion  a'  V  x'  x  a'  .   The  total  area  is  composed  of  these  two 
parts,  the  first  being  equal  to 

Ul  —  /.,«,,  ,  nearly, 
and  the  second,  unity  of  weight  being  taken,  by 


u  being  taken  as  the  volume  of  the  steam. 
But  it  has  been  seen  (§  102)  that 


dT 


and,  hence, 


THERMODYNAMICS  OF   THE   STEAM-ENGINE  435 

and.  since  we  have  found 


to  be  the  latent  heat  of  evaporation, 

^/T.   .     (7) 


Reckoned  per  unit  of  volume  of  steam  admitted,  since 
-      =      ,  and  the  density,  D  =     , 


A,      (8) 


for  which  densities  and  latent  heats  can  be  found  in  the  stand- 
ard '•  steam-tables." 

Ul  and  Ut  being  thus  found,  the  total  work  is 


(9) 


(2)  The  area  of  the  diagram  may  also  be  measured  up 
thus  :  Calling  £//  =  aa'xOa,  UJ  ^a'b'x'xa'  ,  and  also  U/ 
—  u{  _|_  u»  ,  the  total  work  performed, 


ut'  =  r*pdu  =  u;  +  u;  -plVl 


=         udp  +  Aw»  —  PPi 


+  T-TV+P^-P^  •    (10) 


436  A    MANUAL    OF    THE    STEAM-ENGINE. 

and,  as  before,  there  results 


t=  /T;  -  T;I  +  log.    - 


The  work  of  adiabatic  expansion,  £/,',  or,  as  represented  on 
the  diagram,  a'b'x'xa!  ,  consists  of  that  performed  by  the  con- 
version of  a  part  of  both  the  sensible  and  the  latent  heat-energy 
of  the  fluid  into  mechanical  energy.  We  may  write  out  the 
expression  (10)  for  this  work  thus  : 


V;  =JTt-JT.-jTt  log, 


(12) 


Here  JTt  and  JT,  measure  the  work-equivalent  of  the 
sensible  heat  present  in  unity  of  weight  of  the  fluid,  at  the 
beginning  and  at  the  end  of  expansion,  respectively,  reckoned 
from  absolute  zero  ;  p^vt  and  /y/2  are  the  measures  of  the  work 
of  isothermal  expansion,  or  of  energy  due  to  the  efforts/',, 
A  ,  acting  through  the  volumes  vt  and  #a  ,  and  the  quantity 

Ttvt  -~  has  been  seen  to  represent  the  latent  heat  of  vapor- 

ization, H,  at  the  temperature  and  pressure  7",  ,  />,  .      Also,  the 
sum  of  the  third  and  fifth  terms, 


is  the  measure  of  the  latent  heat  of  evaporation  at  /,  ,  T9,  of 
the  fraction,  —  ,  of  unity  of  weight  of  steam,  i.e.,—  /£,  ,  and 

-.   .   (13) 


THERMODYNAMICS  OF   THE    STEAM-ENGINE.          437 

The  work  of  adiabatic  expansion  is  the  equivalent  of  the 
sensible  heat  stored  in  the  fluid  at  its  entrance  into  the  engine, 
minus  the  work  of  isothermal  expansion  represented  by  the 
product  of  the  initial  absolute  pressure  into  the  volume  at 
the  "  point  of  cut-off,"  a  ;  increased  by  the  work-equivalent  of 
the  sensible  heat  at  the  "  period  of  exhaust,"  less  the  work 
represented  by  the  product  of  pressure  and  volume  at  that 

point ;  plus  the  latent  heat  at  entrance,  less  the  proportion,  ~  , 
of  the  latent  heat  of  the  same  weight  of  vapor  at  the  terminal 
temperature  and  pressure.  The  fraction  -— ,  or  the  final  volume 

of  the  fluid  divided  by  the  volume  it  would  occupy  if  it  were 
all  in  the  state  of  dry  and  saturated  steam,  is  the  propor- 
tion of  the  initial  weight  of  dry  steam  which  remains 

unliquefied  by  expansion ;     the  remainder,  -1—  — -,  being  the 

part  which,  condensing,  surrenders  its  latent  heat  for*  trans- 
formation  into  work. 

As  is  readily  seen,  the  heat-energy  stored  as  latent  heat  of 
vaporization,  in  steam,  is  the  principal  source  of  transformed 
energy,  or  work,  and  the  difference  between  such  a  vapor  and 
a  similar  fluid  taking  up  no  latent  heat,  could  such  exist,  may 
be  realized  on  computing  the  respective  quantities  demanded 
for  unit  of  useful  power  developed.  Thus,  the  steam  being 
used  in  the  ideal  engine  and  a  Carnot  cycle,  if  received  at  320° 
F. — corresponding  to  75  Ibs.  per  square  inch,  by  gauge — and 
rejected  into  the  condenser  at  100°  F.,  the  efficiency  would  be 

E  —  — ^ — -  =  0.28,  nearly. 
•  i 

But  the  sensible  heat  added  amounts  to  about  80,000  foot- 
pounds for  such  a  range  of  temperature,  and  the  part  utilized 
would  be  nearly 

u  =  0.28  X  80,000  =  22,400  ft.-lbs. 


43^  A    MANUAL    OF   THE    STEAM-ENGINE. 

It  would  therefore  require  the  supply  of  about 
W—  1,980,000  -r-  22,400  =  88  Ibs., 

nearly,  per  horse-power  and  per  hour;  while,  in  the  actual 
operation  of  good  engines  at  such  pressures  and  temperatures, 
it  is  not  unusual  to  obtain  the  same  quantity  of  work  with  less 
than  one  fifth  this  weight  of  feed-water  supply.  The  use  of 
steam  in  a  non-conducting  and  frictionless,  the  ideal,  engine 
would  similarly  demand  but  about  one  tenth  the  above-com- 
puted quantity. 

In  the  case  of  steam-engines  working,  as  assumed  in  the 
analysis,  without  compression,  or  where  compression  is  neg- 
lected, the  efficiency  must  evidently  be  less  than  if  the  com- 
pression be  adiabatic  and  complete,  as  in  the  Carnot  cycle. 
The  maximum  efficiency  of  fluid  is  thus  reduced,  in  many 
cases,  quite  sensibly,  and  may  be  considerably  diminished. 
The  difference  is  that  between  the  Carnot  ratio  and  that  ratio 
diminished  by  the  quotient  of  work  of  adiabatic  compression  to 
whole  heat  supplied.  For  the  Carnot  cycles,  the  efficiency  is 


and  for  the  assumed  case, 


,  —  T, 

T,  —  T-  ~ 


nearly;   in  which  latter  expression  //  is  the  latent  heat   of 
evaporation. 

For  other  vapors  than  steam,  Jc  must,  of  course,  be  substi- 
tuted for  J.  In  the  case  of  steam  this  loss  is  usually  very 
small,  rarely  amounting  to  an  approximation  to  one  per  cent. 


THERMODYNAMICS  OF  THE  STEAM-ENGINE.          439 

Adiabatic  Expansion  produces  the  liquefaction  of   steam, 
initially  dry  and  saturated,  in  the  proportion,  as  already  seen, 


mf  =  i  — 


This  proportion,  though  small  in  the  older  types  of  engine, 
with  their  comparatively  low  pressures  and  small  ratios  of  ex- 
pansion,  becomes  important  in  later  engines  with  pressures 
ranging  up  toward  10  or  12  atmospheres,  and  ratios  of  expan- 
sion of  15  to  20  or  more.  Thus,  comparing  steam  in  the  ideal 
non-conducting  cylinder,  at  absolute  pressures  of  115  and  of  165 
pounds  per  square  inch,  as  employed  in  modern  compound  and 
triple-expansion  engines,  we  have,  in  the  first  case,  if  expand- 
ing to  8  pounds  terminal  pressure,  over  14  per  cent  adiabatic 
condensation;  in  the  latter,  we  have  17  per  cent,  nearly;  one 
pound  of  the  mixture  giving  x  =  0.86  and  x  =  0.83,  nearly, 
remanent  steam.  The  heat  utilized  is,  in  these  cases,  respec- 
tively, 0.17  and  0.20,  nearly — a  thermodynamic  gain  of  about 
1 8  per  cent.  Raising  initial  pressure  to  220  pounds,  as  in  some 
quadruple-expansion  engines,  the  thermodynamic  gain  is  an 
additional  10  per  cent,  and  at  250  pounds,  absolute  pressure,  15 
per  cent.  This  happens  to  correspond  closely  with  experience, 
with  the  real  engine. 

The  result  is  well  shown  by  the  illustration  given  on  the 
next  page,  from  a  paper  by  Mr.  Parker.*  The  diagram  shows 
the  method  of  expansion  of  steam  at  an  absolute  pressure  of 
140  pounds  per  square  inch  (9^  atmos.)  ;  (a)  when  kept  dry  and 
saturated  ;  (b)  when  expanding  adiabatically ;  and  (c)  as  actually 
worked  in  the  steam-cylinders  of  the  S.  S.  "  Aberdeen,"  de- 
signed by  Mr.  Kirk  for  the  China  trade,  an  example  of  excep- 
tional economy,  f  It  is  seen  that  the  actual  expansion-line  was 

•Economy  of  Compound  Engines;  Trans.  Brit.  Inst.  N.  A.,  1882.  Thurs- 
ton's  Engine  and  Boiler  Trials;  p.  459. 

f  Engines  :  30  ,  45-,  and  7o-incb  cylinders,  the  firs  un jacketed;  4$  feet  stroke 
of  piston.  Steam  125  Ibs.  by  gauge,  in  boiler;  125,  50,  and  15  Ibs.  in  jackets. 
H.  P.  1800;  fuel  per  h.  p.  per  hr.,  1.28  Ibs. 


440 


A    MANUAL   OF   THE  STEAM-ENGINE. 


bounded  very  closely  by  the  adiabatic  line,  thus  showing  the 
internal  condensation  to  be  variable  in  a  manner  similar  to  that 
in  a  non-conducting  cylinder.  The  jacket-wastes,  however, 
amounting  to  about  4  per  cent,  must  be  added  to  the  quantity 

Dotted  line  shows  relative  pressures  and  volumes,  steam 
expanding  adiabatically. 

TABLE  SHOWING  AMOUNT  OF  CONDENSATION  OF  STEAM 

EXPANDING  ADIABATICALLY   FROM   DRY   STEAM   AT    140 
1.BS.    PRESSURE. 


Temperature. 

Pressure. 

Condensation. 

353° 

140  Ibs. 

O.OOO 

347 

130 

.005 

338 

"5 

.012 

329 

102 

.019 

320 

90 

.026 

3H 

79 

•034 

302 

69 

.041 

293 

60 

.049 

284 
275 

11 

'.ril 

266 

39 

.070 

257 

34 

.078 

248 

29 

.086 

239 

26 

•  093 

230 

21 

.100 

221 

18 

.108 

212 

15 

.115 

203 

12 

.123 

194 

IO 

•  131 

185 

8.4 

•  139 

176 

6.8 

.147 

FIG.  140. — ECONOMY  OF  STEAM. 


of  steam  here  shown.  The  table  accompanying  the  diagram 
exhibits  the  computed  adiabatic  condensation  for  the  full  range 
of  expansion,  varying  from  o,  at  the  start,  to  14.7  per  cent  at 
the  end.  For  such  engines,  with  the  progress  of  expansion, 


THERMODYNAMICS  OF   THE  STEAM-ENGINE.          441 

it  would  become,  on  this  scale,  about  4  per  cent  for  steam  at 
70  pounds  absolute  pressure,  6  at  47.  7^  at  35,  10  at  23,  1  1  at 
18,  12  at  14,  and  14  per  cent  at  8£;  or  at  ratios  of  expansion. 
respectively,  of  2,  3,  4,  6,  8,  10,  and  15. 

The  wastes  due  to  action  of  valves,  the  loss  in  passages, 
and  to  maladjustment  of  the  several  parts  of  the  system  to 
each  other,  are  seen,  as  in  other  cases  to  be  presented,  in  the 
variation  of  the  real  diagrams  from  their  respective  portions  of 
the  ideal  curve.  These  wastes  may  be  reduced  somewhat  by 
improved  design  and  construction  ;  but,  on  the  whole,  they 
increase  with  higher  pressures  and  greater  expansion,  and  thus 
exaggerate  the  difficulties  of  securing  higher  economy.  All 
these  points  being  considered,  the  gain  by  still  higher  pressure 
is  seen  to  be  comparatively  small.  As  will  be  seen  later,  this 
condensation  is  cumulative  in  the  compound  engine,  and  can- 
not be  reduced  by  arranging  several  cylinders  in  series.  Insig- 
nificant in  a  single  cylinder,  it  becomes,  as  just  seen,  quite 
large  with  the  high  values  now  usual  for  the  total  ratio  of  ex- 
pansion in  such  engines. 

For  comparison  with  the  methods  of  Rankine,  who  prefers 
the  computation  of  dynamic  energies,  the  system  of  Clausius, 
whose  method  preferably  considers  thermal  quantities,  may  be 
taken,  as  illustrated  by  the  following  summary  of  the  discus- 
sion of  the  ideal  steam-engine  cycle  :* 

Let  W  —  the  weight  of  fluid  taken  : 

/  =    '•   latent  heat  : 

XtX^Xc  —    "   proportion  of  dry  steam  present  ; 
T  —  absolute  temperature  • 
/  =  any  temperature  ; 
Q  =  quantity  of  heat. 

The  "  thermodynamic  function"  of  Rankine,  0,  or  the 
measure  of  Clausius'  "  entropy,"  has  been  obtained  thus  : 


(14) 


*For  a  complete  exposition  of  Clausius'  system,  consult  Peabody's  "Ther- 
modynamics of  the  Steam-engine;"  N.  Y.,  J.  Wiley  &  Sons;  1889. 


442  A   MANUAL    OF   THE  STEAM-ENGINE. 

when  Q  is  the  measure  of  heat  transferred,  in  thermal  units. 

When  we  heat  water  from  the  minimum  o°to  any  maximum 
temperature,  /,  in  the  steam-boiler,  the  only  change  noted  is 
that  of  temperature  and  we  have  the  change  of  entropy : 


but  in  vaporization,  dt  =  o, 

O"  -  —  • 
7"' 

and  the  total  change  is  measured  by 


in  adiabatic  expansion,  d<j>  =  o,  and 

xl  . 

-=r  =  constant. 


f'cdt  _ 

)  T" 

t/  o 


Then,  in  the  four  operations  constituting  an  ideal  engine 
cycle,  we  have,  for  the  case  of  maximum  efficiency : 

(A)  Expansion  of  water  into  steam  at  constant  temperature 
and  pressure,  this  action  occurring  in  the  boiler ;  the  heat  de- 
manded is 

QI=  Wl,(xb-x^ (17) 

(E)  Adiabatic  expansion  to  back-pressure ;  no  heat  being 
gained  or  lost : 

(C)  Compression  at  constant  pressure  and  temperature  cor- 
responding to  the  back-pressure,  in  which  operation  heat  is  re- 
jected to  the  amount 

-*<) (18) 


THERMODYNAMICS  OF   THE   STEAM-ENGINE.          443 

(D)  Adiabatic  compression  : 


f (19) 

We  have,  from  the  above, 

,,-,.=^,-^ 

whence 

T 

(20) 


The  efficiency  thus  becomes,  in  accordance  with  Carnot's 
law: 


When,  as  usually  assumed,  xa  =  o,  and  xb  =  I,  the  work 
done  is 


and  the  weight  of  fluid,  for  a  given  work, 

-i-V  ......  « 

The  quantity  of  heat  demanded  is  measured,  in  units  of 
work,  by 

U.  ......    (23) 


, 

*i         *i 

The  weight  of  water  required  is  thus 

W=;     .......    (24) 


444  A    MANUAL   OF   THE  STEAM-ENGINE. 

and,  per  horse-power  and  per  hour,  this  becomes 

33000X60        Tt 


JP,       T,  -  TV 


Professor  Peabody  computes,  on  the  assumption  J  =  778, 
ideal-engine  efficiencies  as  follow : 

WEIGHTS   OF   STEAM   DEMANDED.      IDEAL   CASE. 

Non-condensing. 
Condensing. 


A 

r,-  T, 

M 

7-,-  T* 

M 

(by  gauge) 

Ti 

Ibs. 

T 

Ibs. 

30 

0.215 

12.8 

0.084 

32.8 

60 

0.249 

II.4 

O.I24 

22.9 

10© 

0.278 

10.5 

0.157 

18.4 

150 

0.303 

9.8 

0.186 

1  6.0 

200 

0.320 

9-5 

0.2O7 

14.6 

300 

0.347 

9.0 

0.238 

13-1 

It  can  now  be  seen  that,  as  already  stated  (§  93),  the  mag- 
nitude of  the  quantity  Q  above,  which  is  a  measure,  here, 
of  the  latent  heat  of  vaporization,  determines  the  amount 
of  energy  which  can  be  transformed  per  unit  of  weight,  and 
that  the  best  working  fluid,  in  this  respect,  is  that  having  most 
energy  thus  stored  ;  while  the  thermodynamic  efficiency  is  en- 
tirely independent  of  Q  or  H  and  a  function,  solely,  of  tempera- 
ture.* 

113.  Dry,  Saturated,  Steam  is  often  assumed  to  be  obtain- 
able, and  to  be  capable  of  being  worked  without  condensation, 
the  steam  being  kept  at  the  point  of  saturation  by  heat  sup- 
plied by  a  steam-jacket.  The  fact  that  dry  steam,  or  other 
vapor,  like  gas,  is  a  good  non-conductor  and  non-absorber  of 
heat  makes  it  improbable  that  superheating  can  ever  be  pro- 
duced, to  any  sensible  extent  at  least,  by  the  use  of  the  jacket. 

*  See  Appendix  for  process  of  transformation  of  Eq.  6,  p.  434. 


THERMODYNAMICS  OF  THE  STEAM-ENGINE.          445 
For  this  case,  we  have  found,  following  Rankine, 
H' 

V=^ 
1  dT 

in  which  the  latent  heat  of  evaporation,  //',  may  be  expressed 
conveniently  by  the  expression,  derived  from  Regnault, 

H*  =  a-bTt    .......     (i) 


in  which,  in  British  measures,  a  =  1,109,550  foot-pounds,  and 
b  =  540-4.     Then,  for  this  case,  b\  is  as  before,  and 


{/,=  / 
•// 


"«//= 


=  a\oge-6(Tt-TJ,    ....    (2) 
-*t 

and,  adding  Or,=/A. 


.     (3) 
-«» 

The  net  work  done  is  measured  by  the  value  of  £/,  as  above, 
less  the  work  of  back-pressure  on  the  opposite  side  of  the  pis- 
ton, resisting  its  advance,  which  work  is 

U,  =  vj>,*  .........     (4) 

when/,  is  the  total  back-pressure,  and 

Um=U>  +  Um-U.  ......    (5) 

Thus  the  net  work  done,  when  the  expansion  is  adiabatic,  is, 
per  unit  of  weight,  as  has  been  seen, 


44^  A    MANUAL    OF   THE   STEAM-ENGINE. 

and,  as  now  shown,  for  saturated  steam,  in  a  jacketed  engine, 

A-A);  .   .   (6) 


in  which  expressions  the  pressure  and  corresponding  tempera- 
tures are  either  known  or  may  be  obtained  from  the  steam- 
tables. 

In  all  cases,  the  total  heat  demanded  is  that  required  to 
raise  all  the  water,  used  in  cylinder  and  jacket,  from  the  tem- 
perature at  which  it  is  received  into  the  boiler  up  to  that  of 
evaporation,  and  to  produce  from  it  steam  of  the  temperature 
and  pressure,  J",  ,  pt  ,  at  which  its  expansion  in  the  steam-cylin- 
der begins.  The  heat  transformed  into  mechanical  work  is 
always  measured  by  the  work  performed,  as  shown  by  the  in- 
dicator-diagram, and  the  difference  between  the  total  amount 
of  heat  expended  and  the  thermal  equivalent  of  the  net  work 
done,  as  thus  measured  by  the  area  of  the  diagram  exhibiting 
the  cycle  worked  through,  is  discharged  from  the  system  as 
unutilized  heat. 

In  this  second  typical  ideal  case,  the  steam  is  assumed  to 
be  maintained  in  the  dry  and  saturated  condition  by  continually 
supplying  to  it,  as  it  expands,  so  much  heat  from  the  jacket  as 
will  prevent  that  liquefaction  which  would  take  place  in  the 
course  of  that  adiabatic  expansion  which  would  occur  in  a  non- 
conducting cylinder.  Since  this  involves  the  supply  of  heat 
at  all  temperatures  intermediate  between  that  of  the  "prime" 
steam  and  that  of  exhaust  and  back-pressure,  the  efficiency  of 
heat  so  supplied  must  be  less  than  that  of  the  heat  entering 
with  the  boiler-steam.  This  method  is  therefore  a  method  of 
waste  of  steam  and  of  heat,  as  will  be  shown,  more  fully,  later, 
by  computation.  This  introduction  of  a  wasteful  expedient 
will,  however,  be  seen,  in  the  real  engine,  to  have  for  ivs  purpose 
the  reduction  of  a  greater  waste  ;  and  the  net  result  is  usually 
found  to  be  a  sensible,  and  often  an  important,  gain.  More 
heat  is  supplied  than  in  the  first  typical  case,  and  more  work 
is  done,  per  pound  of  steam  ;  but  the  work  is  increased  in  less 
proportion  than  the  heat-supply. 


THERMODYNAMICS  OF   THE  STEAM-ENGINE.          447 

The  condensation  of  steam  expanding  adiabatically  may  be 
neglected  at  low  ratios  of  expansion  ;  but  it  becomes  very  con- 
siderable, as  shown  elsewhere,  at  large  ratios,  and  the  jacket 
must,  in  such  cases,  supply  large  amounts  of  heat.  The 
assumption  here  made  as  to  the  effective  operation  of  the 
jacket  may  be  taken  to  be  that  of  nearly  maximum  value.  In 
the  compound  engine,  this  condensation  is  cumulative,  and  is 
not  reduced  or  affected  by  the  action  which  distinguished  that 
type  and  gives  it  its  efficiency  in  the  case  of  the  real  engine. 

Could  the  action  of  the  jacket  be  made  effective  in  the 
manner  here  assumed,  and  not  a  source  of  waste  during  the 
exhaust  period,  the  ideal  and  the  real  engine  would  have  a 
sensibly  common  efficiency.  Experience  indicates  that  a  jacket 
of  such  effective  action  as  to  produce  dry  and  saturated  steam 
at  the  end  ef  the  expansion-period  actually  does  approximate 
most  closely  to  the  ideal  ;  but  in  any  given  case,  this  can  only 
occur  under  very  nicely  adjusted  and  unstable  conditions. 

114.  The  Efficiency  of  Cyclical  Operations  is  evidently 
always  measured  by  the  ratio  of  the  net  work  done  by  the 
working  fluid  to  the  work-equivalent  of  the  total  heat-energy 
sent  into  the  engine,  and  either  transformed  or  simply  trans- 
ferred with  reduction  of  temperature.  To  determine  this  effi- 
ciency, therefore,  it  is  only  necessary  to  find  a  method  of 
measuring  the  total  quantity,  //,  of  heat  supplied,  and  the  net 
work,  Um  performed  by  the  fluid,  and  the  efficiency  is  then 


The  total  heat  supplied  to  steam,  dry  and  saturated,  per 
unit  of  weight,  is  given  in  the  "  steam-tables."  When  super- 
heated, additional  heat  of  the  amount 

H=K(Ts-T,)w 


is  demanded,  T,  —  Tt  being  the  range  of  temperature  added  by 
superheating.     The  work  performed  is,  in  practice,  obtained  by 


44^  A    MANUAL    OF    THE    STEAM-ENGINE. 

the  use  of  the  "  steam-engine  indicator,"  and  is  measured  by 
the  area  of  its  diagram.  Dividing  the  work  represented  by  the 
latter,  as  performed  in  the  unit  of  time,  by  the  mechanical 
equivalent  of  the  total  heat  supplied  to  the  steam  passing 
through  the  engine  in  the  same  time,  the  efficiency  is  obtained. 

In  the  ideal  steam-engine,  this  usually  varies,  under  familiar 
practical  conditions  as  to  temperature  and  pressure,  from  ten 
to  about  twenty  per  cent,  and,  in  real  engines,  from  about  fif- 
teen per  cent  down  to  five,  or  even  less  ;  the  difference  being 
due  to  the  wastes  which  have  been  described. 

The  equations  obtained  on  the  assumption  that/z'"  =  const., 
using  n  =  1.0646  for  saturated  steam,  n  —  1.135  f°r  adiabatic 
expansion  of  steam  initially  dry,  and  n  =  1.333  f°r  superheated 
steam,  or  steam  gas,  give  fairly  approximate  results,  as  com- 
pared with  the  exact  expressions  just  given. 

Assuming,  as  is  usually  approximately  true,  that  the  expan- 
sion is  hyperbolic,  we  always  have 

pv  =  const., 
and 


whence,  as  seen  in  the  diagram,  the  total  work  of  the  isothermal 
and  isopiestic  compression,  during  the  exhaust  period,  is  equal 
to  that  of  the  steam-stroke  up  to  the  point  of  cut-off,  and  the 
net  work  performed  is  that  done  during  expansion  after  cut-off, 
and  this  is  substantially,  as  elsewhere  shown,  the  equivalent  of 
the  latent  heat  of  expansion  ;  which  is  thus  also  the  measure 
of  the  useful  work  per  stroke. 

Efficiency  of  fluid  may  be  measured  by  the  ratio  of  the 
quantity  of  heat-energy  demanded  in  the  unit  of  time  by  the 
ideal  engine,  of  efficiency  unity,  to  the  quantity  actually  con- 
sumed per  indicated  horse-power.  Per  minute,  therefore, 

42.75  B.T.U. 

-Q-  -; 

when  Q  is  the  last-mentioned  quantity  in  B.  T.  17. 


THERMODYNAMICS  OF   THE  STEAM-ENGINE.          449 

115.  The  Conditions  of  Maximum  Efficiency  of  Fluid 
are  substantially  the  same  in  all  forms  of  heat-engines,  and  are. 
as  stated  as  early  as  1824  by  Carnot  for  the  ideal  engine. 
maximum  range  of  temperature,  and  the  reception  of  all  heat 
at  the  higher,  and  its  rejection  wholly  at  the  lower,  tempera- 
ture. For  the  real  engine,  another  essential  condition  is  the 
reduction  of  wastes  from  the  exterior  by  conduction  and  radia- 
tion, and  by  initial  condensation  on  the  interior  of  the  working 
cylinder,  to  a  minimum. 

For  vapor  and  for  gases,  alike,  the  maximum  limit  of 
efficiency  is 

800  -  6co 


for  example   for  the   not   uncommon  absolute   temperatures 
8ooc  F.  and  600°  F. 

In  the  ideal  steam-engine,  steam  is  produced  and  isother- 
mally  expanded,  in  boiler  and  engine,  at  the  highest  possible 
pressure  and  temperature,  and  is  then  reduced,  by  perfectly 
adiabatic  expansion,  to  the  lowest  possible  pressure  and  tem- 
perature, and  is  compressed,  or  is  rejected  isothermally.  at  this 
minimum.  Where  the  pressure  has  a  limit,  superheating  is  re- 
sorted to  to  increase  the  temperature  of  the  fluid  and  the  range 
of  temperature  worked  through.  In  real  engines,  the  magni- 
tude of  the  losses  by  conduction  and  radiation,  and  especially 
internal  wastes,  modify  the  conditions  of  maximum  efficiency. 
restricting  the  economical  range  of  adiabatic  expansion,  and 
thus  limiting  the  attainable  efficiency.  This  subject  will  be 
considered  at  some  length  in  a  later  portion  of  this  work.  The 
quantity  of  heat  required,  in  doing  a  given  amount  of  work,  in 
the  real  engine,  will  be  found  to  be  almost  invariably  very 
greatly  in  excess  of  that  computed  for  its  ideal  representative, 
and  the  gain  by  increased  pressure  and  temperature  and  by 
expansion  will  be  seen  to  be  seriously  diminished  by  the 
causes  operating,  in  the  manner  already  described,  in  all  actual 
heat-engines. 


450  A    MANUAL    OF   THE   STEAM-ENGINE. 

Maximum  efficiency  can  only  be  secured,  as  in  the  ideal  en- 
gine, by  adiabatic  expansion. 

116.  The  Theory  of  the  Efficiency  of  Ideal  Engines 
applying  steam  or  other  vapor  as  the  working  fluid  is  simple 
and  exact ;  but  the  results  obtained  in  this  case  differ,  usually, 
very  widely  from  those  practically  reached  in  the  real  engine  of 
which  it  is  the  representative.  These  differences  are  consid- 
ered elsewhere ;  in  the  present  article  the  ideal  case,  only,  is  to 
be  illustrated. 

The  quantity  of  heat,  Hl ,  being  received  by  the  engine,  and 
the  amount,  //,,  emitted,  the  difference,  Hl  —  ffy,  is  converted 
into  work.  The  efficiency  is,  therefore, 


HI 

Following  Rankine's  method  of  treatment,  we  have  (§  112), 
en  re'sume',  when 


—  =  r  —  ratio  of  expansion  ; 

A  >  A  i  A  =  initial,  terminal,  and  back  pressures,  absolute  ; 

7",  ,  Tu,  T3,  TI,  Tb,  T6  =  temperatures  of  entering  steam,  of 
steam  at  the  end  of  adiabatic  expansion  and  during  the 
return  stroke,  and  of  feed-water,  of  condensation,  and  of 
atmosphere,  respectively  ; 

and  when  the  work  of  unity  of  volume  is  considered 


for  the  ratio  of  expansion  ; 


THERMODYNAMICS  OF  THE  STEAM-ENGINE.          45 1 
the  work  of  the  fluid  per  cubic  foot ; 

^  =  ,.-A=A (3) 

is  the  mean  effective  pressure ;  which  also  measures  the  work 
done  per  unit  of  volume  swept  through  by  the  piston ; 

TT    TJ 

-Jr-i=[/A(3T.-^  +  Al-r,     ...     (4) 

the  heat  expended  per  unit  of  that  volume ;  and  the  efficiency 
of  the  fluid  becomes 


The  quantity  of  feed-water  demanded  will  be  measured  by 
D, :  or,  per  unit  of  volume  of  cylinder, 

W=^ (6) 

The  heat  emitted  will  be 

fia=<S^ (7) 

per  unit  of  volume  of  cylinder,  and  the  volume  swept  over  by 
the  piston,  per  minute,  per  horse-power,  must  be  equal  to 


33.000      33.000  r 
p.  ™,    " 


.     ....    (8) 


y        4500  _  4500*; 

in  British   and   metric   measures,  respectively,  the   heat   ex- 
pended per  hour  being 

fft       1,980.000 
Ht  =  1,980,000-^  = j , 


Hm       270,000 
H*  =  270,000  -y-  =  — £ — , 

in  the  two  measures,  respectively. 


...     (9) 


452  A    MANUAL   OF   THE   STEAM-ENGINE. 

Also,  adopting   the   approximate    formulas   for   this  case 
(§  102),  much  simpler  expressions  become  available,  thus: 

r  =  vy  -r-  vt  ;    ...........  (10) 

p*=pr-*\      .........     .     .  (ii) 

pm  =  A(Ior~  l—  9r  ~  ^)  ;  .......  (I2) 

pt  =  pl(ior-  -9^'V°)-A;  .....  (13) 

and  the  work  per  unit  of  steam  admitted  is 

gr-^)  -rpt,  .......  (14) 


in  which  the  approximate  exponent  n  =  \°-  may  be  used  for  the 
average  case  as  sensibly  correct. 

Rankine  has  also  shown  that  the  heat  demanded,  in  foot-lbs. 
per  cubic  foot  of  cylinder,  may  be  taken  as 

.13,333AJf4000 


while  the  pressure  which,  acting  through  the  volume  of  the 
cylinder,  or  the  equivalent  "  heat-pressure,"  which  would  do 
the  same  amount  of  work,  is,  in  pounds  per  square  inch, 


The  Efficiency  of  Steam  kept  Dry  and  Saturated,  expanding  in 
a  cylinder,  permeable  to  heat,  and  receiving  just  sufficient  from 
any  source,  as  a  "  steam-jacket,"  to  keep  the  fluid  in  that  con- 
dition, is  computed,  as  already  shown,  in  part,  thus  : 


(15) 

U'  =  a  log,  ^-b(T-  T.)  +  »,( A  -A)-    •     (16) 


THERMODYNAMICS  OF   THE   STEAM-ENGINE.          453 

The  heat  expended  per  unit  weight  of  steam  is 


-«rlf  .  (17) 


TTf 

and,  per  unit  of  volume  of  piston-path,  —  . 

"• 

The  values  of  /,  and  Tt  are  obtained  from  Regnault's  ex- 
periments, and  are  given  in  all  "  steam-tables." 

>•  =  £'    .......    <I8> 

rrr 


Or,  adopting  the  approximate  formulas, 
=  constant  ; 


09) 


Vl 

A'-«;     .......  (21) 

~H)-/J^;    .....  (22) 

«);  ..........  (23) 

-A.     .  (24) 


454  A    MANUAL   OF   THE   STEAM-ENGINE. 

It  is  found  that  the  heat  demanded  per  pound  of  steam 
supplied  is  very  nearly 


^  =  iS*M  =  i5ir.;    ....    (25) 
Then  the  efficiency 

E-U'-^-ii^r——^-         (26) 

-'-~  * 


Table  III,  in  the  Appendix,  shows  the  values  of  the  "  cut- 
off," -  ,  the  ratio  /,  -j-  rpm  ,  of  total  work  performed  up  to 

point  of  cut-off  to  the  total  work  (inclusive  of  that  below 
the  back-pressure  line)  done  at  each  stroke,  the  reciprocal, 

rPm  -=-A>  °f  that  ratio,  and  the  ratios,  —  L  and  -A  for  assumed 

f  in  f\ 

values  of  r,  adopting  the  values  of  »  taken  above  in  the  approx- 
imate equations. 

117.  Examples  of  Application  of  principles  and  the 
theory  to  ideal  cases  of  application  of  steam,  illustrating  the 
limit  of  efficiency  which  would  be  attainable  at  familiar  press- 
ures, could  all  wastes  by  conduction,  radiation,  and  leakage  be 
entirely  prevented  by  the  use  of  a  working  cylinder  of  non- 
conducting material,  are  the  following  : 

(i)  Assume  one  pound  of  steam,  at  an  absolute  pressure  of 
100  pounds  per  square  inch,  to  expand  adiabatically,  in  an  en- 
gine-cylinder of  perfectly  non-conducting  material,  down  to  25 
pounds,  and  to  be  exhausted,  on  the  return-stroke,  into  the  at- 
mosphere, the  back-pressure  being  15  pounds  per  square  inch. 
It  is  desired  to  find  the  ratio  of  expansion,  the  efficiency  of  the 
fluid,  and  the  weight  of  steam  and  of  fuel  demanded,  per  horse- 
power per  hour,  the  feed-water  being  supplied  at  I  IO°  Fahr., 
and  the  evaporation  9  pounds  per  pound  of  coal. 

By  the  exact  formulae  for  this  case  (§  112),  the  following 
figures  are  obtained  : 


THERMODYNAMICS  OF  THE.  STEAM-EXG1XE,          455 
DATA. 

pt  =  14*400  Ibs.  per  sq.  ft.;  7",  =  788°^ ; 
PI  =  100  Ibs.  per  sq.  in.;  7",  =  7°1'7'* 
/,=  3,600;  A-=  I57.H5; 

/>,=         25;  A-    45,68o; 

/,=    2,160;  A^    CX2305; 

/»s  =         15 ;  D^—   0106256. 

Evaporation,  9  Ibs.  water  per  Ib.  coaL 

RESULTS. 
Ratio  of  Expansion  : 


=  3-38. 

Work  per  cubic  foot  of  Steam  admitted: 


taking  the  data,  as  given  above, 
=  22,547  foot  Ibs. 

Effective  Pressure  : 


=  46.31  Ibs.  per  square  inch. 
Heat  expended  per  cubic  foot  of  Steam  admitted; 


=  772  x  0.2305  (788.9  -  571-2)  +  157-145 

=  195,884  foot-lbs. 


456  A    MANUAL   OF   THE   STEAM-ENGINE. 

Heat  per  cubic  foot  of  Cylinder  and  equivalent  Heat-pressure  : 


^,  195,884 

=  -y-=A  =  "^3"8~"=  57'954  foot-lbs'; 

—  57)954  Ibs.  Per  scl-  fa-  —  4°2-4  IDS-  per  sq.  inch. 
Efficiency  of  the  Steam  : 


Feed-water  per  cubic  foot  of  Cylinder  per  stroke  : 


^^. 

r          3-38 

Volume  swept  through   by  the  Piston  per  indicated  horse- 
power per  hour  : 

60*^33,000      1.980.000 
/  6671 

Weight  of  Feed-water  and  of  Steam  per  I.  H.  P.  per  hour  : 

W  =  a.o682  X  296.8  =  20.34  pounds. 
Fuel  per  I.  H.  P.  per  hour  : 

W"  —  20.34  -r-  9  ==  2.26  Ibs. 

(2)  The  same  case  by  the  approximate  formulas  :  — 
Ratio  of  Expansion  and  "  Cut-off"  : 

r  =  3-38  ;    -r  =  0.296. 
Mean  Total  Pressure  :* 

Pm 

pm  =  IOO  X  —  =  100  X  0.634  =  63.4  Ibs.  per  sq.  inch. 

*  See  table  for  —  -  ,  and  interpolate. 


THERMODYNAMICS  OF   THE   STEAM-ENGINE.          457 
Mean  Effective  Pressure  : 

A  =  Pm  -  A  =  63-4  -  15  =  48-4  lbs.  per  sq.  inch. 

Same  by  exact  formula  =  46.3  ;  difference  =  2.1. 
Pressure  equivalent  to  Heat  expended: 

2  =  lidl  =  402.;  lbs.  per  „.  inch. 


Same  by  exact  formula  =  402.4;   difference  0.3. 
Efficiency  : 

Pe 

E  =  —  =  0.120. 
A 

Same  by  exact  formula  =  0.115  ;  difference  0.005. 
Feed-water  and  Steam  per  cubic  foot  of  Cylinder,  and  per 
stroke  : 


r          3-35 
Volume  swept  through  by  piston  per  L  H.  P.  per  hour: 


.=  =  ft 

48^  X  144         6069.6 

Feed-water  and  dry  Steam  per  I.  H.  P.  per  hour  : 
W  =  0.0682  X  284  =  19.37  lbs. 

Same  by  exact  formula  =  20.34;  difference  0.97  lb.,  or  five 
per  cent. 

Fuel  per  I.  H.  P.  per  hour  : 

W"  =  19.37  -s-  9  =  ^'S  lbs- 

(3)  Assume  one  pound  of  dry,  saturated  steam  to  expand 
in  a  jacketed  cylinder,  receiving  just  sufficient  heat  from  the 
jacket  to  prevent  condensation  by  doing  work.  To  find  the 


458  A    MANUAL   OF   THE    STEAM-ENGINE. 

efficiency,  etc.,  as  before,  when  the  data  are  as  follows,  the 
method  being  slightly  different  from  the  preceding  : 

/,  =  14,403;         vt  =  4.35  cu.  ft.  (by  table)  ; 
/>  =       10°  ;         v^  =  37.83  cu.  ft.  ; 
/a  =     1440  ;        W  -r-  W"  =  10. 
P,=        10  ; 
/.=      720; 

P,=       5; 

Ratio  of  Expansion  : 


4-35 
Work  per  pound  of  Steam  : 

U=  U,  -  U,  +  v,(fi,  -A);  (see  table  for  £7;) 
=  361,250  —  226,662  -j-  37-83  (1440  —  720)  =  161,826  ft.-lbs. 

Mean  Effective  Pressure  : 

U       161,826 
A=A,-A  =  -  =  —  — 

=  4277-7  Ibs.  per  sq.  ft.  =  29.7  Ibs.  per  sq.  inch. 

Available  Heat  : 

9 

L=  U,-  U*  +  ff,  -  h,  ;  (see  tables  ;) 
=  361,250  —  226,662  +  880,756  —  69,522; 
=  945,822  ft.-lbs. 


Heat-pressu  re  '  : 

945,822 

~^^ 

=  173.6      "     "     sq.  inch. 


L       945,822 

=      ~      =  25'502  lbs-  per  sq-  ft 


Efficiency  : 


THERMODYNAMICS  OF  THE   STEAM-EXGIXE.          459 
FfiAwater  amd  Steam  per  cubic  foot  traversed  bj  piston  : 

w=  —  =^=  -^-  =  00264  n>. 

rvt       r       37-83 

V'obtme  traversed  by  piston  per  /.  H.  P.  per  hour  : 

F=6QX33.ooo 
29-7XM4 

Feed-water  and  Steam  per  I.  H.  P.perhonr: 
W  =  00264  X  463  =  12.22  Ibs- 

Fuel  per  I.  H.  P.  per  konr: 

W"  =  12.22  -=-  9  =  1.36  Ibs. 

(4)  Same  case  by  approximate  formulas  (§112): 


.  =  A  X  035  =  ioo  X  0.35  =  35  HK.  per  sq.  inch  ; 
/.=/.  ~A=  35  -  5  =  30lbs-  per  sq.  inch; 


33.000  X  60 
Cubic  feet  traversed  per  hour  per  I.  H.  P.  = 


=  458. 

Fe  id-water  and  Steam  per  I.  H.  P.  per  konr  =  45»  X  0x1264 

—  12.09. 


4&0  A    MANUAL   OF    THE   STEAM-ENGINE. 

Fuel  per  I.  H.  P.  per  hour  =  12.09  -*•  9  =  !-34  IDS- 

The  differences  between  the  two  sets  of  results  are  seen  to 

be  about  one  per  cent,  only. 

(5)  Assume  the  following  data,  from  Rankine,  as  taken  from 

an  engine  constructed  for  a  somewhat  famous  ship,  the  Thetis, 

built  by  Rowan  &  Co.,  and  the  Messrs.  Scott :  * 

.  Engine  of  226  indicated  horse-power,  calculated  by  exact 

formulae : 

DATA. 

Bottom  of        Top  of 
Cylinder.       Cylinder. 

P 

Pressure  of  admission, io8i  104 

144 

Back-pressure,  — -- 3.3  4.0 

144 

Ratio  of  expansion,  r 16  14 

Temperature  of  feed-water,  Tt,  about  122°  Fahrenheit. 


CALCULATED    RESULTS. 

Bottom.  Top. 

Final  volume  of  I  Ib.  of  steam,  vy  =  rvl  .  .        64.27  58.52 

U,  —  Ut  ...............................     170,151  162,726 

",(A  -  A)-  •  •  -  ........................      21,286  19,382 


Work  of  i  Ib.  steam,  U'  ................     191,437        182,108 


Mean    effective    pressure   in    pounds   per 

inch.  -  __P™  -  A 
M4 


Mean  of  both  results  ...................  21.15 

Mean  observed  result  of  a  series  of  dia- 

grams ...............................  21.00 


Difference _[_  o.  1 5 

Being  within  the  limits  of  errors  of  observation. 

*  Steam-engine;  1859;  P- 407. 


THERMODYNAMICS  OF   THE   STEAM-EXGIXE  461 

Bottom.  Top. 

Heat  expended  per  pound  of  steam,  H' ...   9/5,301        966.524 
Equivalent  pressure  in  pounds  per  square 

inch,  ph  -r-  144 105  115 

Mean 1 10 

Efficiency, *  ~     0.196  0.188 

A 
Mean 0.192 

(6)  Same  case  calculated  by  approximate  formulae  : 


DATA. 

Lbs.  on  the 
square  inch. 

Mean  pressure  of  admission,  — -- io6j 

Back-pressure,  ^ 3-65 

Mean  cut-off.  —  =  .067  =  — . 

r  1S 


RESULTS. 

'Mean  gross  pressure,  ^-  =  io6j  X  .232 =  24.6 

Mean  effective  pressure,  -"- — — ,  calculated 20.9? 

observed..  2i.co 


Difference   —  0.05 

Pressure  equivalent  to  expenditure  of  heat  =  pk  -r-  144  1 1  o 

Efficienc>',  0.19. 

The  engine  was  a  two-cylinder  compound,  and  the  mean 


462 


A  MANUAL    OF   THE   STEAM-ENGINE. 


effective  pressure  has  reference  to  the  larger  cylinder,  which 
was  of  four  times  the  capacity  of  the  smaller. 

At  2^  pounds  of  steam  per  hour  per  horse-power,  for  effi- 
ciency unity,  this  performance  corresponds  to  13  pounds,  neg- 
lecting all  wastes  other  than  thermodynamic ;  and  to  1.44 
pounds  of  fuel  at  an  evaporation  of  nine  pounds  steam  per 
pound  of  coal.  These  figures  would  probably  be  increased  by 
not  less  than  20  per  cent  by  the  extra  thermodynamic  wastes ; 
or  to  15.6  pounds  of  steam  and  1.75  pounds  of  fuel,  nearly. 

Accepting  Rankine's  figures,  we  have  the  following : 


CONDENSING  STEAM-ENGINES  WITH    DRY   SATURATED  STEAM. 

BACK-PRESSURE,  /3  -f-  144,    ASSUMED   AT   4   LBS.    ON   THE   SQUARE   INCH. 


Examples. 

Ratio  of  Expansion,  r,  and  Effective  Cut-off,  -. 

(l)  /,  -4-   144  =  20. 

10. 

5- 

3-33 

2-5 

2. 

T-7 
0.6 

ol5 

t'.o 

8  8 

i«:i 

AVii1**'44'.'":: 

86 

Q 

Efficiency  of  steam  .  . 

•095 

.090 

.083 

•075 

.0625 

(2)  /,  •«-  144  =  40. 

16.2 

26.2 

29.6 

32.0 

,60 

A  -*-.i44  

124 

248 

310 

37ucc 

496 

620 

y 

(3)  P\  •+•  i44  =  60. 

(A,  -/3)-«-M4  

A  •*•  144  

14.8 

26.3 

34-9 

41.4 

*a 

50.0 

54-6 

56.0 

Efficiency  of  steam  .  . 

•159 

.140 

•'25 

.in 

.100 

.090 

•073 

.060 

(4)  /j  -t-  144  =  80. 

(A.  ->!>-•-  144  

21.  I 

36.4 

47-8 

56.5 

63.2 

68.0 

74-i 

76.0 

Efficiency  of  steam.  . 

I24 
.170 

248 
.147 

37-8 

.114 

620 

.102 

744 
.091 

992 
.074 

1240 

.061 

<5)  /i  •*•  144  =  ioo. 

</.->!)-••  M4  
A  •*•  144  
Efficiency  of  steam.  . 

27.4 
'55 

•'77 

.15° 

60.8 
465 

71.6 
620 
.115 

80.0 

775 
.103 

86.0 
930 
.092 

93-6 
1240 

•075 

96.0 
1550 

.062 

THERMODYNAMICS  OF  THE  STEAM-ENGINE,  463 

NON-COXDEXSIXG  STEAM-EXCISES  WITH   DRY  SATURATED 
STEAM. 

KACK-PKESSTKE  /i  -5-  144,   ASSTXED  AT    IS  L«&.  OX   THE  SQCAKE  ESCH. 


r.  Md  KffeOTC  Cw-Of,  1. 


•4     I  M     I    *-I     I    «-^i    I    mj» 

•-4      I    «-5      i|    »-«      (!    o.«      I    «_o 
1-4 


(«»»/I-*-"4«  = 


Taking  the  temperature  of  feed-water  at  such  a  point  as 
will  give  nine  pounds  of  water  evaporated  into  dry  steam  per 
pound  of  fuel,  for  the  condensing,  and  ten  pounds  for  a  non- 
condensing,  engine — a  heater  being  assumed  to  be  used — and 
2.5  pounds  of  steam  per  horse-power  per  hour  at  efficiency 
unity,  it  is  easy  to  make  a  comparison  of  the  probable  ideal 
and  the  probable  actual  efficiencies  of  these  various  engines  in 
terms  of  heat,  steam,  and  fuel,  demanded  per  unit  of  power  in 
the  unit  of  time. 

The  following  are  efficiencies  computed  for  the  perfect, 
ideal,  engine,  by  CotterilL  which  may  afford  equally  interesting 
comparisons :  * 


464 


A    MANUAL    OF   THE    STEAM-ENGINE. 


Therma! 

Lbs. 

Lbs. 

/, 

Units 

Steam 

Carbon 

Engine. 

F&. 

Ibs.  per 
sq.  in. 

I.EP. 

I.1TP. 

i.S?.rP. 

Efn- 
ciency. 

per  min. 

per  hour. 

per  hour. 

1 

401+461 

250 

195 

11.4 

0.8o6 

O.2I9 

Non-condensing;    J 
T3  =  212°  +  461°  F.' 

363  +  46  1 
341  +  461 
312  +  461 

1  60 
1  2O 
80 

233 
266 

329 

13-8 
I5.8 
19.9 

0.964 
I.  10 

1.36 

0.183 
0.161 

0.130 

287  +  461 

55 

427 

26.0 

J-77 

O.IOO 

341  +  461 

120 

M3 

7-5 

0.592 

0.299 

Condensing; 
Ts  =  100°  +  461°  F.' 

324  +  461 
293  +  461 
250  +  461 

95 
60 
30 

150 
I67 
203 

8.1 
9.0 

II.  2 

0.621 
0.691 
0.840 

0.285 
0.256 

O.2II 

228  +  461 

20 

230 

12.8 

0.952 

0.186 

Binary-vapor;       ( 
Steam  and  ether;    '•< 
Ta  —  60°  +  461°  F.  ( 

341  +  461 
293  +  461 

120 
60 

122 

138 

6.2 

7-3 

0.505 
o.57i 

0.351 
0.309 

Air-engine;          ( 
r3=6o°  +  46i0  F.I 

660  +  461 

— 

79-8 

— 

0-33 

0.536 

Professor  Cotterill  has  shown  that  if  the  heat  of  the  feed- 
water  could  be  raised  to  boiler-temperature,  by  means  of  a 
heater  so  constructed  as  to  receive  heat  by  a  graded  system  of 
transfer,  such  that  the  pressures  of  steam  at  transfer  could  be 
gradually  varied  throughout  the  whole  range,  the  steam-engine 
might  be  given  the  efficiency  of  the  Carnot  cycle.  The  heat 
expended  would  be 


that  rejected, 


and  the  efficiency  would  be 


L  is  the  latent  heat  of  evaporation,  supplied  by  the  boiler. 


*  Cotterill;  2d  ed.,  p.  420. 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


465 


The  following  table  gives  the  multipliers  required  to  de- 
termine the  mean  absolute  preasure  of  steam  when  the  initial 
pressure  and  the  ratio  of  expansion  are  known.  The  product 
of  the  tabulated  constants,  by  the  initial  pressure.  /, ,  is  the 
required  mean  absolute  pressure. 

CONSTANTS   FOR   MEAN    AND   TERMINAL   PRESSURES. 


II.  Dry  at  Tempera- 


III.  Condensing  at 


Cut-off. 

r" 

&£™l          '  sr-L 

in.   v-uuucuajnjj  at 

Mean. 

Terminal.    1       Mean. 

Terminal.          Mean. 

Terminal. 

• 

\ 

.847 

•5                   -839              -479              -833              -463 

' 

t 

-7 

•333 

.687              .311              .678              .295 

-597 

•25 

•582              .229              .571              .214 

.522 

.2 

.506 

.181 

•495 

.167 

.465 

.167 

•449 

•149 

437 

•137 

.421 

.143 

-405 

.126 

•393 

.115 

.383 

.125 

.369 

.11 

•357 

.099 

-355 

.in 

•339 

.097 

.328 

.087 

1 

T 

.330 

.1 

•314 

.087 

.303 

.077 

.309 

.091 

.293 

.077 

.282 

•07 

I- 

.290 

.083 

•275 

.071 

.264 

-063 

: 

•274 

.077 

.259              .065 

.249 

.058 

t 

.26 

.071 

.245              .06 

•235 

•053 

1 

•247 

.067 

.233 

.056 

.223 

.049 

! 

•  236 

.062 

.222                  .052                  .212 

.046 

-992 

-875 

.991             .868             .991 

.862 

I 

.966 

•75 

.964                  .737                  .962 

-726 

1         -919 

.025              .914              .607              .911 

•593 

{ 

\               -743 

•375              -732              -353              -723              -336 

Case  I  is  that  of  steam  kept  at  the  initial  temperature  while 
expanding:  Case  II  is  that  of  Rankine's  jacketed  engine; 
Case  III  is  that  of  the  non-conducting  cylinder.  (See  also 
Table  III,  Appendix.) 

The  fall  in  pressure,  along  the  admission-line,  up  to  the 
point  of  cut-off,  in  well-designed  engines,  having  detachable 
cut-off  valves,  in  the  best  cases,  should  not  exceed  about  one 
pound  per  square  for  each  one-tenth  stroke  up  to  that  point. 
It  is  usually  much  more,  in  other  types  of  engine. 

The  true  ratio  of  expansion  is  measured  by  the  quotient: 
volume  of  cylinder,  plus  clearance,  at  the  point  of  actual  "  cut- 


466"  A    MANUAL    OF    THE    STEAM-ENGINE. 

off,"  divided  by  volume  of  cylinder,  plus  clearance,  taken  at  the 
end  of  expansion  ;  which  point  is  seldom  coincident  with  the 
end  of  the  stroke. 

118.  The  Limit  of  Actual  Efficiency  is  now  determined. 
From  what  has  already  been  stated,  in  reference  to  the  differ- 
ences arising  between  the  ideal  and  the  real  steam-engine,  it 
will  be  understood  that  the  quantities  of  steam  and  of  fuel 
above  given  are  magnitudes  representing  limits  which  may  per- 
haps be  approached,  but  which  can  never  be  actually  reached, 
in  practice.  The  consumption  of  heat,  steam,  and  fuel,  by  even 
the  best  types  of  steam-engine,  exceeds  these  figures  by  from 
one  fourth  to  one  half ;  the  excess  varying  with  circumstances, 
already  described,  affecting  the  physical  wastes. 

Assuming  as  data  the  same  initial  and  back  pressures,  and 
the  same  ratio  of  expansion,  and  computing  the  expenditure  of 
heat,  steam,  and  fuel  for  the  cases  of  the  non-conducting  and 
the  jacketed  engine,  it  will  be  found  that  the  latter  has  lower 
efficiency.  In  practice,  however,  it  is  found  that  the  enclosing 
of  the  working  cylinder  in  a  steam-jacket  may  produce  real 
economy;  it  is  thus  evident  that  the  advantages  attendant  upon 
the  second  of  the  two  above-described  methods  of  working 
steam  are  due  wholly  to  causes  distinguishing  the  real  from  the 
ideal  case.  In  the  ideal  engine,  keeping  the  steam  saturated, 
during  expansion  with  reduction  of  pressure  and  temperature, 
is  disadvantageous. 

Comparing  the  curves,/^  =  const.,  pv1-1'^  =  const., pv1-^  = 
const.,  for  the  several  methods  of  expansion,  it  is  seen  that  the 
curve  for  saturated  steam  lies  nearer  the  curve  of  Boyle  and 
Mariotte  than  does  that  of  superheated  steam ;  and  that,  vol- 
ume for  volume,  steam  kept  dry  and  saturated  does  more  work 
than  even  superheated  steam,  the  initial  temperature  being  the 
same.  Weight  for  weight,  however,  superheated  steam  does 
most  work,  and  has  the  higher  efficiency;  since  it  contains  more 
heat  than  saturated,  and  can  expend  it  in  work  more  efficiently 
in  proportion  to  its  higher  temperature  and  its  less  liability  to 
condensation  upon  the  surfaces  of  the  steam-cylinder  previous 
to  the  commencement  of  expansion. 


THERMODYNAMICS  OF   THE   STEAM-EXGIXE.          467 

119.  The  Vapor-engine  Cycles,  Figs.  137, 138,  differ,  often 
very  greatly  in  form,  from  those  familiar  as  illustrated  by  air- 
and  gas-engines.    The  isothermal  line  being  isopiestic,  the  first 
portion  of  the  diagram,  traced  during  expansion,  instead  of  being 
an  equilateral  hyperbola,  becomes  a  horizontal  straight  line,  a 
line  parallel  with  the  axis  of  abscissas.    Adiabatic  expansion  is 
represented  by  a  line  closely  resembling  that  for  gases,  but  one 
which  falls  somewhat  more  rapidly,  and  thus  deviating  also 
from  the  common  hyperbola,  as  has  been  already  indicated. 
The  ideal  cycles  are  usually  composed  of  these  curves,  and  often 
of  these  combined  with  lines  of  equal  pressure  and  of  equal  vol- 
ume.    In  the  case  of  real  steam,  or  vapor,  engines,  the  actual 
cycles  and  curves  approximate  more  or  less  closely  to  those  of 
the  corresponding  ideal  engine,  accordingly  as  the  engine  is 
more  or  less  well  designed,  well  constructed,  and  well  operated : 
but  some  considerable  differences  almost  invariably  exist. 

The  action  of  the  metal  in  conducting,  and  in  radiating,  heat 
to  and  from  the  working  substance  causes  changes  in  the  form 
of  the  lines  composing  the  diagram,  and  the  imperfect  action  of 
the  valve-gear,  the  mechanism  controlling  the  introduction  and 
discharge  of  the  working  fluid,  produces  considerable  variations 
of  the  forms  of  the  lines,  and  especially  of  their  junctions.  In 
the  designing  of  engines,  and  in  computing  their  probable 
power  and  efficiency,  ideal  diagrams  are  employed  which  are  so 
chosen  and  laid  down  as  to  represent,  with  as  close  approxima- 
tion as  possible,  the  actual  cycle  of  the  engine. 

120.  The  Distribution  of  Energy  in  Real   Engines  is 
Wtly  different  from  that  thus  far  found,  in  the  study  of  the 
ideal  engine.     The  latter  is  a  purely  thermodynamic  system  ; 
while  the  former  illustrates  not  only  the  thermodynamic  trans- 
formations and  transfers  of  heat-energy,  but  also  transfers  and 
losses  by  every  method  of  conduction,  convection,  and  radia- 
tion rendered  possible  by  the  nature  of  the  material  employed, 
and  bv  the  structure  of  the  machine.     Of  all  the  heat  received 
by  the  engine  from  the  boiler,  and  temporarily  stored  in  the 
steam  supplied  to  the  engine,  but  a  small  portion  is  commonly 
transformed  into  useful  work,  even  in  the  ideal  case ;  while,  in 


468  A   MANUAL   OF   THE   STEAM-F.NGINE. 

the  actual  engine,  as  has  been  shown,  wastes  occur,  in  addition 
to  the  unavoidable  thermodynamic  loss,  which  often  result  in 
doubling,  and,  in  small  engines,  much  more  than  doubling, 
the  consumption  of  heat,  steam,  and  fuel,  and  the  cost  of  their 
supply. 

Of  all  these  losses  and  wastes,  that  by  internal,  or  so-called 
cylinder,  condensation  is  that  which  offers  the  problem  with 
which  the  engineer  is  now  most  concerned.  As  elsewhere  re- 
marked by  the  Author,  "a  comparison  of  the  quantities  of  steam 
demanded  to  supply  an  engine  thermodynamically  '  perfect ' 
with  the  actual  quantities  required  by  even  the  best  of  engines 
exhibits  so  wide  a  difference  that  it  becomes  obvious  that  the 
determination  of  the  efficiency  of  an  engine,  and  the  solution 
of  questions  involving  those  of  heat-expenditure,  are  not  prob- 
kms  in  thermodynamics,  simply.  The  mathematical  theory 
of  the  steam-engine  is  not  yet  in  so  satisfactory  a  state — and 
cannot  be  until  the  correct  theory  of  this  transfer  of  waste  heat 
can  be  introduced  into  it — that  the  engineer  can  often  use  it 
in  every-day  office  work,  with  much  confidence,  unless  checked 
by  direct  experiment."  * 

The  wastes  in  the  actual  engine  are  found,  by  examination 
of  the  results  of  many  trials,  to  vary  greatly  in  even  what  is 
considered  good  practice.  The  loss  at  the  boiler,  in  ash,  from 
the  recorded  weight  of  fuel  is  from  about  6  per  cent,  with  the 
best  coals,  to  10  and  15,  with  very  good  fuel,  and  up  to  20  and 
25  per  cent  with  bad  samples.  The  boiler  should  not  "prime" 
more  than  3  or  5  per  cent,  even  if  it  does  not  produce  dry 
steam  ;  but  double  these  figures  are  not  uncommon.  In  large 
jacketed  engines  using  saturated  steam,  the  jackets  may,  if  in- 
efficient, condense  less  than  five  per  cent  of  the  steam  made; 
but,  if  efficient,  they  may  condense  an  amount  which  approxi- 
mately measures  the  work  done  by  the  engine — 10  per  cent  or 
more — or  they  may  even,  by  extensive  transfer  of  heat  during 


*  "On  the  Several  Efficiencies  of  the  Steam-engine,  and  on  the  Conditions 
of  Maximum  Economy."  Trans.  Am.  Soc.  of  Mechanical  Engineers;  April  1882. 
Journal  of  the  Franklin  Institute;  May  1882. 


THERMODYNAMICS  OF   THE   STEAM-EXGI\'E.          469 

the  period  of  exhaust,  or  when  the  prime  steam  is  wet,  cause  a 
waste  of  considerably  larger  magnitude.  The  use  of  a  steam 
feed-pump  may  waste  3  to  5  per  cent,  and,  in  defective  con- 
structions, considerably  more.  Independent  air-pumps,  now 
quite  common,  will  increase  the  wastes  5  or  10  per  cent,  and, 
where  not  efficient,  may  make  this  item  as  much  as  15  per 
cent. 

The  magnitude  of  the  waste  of  heat  by  internal  alternate 
storage  and  restoration  is  variable,  not  only  with  the  conditions 
of  operation,  but  also  with  the  character  of  the  working  fluid. 
It  is  comparatively  small  with  gases,  large  with  condensable 
vapors,  and  peculiarly  large  with  saturated  or  wet  steam.  The 
ratio  of  work  done  per  pound  of  the  working  fluid  to  that  which 
it  might  perform  in  a  non-conducting  cylinder  measures  a  cer- 
tain efficiency  which  we  may  call  the  Working  Efficiency  of  the 
Fluid. 

The  following  tabular  statement  of  the  distribution  of 
losses  and  of  quantities  of  heat  applied  usefully,  in  a  marine 
engine,  as  given  by  Hunt  and  Skeel,*  corresponds  to  a  con- 
sumption of  2£  pounds  of  coal  per  horse-power  per  hour.  The 
best  engines  of  the  present  time  demand  two  thirds  this  quan- 
tity or  less. 

One  hundred  pounds  of  coal  contain  in  heat-units 

Deduct  heat-units  for  weight  of  ash 


Total  number  of  heat-units  in  100  pounds  coal 1,200.000 


Available  heal 1,200,000  100 

Loss  of  beat  by  the  chimney MO.OOO  ,   i6| 


Available  to  make  steam 1,000,000  83$ 

Loss  by  leakage  and  condensation aoo.ooo  16} 


Available  to  do  work  on  the  piston 

Loss  of  heat  rejected  from  cylinder 660,000  55 


"Methods  of   Testing  Steam-engines,"  etc.     Journal  of  the  Franklin 
;  Dec.  1874- 


47°  A    MANUAL    OF   THE   STEAM-ENGINE. 

Heat-units.  per  cen 

Transformed  into  work 140,000  ii£ 

Loss  by  frictional  resistances 40,000  3$ 

Available  to  turn  the  screw 100,000  Si- 
Loss  by  useless  resistances 20,000  i  j 


Balance  usefully  applied  in  propulsion 80,000  6£ 

121.  The  Method  of  Operation,  in  the  process  of  distri- 
bution of  energy,  in  the  actual  case,  is  the  following :  The 
supply  of  energy  delivered  to  the  machine  is  brought  from  its 
storage  reservoir,  the  steam-boiler,  by  the  steam  which  is  its 
vehicle,  in  the  form  of  heat.  The  engine  converts  a  small  part  of 
this  energy  into  the  mechanical  form,  and  applies,  it  to  the  per- 
formance of  work ;  while  the  remainder  is  wasted  by  transfer, 
untransformed,  to  surrounding  masses,  such  as  the  atmosphere, 
the  environing  walls,  and,  in  the  case  of  the  condensing  engine, 
to  the  water  by  which  the  steam  is  condensed  and  which  con- 
veys the  heat  thus  acquired  into  the  water-ways  of  the  country. 
Of  the  work  developed  by  conversion  of  heat-energy,  a  part  is 
expended  in  driving  the  engine  itself,  and  is  therefore  a  waste; 
while  the  remainder  is  applied  to  the  purpose  for  which  the 
engine  is  designed.  Of  the  untransformed  and  wasted  heat, 
the  greater  part,  in  the  very  best  engines,  is  that  inevitable  waste 
which  the  second  law  of  thermodynamics  indicates,  and  the 
measure  of  the  proportion  of  which,  in  the  perfect  engine, 

must   always   be  ~ ;    the   remainder  is  mainly  transferred  to 

the  "  exhaust "  by  the  process  of  cylinder,  or  internal,  waste 
to  be  more  fully  considered  later ;  in  which  waste  conduc- 
tion, storage,  restoration,  and  convection  play  the  leading 
part ;  while  a  small  portion  is  directly  conducted,  or  radiated, 
to  objects  immediately  adjacent  to  the  machine. 

Each  of  these  wastes  reduces  the  efficiency  of  the  engine, 
and  their  total  enormously  restricts  it ;  making  the  difference 
between  the  ideal  and  the  real  case  so  great  as  to  absolutely 
preclude  the  possibility  of  predicting  the  quantity  of  steam 


THERMODYNAMICS  OF   THE   STEAM-ENGINE.          tfl 

and  of  fuel  required,  or  the  cost  of  operation,  of  the  actual 
engine,  until  all  these  losses  can  be  closely  estimated.  Experi- 
ment and  experience  have  supplied  data  on  which  all  such 
estimates  are  now  based. 

122.  The  Methods  of  Waste,  in  all  known  forms  of 
heat-engine,  considered  in  detail,  are  the  same  in  character, 
but  are  very  different  in  their  proportion  in  different  types  of 
engine.  In  the  non-condensing  steam-engine,  the  thermo- 
dynamic  waste  is  greater  than  in  the  condensing  engine ;  the 
loss  by  conduction,  internal  and  external,  is  less;  the  waste 
by  friction  of  engine  is  less ;  and  the  total  of  all  losses  may  be 
either  greater  or  less,  accordingly  as  the  gain  by  increased 
range  of  temperatures  of  operation  in  the  latter  is,  or  is  not, 
compensated  by  the  difference  in  the  sum  of  wastes  other  than 
thermodynamic,  and  necessary  losses  of  different  kinds.  In 
the  hot-air  engine,  the  great  range  of  temperature  worked 
through  decreases  the  proportional  necessary  thermodynamic 
waste,  while  increasing  the  other  losses ;  but  the  resultant 
actual  efficiency  is  high.  The  same  is  true  of  the  water- 
jacketed  gas-engines,  in  which  the  wastes  by  conduction  of 
heat  are  enormously  increased  by  the  action  of  the  jacket; 
while  the  thermodynamic  efficiency  of  fluid  is  high,  and  the 
unavoidable  thermodynamic  waste  correspondingly  low. 

The  efficiency  of  fluid  and  of  engine  has  often  been  studied 
by  standard  authorities,  but  almost  invariably  as  a  problem 
in  thermodynamics,  simply;  and  the  losses  occurring  in  conse- 
quence of  the  working  of  steam  in  a  cylinder  composed  of  a 
good  conductor  of  heat  have  been  left  unnoted,  although 
frequently  the  most  important  of  all  the  expenditures  of  heat 
taking  place  in  the  engine. 

The  process  of  exhaust-waste  which  has  been  described  is 
thus  seen  to  be  one  of  the  most  serious  causes  of  loss  of  heat  in 
the  modern  steam-engine.  It  is  this  method  of  waste  which 
prevents  the  engineer  attaining  even  an  approximation  to  the 
estimated  gain  due  to  considerable  expansion.  It  is  this  which 
fixes  a  limit  practically  to  our  expansion  of  steam  in  a  single  cylin- 
der :  which  limit  has,  as  yet,  in  ordinary  forms  of  engine,  been 


47  2  A    MANUAL    OF   THE   STEAM-ENGINE. 

little  altered  by  the  expedients  which  have  been  adopted  to  ex- 
tend it.  It  has  been  found  by  experience  that  with  steam  of 
60  to  75  pounds  pressure  (four  or  five  atmospheres),  no  gain  in 
efficiency  can  usually  be  secured  by  expanding  more  than  five 
or  six  times  in  the  simple  unjacketed  engine.  Passing  this 
limit,  the  losses  due  the  wasteful  transfer  of  heat  to  the 
exhaust  steam  increase  much  more  rapidly  than  the  gain  due 
to  the  increased  conversion  of  heat  into  work  by  expansion. 

When  the  steam  is  so  far  superheated  that  the  mass  taken 
into  the  cylinder  may  surrender  to  the  metal  all  the  heat 
required  to  warm  it  up  to  the  temperature  due  the  steam- 
pressure,  without  itself  falling  to  the  temperature  of  saturation 
at  that  pressure,  this  loss  is  reduced  to  a  minimum.  But  any 
such  saving  is  always  effected  at  the  sacrifice  of  some  thermo- 
dynamic  efficiency.  Steam-jacketing  produces  its  well-known 
benefit  by  similarly  checking  the  waste  due  to  this  condensa- 
tion and  re-evaporation. 

The  losses  by  the  rejection  of  heat  from  the  engine  without 
transformation  have  thus  been  seen  to  be  due  to  two  entirely 
different  causes :  the  first,  thermodynamic  waste  and  physical 
heat-transfer,  can  evidently  only  be  saved  by  some  as  yet 
unknown  and  radical  change  of  type  of  engine  ;  the  second, 
which  has  been  diminished,  but  has  never  been  wholly  checked 
by  any  known  expedient,  seems  very  probably  to  require,  also, 
radical  treatment  to  effect  its  cure. 

As  is  so  well  illustrated  by  the  investigations  of  Dr. 
Kirsch,  the  film  of  metal  to  which  the  fluctuations  of  tempera- 
ture producing  cylinder-condensation  are  mainly  confined, 
receives  alternating  waves  of  high  and  low  temperature,  which 
rapidly  traverse  the  iron,  entering  and  leaving  with  the  en- 
trance of  steam  and  the  occurrence  of  the  exhaust ;  but  always, 
on  entering,  fading  into  the  mean  temperature  within  the  mass, 
and  always  restricted,  at  maximum  altitude,  to  the  surface  on 
the  steam  side.  Their  rate  of  alternation  is  that  of  succession 
of  piston-strokes ;  and  it  is  thus  proportional  to  the  speed  of 
rotation  of  the  engine,  the  depth  affected  becoming  less  and 


THERMODYNAMICS  OF   THE  STEAM-EXGIXE.          473 


less  and  the  waste  correspondingly  reduced  as  this  speed  in- 
creases, indefinitely. 

Thus,  in  Fig.  141,  the  method  of  heat-transfer  between 
steam  and  cylinder  is  shown,  as  it  takes  place,  stroke  by 
stroke,  in  the  heads  of  unclothed  or  inefficiently  clothed,  in 
well-covered  and  in  well-jacketed  engines,  respectively. 

For  example,  in  A  we  have  the  first  and  second  cases, 
(i)  When  the  cylinder  is  in  operation,  its  mean  temperature 

A 

B 

a 

T' 

Tj 


on  the  inner  face,  ab,  is  XTm ,  and  greater  than  on  the  outside, 
a/,  where  it  is  07".;  since  heat  is  continuously  draining  into  the 
outer  air  from  the  hot  metaL  With  varying  steam-pressures, 
the  former  temperature  rises  and  falls,  from  a  maximum,  7*,,  at 
the  beginning  of  the  forward,  to  a  minimum,  T, ,  at  the  end  of 
the  return  stroke  of  piston.  The  mean  for  the  whole  cycle  is 
represented  by  the  line  TmTf;  and  the  extreme  fluctuations 
by  T.Ti  and  TmTr  The  area  T,fTtTt  measures  the  heat 
stored  per  unit  of  area ;  and  this,  added  to  the  waste  by  out- 
flow at  TM ,  is  the  total  thermal  loss  on  the  head. 

(2)  Similarly,  if  fully  protected  against  loss,  externally, 
TmTm  becomes  the  mean  line  for  the  whole  thickness  :  7> T, 
the  fluctuation,  and  this  loss,  due  to  it.  is  TtfT,Tt ,  substantially 
as  before ;  but  to  this  loss  is  not,  in  this  case,  superadded  the 
drain  outward.  This  latter  loss  is,  in  the  figures,  much  ex- 
aggerated. In  actual  work,  the  internal  waste  is  usually  much 
the  greater. 


474  A  MANUAL    OF    THE   STEAM-ENGINE. 

(3)  When  the  engine  is  well-jacketed,  the  temperature  of 
the  interior  fluctuates  as  before,  as  seen  in  B,  where  the  dotted 
line  is  that  of  mean  temperature  for  the  preceding  case,  and 
T3Tm  is  that  for  the  jacketed  engine;  but  the  exterior  is  held 
up  to  the  temperature,  7^,  of  "prime  steam"  or  higher  by 
contact  with  jacket-steam  having  equal  or  greater  pressure. 
The  result  is  to  produce  a  drain  of  heat  inward,  instead  of,  as 
in  the  preceding  cases,  outward,  and  to  restrict  the  minimum 
temperature,  7",,  in  its  fall,  and  to  throw  the  whole  area, 
T.eT^T,,  upward  toward  T,  ,  and  to  reduce  its  magnitude, 
correspondingly  decreasing  internal  wastes  by  that  method. 
Could  this  process  be  made  absolutely  effective,  and  7",  =  Tlf 
internal  or  "  cylinder  condensation"  would  cease,  and  the  only 
internal  loss  would  be  by  transfer  from  the  jacket  to  the  cylin- 
der in  the  same  manner  as,  in  the  preceding  cases,  heat  passes 
outward. 

Thus,  with  the  jacketed  cylinder,  there  are  three  of  these 
wastes  :  loss  through  the  lagging,  externally  ;  loss  by  interior 
storage  and  restoration  of  heat  in  and  from  the  metal  ;  internal 
discharge  by  drainage  from  the  jacket.  Calling  these  Ha,  Hb, 
Hc  ,  and  the  total  H, 


and  the  values  of  the  quantities  vary  with  type  and  construc- 
tion of  engine.  In  case  I,  H  is  largest;  though  //t.  =  o;  in 
case  2,  H  is  reduced  by  the  reduction  of  Ha  to  a  small  quan- 
tity, and  the  H  —  Hb,  nearly;  while  in  case  3,  although  Hc  is 
introduced,  it  may,  by  producing  a  larger  reduction  of  Hb,  give 
a  total  value,  H,  in  some  cases,  considerably  less  than  in  either 
of  the  other  cases. 

It  is  here  obvious  that  the  jacket  will  be  useful,  useless,  or 
wasteful,  accordingly  as  it  reduces  Hb  more,  an  equal  amount, 
or  less  than  its  own  characteristic  waste,  Hc. 

In  Fig.  142  is  shown  the  action  of  the  metal  during  the 
movement  of  the  engine  through  its  cycle,  and  the  fluctuations 
already  alluded  to.  The  inner  face,  Oa,  varies  in  temperature 
from  7",  to  7a,  about  the  mean,  Tm,  as  before,  the  successive 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


475 


isothermals  taking  the  forms  exhibited,  as  the  waves  of  heat 
cross  the  metal  towards  X,  the  line  OX  representing  the  tem- 
perature of  the  outside  atmosphere,  and  the  successive  lines, 
above,  are  the  successive  positions  of  the  isothermals,  as  the 
flow  fluctuates  in  the  lagged  but  unjacketed  cylinder.  In  the 
jacketed  engine,  the  same  general  effect  would  be  seen ;  but 
the  line  71,7*,  would  have  the  opposite  inclination,  as  already 
seen. 

In  quick-working  engines,  the  action  of  the  cylinder-walls 
results  in  producing  a  film  of  water  on  their  surfaces,  and  the 


FIG.  142.— VAR 


steam  remaining  uncondensed  is  but  very  slightly  and  superfi- 
cially affected ;  it  passes  out  still  dry.  In  slow  engines,  the 
mass  of  steam  may  probably  be  rendered  comparatively  wet. 
On  the  other  hand,  the  process  of  expansion,  after  cut-off, 
results  in  producing  water,  diffused  throughout  its  mass,  which 
can  neither  affect  nor  be  affected  by  the  surrounding  walls. 

In  the  transfers  of  heat  between  engine  and  steam,  the  con- 
tact of  cylinder  and  cooler  dry  steam  has  little  effect ;  but 
moisture  on  the  surface  of  the  metal  and  its  re-evaporation  has 
a  most  decided  and  important  effect. 

A  glance  at  these  diagrams  of  heat-flow  shows  that,  to  se- 
cure usefully  sustained  temperatures  on  the  working  face  of  the 


4/6  A   MANUAL    OF    THE   STEAM-ENGINE. 

cylinder-wall,  the  temperature  and  steam-pressure  in  the  sur- 
rounding jacket  must  be  higher  as  the  thickness  of  that  wall  is 
greater,  in  order  to  maintain  any  given  head  and  inclination  of 
the  mean  temperature  line.  Conversely  :  the  thinner  the  wall, 
the  less  the  necessary  head  and  the  more  effective  the  jacket 
for  any  given  pressure  and  temperature  of  its  steam,  in  excess 
of  the  mean  temperature  of  the  inner  face  of  the  cylinder-wall. 

It  will  be  seen  that  the  higher  the  speed  of  engine,  the 
thinner  the  film  of  metal  affected  by  these  measurable  variations 
of  temperature  and,  consequently,  the  less  useful  the  jacket. 
In  other  words,  also,  the  higher  the  speed  and  the  thinner  this 
film,  the  higher  is  the  temperature  needed  for  efficient  action 
of  the  jacket.  Experience  confirms  this  deduction  by  showing 
that  the  jacket  has  very  slight  effect,  as  usually  applied  to 
"high-speed"  engines.  To  make  it  useful,  a  way  must  evidently 
be  found,  either  to  greatly  reduce  the  thickness  of  the  cylinder- 
walls — as,  indeed,  has  been  proposed,  many  years  since — or  to 
raise  the  temperature  of  jacket  considerably,  thus  securing  in- 
creased heat. 

As  stated  by  M.  Dwelshauvers-Dery,  the  principle  of  Hirn 
applies  to  all  engines,  thus: 

Between  any  two  given  successive  positions  of  the  piston, 
the  quantity  of  heat  transformed  in  the  performance  of  external 
work,  plus  that  derived  from  the  metal  of  the  cylinder,  gives  a 
sum  equal  to  that  of  the  variation  of  the  internal  heat  of  the 
steam,  plus  that  introduced  by  newly  entering  steam,  if  any,  or 
minus  that  lost  with  rejected  steam,  if  any.* 

123.  The  Magnitudes  of  Losses  in  the  steam-engine  have 
been  ascertained  with  considerable  accuracy,  for  the  principal 
types  and  for  engines  of  ordinary  sizes  working  under  familiar 
conditions.  In  general,  it  may  be  said  that  the  actual  total 
efficiency  of  engine  ranges  from  an  average  of  about  fifteen  or 
sixteen  per  cent,  in  the  best  cases,  down  to  five  for  ordinarily 
good  engines,  and,  often,  to  much  lower  figures.  A  perfect 
steam-engine  of  efficiency  unity,  working  under  the  best  of 


*  Dwelshauvers-Dery:  Expose,  §  2. 


THERMODYNAMICS  OF    THE   STEAM-EXGIXE.          477 

familiar  conditions  as  to  temperatures  and  pressures,  should  de- 
mand but  about  two  and  a  quarter  pounds  of  feed-water  and 
steam,  per  horse-power  and  per  hour.  The  best  recorded  figures 
are  about  five  times  as  great :  and  twenty-five  to  thirty  pounds 
are  the  figures  commonly  guaranteed  for  large  sizes  by  good 
builders  of  simple  engines.  For  small  engines  of  ordinary  con- 
struction, the  consumption  of  steam  and  the  wastes  are  often 
enormously  great. 

The  distribution  of  energy  in  evaporation  in  a  case  of  ex- 
cellent performance  of  a  boiler  tested  by  Sir  Frederick  Bram- 
well  and  Mr.  W.  Anderson  was  as  below  :* 

B.  T.  U.  Per  ct. 

Evaporating  the  water  in  the  wood 9557  0.32 

Heating  wood  and  air 3884  .13 

Evaporating  moisture  in  coal 8374  .29 

Heating  coal  and  air 129,321  4.44 

Displacing  atmosphere 53>394  T-83 

Heating  excess  of  air 130,980  ) 

Displacing  atmosphere  by  ditto 53»5O9  ) 

Making  steam 2,090,300  71.78 

Radiation  and  convection 271 ,307  9.32 

In  ash 53,915  1.85 

Balance  unaccounted  for 107,552  3.70 


Totals. . . . '. 2,912,093     100.00 

The  heat  received  from  the  fuel,  at  the  furnace,  may  be 
taken  as  distributed,  in  a  good  example,  thus : 

Total  heat  received              Waste  at  chimney 25 

"       "  condenser 55 

"       "  by  radiation ...  5 

Usefulwork 15 

the   fuel  at  the  furnace,   100  |      Total 100 

*  Tburston:  Engine  and  Boiler  Trials;  p.  361. 


478 


A    MANUAL    OF   THE   STEAM-ENGINE. 


The  "  working  efficiency  of  the  fluid  "  is  here  about  73  per 
cent,  the  exhaust  waste  being  about  one  half  cylinder-conden- 
sation. 

In  the  case  of  an  economical  condensing  engine,  consuming 
one  kilogram  (2.2  Ibs.)  of  good  fuel  per  hour  per  horse-power, 
M.  Hirsch  gives  the  following  as  a  fair  distribution  of  the  heat 
produced  :* 

Calories  Calories 

Coeffic.  expended,  remaining. 

Heat  of  combustion i.oo        0.50  100.00 

(1)  Received  from  the  boiler 60  40.00  60.00 

(2)  Thermodynamic  efficiency 27  43.80  16.20 

(3)  Imperfection  of  cycle 60        6.48  9.72 

(4)  Efficiency  of  machine 77         2.22  7.50 

(5)  Total  efficiency O-°75  92.50  7.5 

In  a  familiar  form  of  simple  non-condensing  engine,  doing 
fair  work,  the  Author  has  found  the  following  distribution  of 
energy  received  from  the  boiler : 


Received. 
Heat-energy  stored  in  steam, 

dry  and  saturated  at  the  en- 
gine, in  per  cent 100 

Total loo 


Expended. 


Per  cent. 


Waste  by  external  con- 
duction, etc 6 

Waste  by  internal  con- 
duction   33 

Waste,  therniodynamic  41 

"         by  friction 8 

Useful  work 12 

Total .  .  ,100 


Here  the  working  value  of  the  fluid  is  70  per  cent. 

In  the  case  of  the  best  compound  triple-expansion  engines 
with  steam  at  the  same  pressure  (100  Ibs. ;  atmos.  absolute ; 
nearly),  cylinders  jacketed  and  expanding  about  12  times,  the 
following  is  a  fair  distribution  : 


*  Congrfes  International  de  Mecanique  appliqu6e;  1881;  vol.  IV. 


THERMODYNAMICS  OF   THE   STEAM-ENGINE.          4/9 


Received. 


Heat -energy  stored  in  steam, 
as  received  from  the  boiler, 


Expended.  Per  cent. 

External  wastes 10 

Internal       "       25 

Thermodynamic  wastes     36 


Friction  wastes 13 

per  cent 100  j   Useful  work 16 

Total ioo  Total 100 

In  this  case,  the  working  efficiency  of  the  fluid  is  70  per 
cent. 

The  following  are  figures  given  by  Professor  Ewing,  de- 
duced from  data  supplied  by  Mr.  Main:* 

B.T.U. 

Heat  supplied  engine  per  rev 1 377 

"  "  "       by  jackets 212 

"    total  B.  T.  U 1589 

"     returned  to  boiler 38 

"     net  supply 1551 

"     converted  into  work 227 

"     rejected 1324 

Efficiency fffr  =  0.146 

Thermodynamic  Efficiency O-335 t 

In  all  cases  assuming  that  the  expansion  may  be  taken  as 
hyperbolic,  the  work  done  in  a  cylinder  of  given  volume  will 
vary  nearly  as  log,  r ;  but  the  cost  of  that  work  may  vary 
enormously,  and  entirely  without  direct  relation  to  the  volume, 
f\  ,  of  the  steam  at  the  point  of  cut-off. 

The  early  trials  of  the  Owens  College  experimental  engine 
elsewhere  described  (see  frontispiece)  are  reported  by  Pro- 
fessor Reynolds  to  have  given  data  and  an  account,  as  deduced 
by  Mr.  Cowper,  as  follows:  J 

•Minutes  Proc.  lost.  C.  E.;  vol.  LXX.  Also.  Thurston:  Engine  and  Boiler 
Trials:  p.  298. 

fEncy.  Britannka. 

t  Proceedings  Brit.  Inst.  C.  E.;  1889.  Van  Nostrand's  Science  Series;  No. 
99;  1890. 


48o 


A   MANUAL   OF   THE   STEAM-ENGINE. 


Dr.  B.T.U.         Percent. 

To  steam  in  cylinders 14, 1 54  8 1 

"         "       "  jackets 3,325  19 


17479 
Cr.  B.T.U. 

By  indicated  work — efficiency. 3,085 

"    heat  rejected 12,862 

"       "     radiated 1,176 

"       "     lost  from  hot-well 356 


100 

Per  cent. 

177 

73-6 
6.7 

2.0 


17,479        i  oo.o 

The  effect  of  back-pressure  in  limiting  thermodynamic  trans- 
formation and  the  efficiency  of  expansion  is  well  exhibited  by 
the  following  tables,  computed  by  Mr.  Buel : 

IDEAL    ENGINE;    NO    BACK-PRESSURE. 


Point  of 
Cut-off. 

Mean  Total  Pressure, 
pounds  per  square 
inch. 

Relative  Area  of 
Cylinders. 

Relative  Amounts  of 
Steam  used. 

Per  cent  of 
Saving. 

1 

2 

3 

4 

5 

I 

100.  0 

I.OO 

I.OOO 

i 

96.4 

1.04 

.780 

22.  0 

84.7 

1.18 

.590 

41.0 

£ 

70.0 

i-43 

•477 

52.3 

i 

3:2 

1.68 
2-15 

.420 
•358 

58.0 
64.2 

38.5 

2.60 

•325 

67.5 

T* 

29.0 

3-45 

.288 

71.2 

IDEAL   ENGINE;    BACK-PRESSURE    17$   LBS. 


Point  of 
Cut-off. 

Mean  Effective 
Pressure,  pounds 
per  square  inch. 

Relative  Mean 
Pressure. 

Relative  Area 
of  Cylinders. 

Relative  Am'ts 
of  Steam  used. 

Percentage 
of  Saving. 

1 

2 

3 

4 

5 

6 

I 

82.5 

I.OOO 

I.OO 

I.OOO 

i 

78.9 

•959 

1.04 

.780 

22.  0 

i 

67.2 

.815 

1.23 

.615 

38.5 

* 

52-5 

.636 

i-57 

•523 

47-7 

i 

42.2 

•512 

1-95 

.488 

51.2 

* 

2Q.O 

•352 

2.84 

•473 

52.7 

i 

21.0 

•255 

3-92 

.490 

51-0 

T1* 

ii  5 

.140 

7-15 

•596 

40.4 

THERMODYNAMICS  OF   THE   STEAM-ENGINE.          48! 

From  this  table  it  appears  that,  under  the  assumed  condi- 
tions, the  most  economical  point  of  cut-off  is  about  one  sixth 
of  the  stroke,  since  the  saving  is  decreased,  whether  the  cut-off 
is  lengthened  or  shortened,  from  this  point.  The  conditions 
assumed  are  such  as  accord  well  with  modern  practice.  Ex- 
changing the  initial  or  back  pressure  to  suit  a  condensing  en- 
gine different  results  will  be  obtained,  but  the  table  is  sufficient 
to  show  the  mode  of  application  for  any  given  data  as  first 
shown  by  Clark. 

The  cause  of  increased  back-pressure  is  resistance  to  the 
escape  of  the  steam  from  the  cylinder,  by  which  the  mean 
back-pressure  is  raised  from  I  to  3  Ibs.  on  the  square  inch. 
There  is  as  yet  no  satisfactory  theory  of  that  resistance,  and  it 
cannot  be  computed  for  any  proposed  engine  by  means  of  a 
general  formula. 

The  back-pressure  in  proposed  engines  can  be  estimated 
roughly  from  the  results  of  experience.  The  following  is  a 
summary  of  some  such  results  : 

Mean  Back-pressure,/*. 
Lbs.  on  the         Lbs.  on  the 
square  foot.        square  inch. 

Ratio  of  expansion  from  \\  to  3.  .         720  5 

from  4  to  7...  64810504       4^  to  3$ 
from  8  to  15  .  .   504.  to  432       3^  to  3 

The  diagrams  show  only  the  effective  pressures  of  the 
steam,  and  not  the  absolute  pressures,  which  are  usually  left  to 
be  roughly  estimated  by  guessing  the  probable  atmospheric 
pressure.* 

Mr.  Beer  takes  the  back-pressure  as 

A=A  +  Q-03A, 


for  non-condensing  and  for  condensing  engines,  respectively  ; 
in  which  /.  is  the  pressure  of  the  atmosphere  or  in  the  con- 
denser, assuming  moderate  engine-speed  and  liberal  port-areas. 


482  A  MANUAL    OF   THE   STEAM-ENGINE. 

124.  The  Thermodynamic  Loss,  which  unavoidably  takes 
place  in  all  heat-engines,  has  been  seen  to  have  a  magnitude 
which  is  absolutely  definite,  and  easily  determinable.  Of  all 
the  heat  subject  to  thermodynamic  conditions,  and  not  lost  by 

T  —  T 
conduction  or  radiation,  one  portion,  never  exceeding     '     — ', 

has  been  found  to  be  converted  into  mechanical  energy;  while 

the  remainder,  measured  by  a  fraction  never  less  than  ~,  is,  as 

A 

has  been  seen,  necessarily  and  inevitably  rejected  untrans- 
formed ;  this  constitutes  the  "  unavoidable  thermodynamic 
loss,"  which,  only,  is  considered  by  the  pure  science  of  ther- 

2" T 

modynamics.      The   part   utilized,  -±-~ — !,  being  divided  by 

T  —  T       T 
the   sum    of   these    two    parts,  — -= —  -j-  —  =  i,  gives   the 

measure,  as  already  seen,  of  the  maximum  possible  thermo- 

T  —  T 
dynamic  efficiency  of  the  fluid,  — —^ — 

The  efficiency  of  any  real  engine,  operated  under  familiar 
conditions,  is  measured  by  the  quotient  of  converted  heat 
divided  by  the  sum  of  all  expenditures,  whether  useful  or 
wasteful.  Thus  the  figure  for  efficiency,  just  obtained,  is  re- 
duced in  proportion  to  the  increase  of  the  total  heat-supply 
compelled  by  the  aggregate  of  these  wastes  ;  and  the  propor- 
tion of  thermodynamic  waste  is  at  the  same  time  correspond- 
ingly reduced.  The  latter,  in  many  cases,  thus  becomes  forty 
or  fifty  per  cent  of  the  total,  instead  of,  as  for  the  ideal  case, 
eighty-five  or  ninety  per  cent ;  the  extra-thermodynamic  wastes 
of  the  engine  often  equalling,  or  even  exceeding,  the  quantity 
of  heat,  or  of  steam,  demanded  in  the  purely  thermodynamic 
process  of  its  operation. 

In  all  cases,  with  real  engines,  the  quantity  taken  as  unity, 
with  which  the  useful  work  is  compared,  and  on  which  the 
measure  of  efficiency  is  based,  is  the  sum  of  all  expenditures 
of  heat,  and  not  simply  the  heat  thermodynamically  demanded. 


THERMODYNAMICS  OF   THE   STEAM-ENGINE.          483 

125.  The  Conditions  of  Maximum  Efficiency  of  fluid,  in 
all  real  engines,  other  things  equal,  are  precisely  the  same  as 
with  the  ideal  engine  of  thermodynamic  science,  viz.,  maximum 
range  of  temperature  worked  through  and  maximum  value  of 

•p  "p 

the  expression        _, — -.     The  higher  the  pressures  and  the 

temperatures  of  the  working  fluid  supplied,  and  the  lower 
those  of  rejection,  the  higher  the  efficiency  of  operation  of  the 
actually  working  substance.  But  it  does  not  follow  that  the 
actual  total  efficiency  will  be  similarly  increased. 

It  may  happen  that  the  extra-thermodynamic  wastes  may 
also  increase  with  increased  efficiency  of  fluid,  by  this  change 
of  thermodynamic  conditions,  and  to  such  an  extent  as  to 
produce  an  actual  decrease  of  total  efficiency.  This,  which  is 
a  common  experience,  if  not  universal,  is  illustrated  by  the 
familiar  fact  that,  for  every  engine  of  ordinary  construction,  a 
ratio  of  expansion  may  always  be  found,  beyond  which  the 
range  of  temperatures  and  pressures  being  increased,  an  actual 
loss  is  produced  by  the  consequent  increase  of  internal  wastes 
due  to  "  cylinder-condensation." 

Should  it  be  practicable,  in  any  case,  to  prevent  exaggera- 
tion of  losses  by  wastes  of  heat  through  internal  and  external 
conduction  and  radiation,  these  same  conditions  lead  to  in- 
creased efficiency  of  heat-transformation,  with  the  real,  as  with 
the  ideal,  engine.  It  is,  in  fact,  in  this  way  that  all  recent  im- 
portant improvements  in  the  economical  operation  of  the  en- 
gine have  taken  place ;  the  wastes  having  been  checked,  while 
the  practicable  range  of  expansion,  and  of  working  temperature, 
has  been  extended. 

126.  Heat-wastes  by  Conduction  and  Radiation  have 
been  classed  as  of  two  kinds :  external  losses  of  heat,  and  in- 
ternal heat-wastes.     Of  these,  the  first  take  place  by  conduc- 
tion of  heat  from  the  cylinder  to  the  engine-frame  :  by  radiat- 
ing from  the  heated  cylinder-heads ;  and  from  the  alternately 
heated  and  cooled  piston-rods  and  valve-rods,  as  they  move 
into  and  out  of  the  steam-space,  and  even  from  the  carefully 
clothed  exterior  of  the  cylinder. 


484  A   MANUAL   OF   THE   STEAM-ENGINE. 

An  allowance  of  one  British  thermal  unit  per  hour,  per 
square  foot,  or  of  nearly  three  calories  per  square  metre,  will 
usually  cover  the  losses  in  the  ordinary  engine  from  protected, 
well-lagged,  surfaces.  This  corresponds  to  about  o.oor  pound 
of  steam  condensed  by  one  square  foot,  or  to  nearly  0.005 
kilogramme  liquefied  by  a  square  metre.  For  any  given  en- 
gine, this  loss  may  be  assumed  constant,  and  may  often  be 
neglected,  as  unimportant,  in  presence  of  so  many  other  more 
serious  wastes.  The  slight  leaks  of  steam  and  of  hot  water 
about  the  rods  will,  practically,  often  be  found  much  more  im- 
portant, economically.  If  it  be  taken,  in  engines  of  moderate 
size  and  power,  as  five  per  cent,  it  will  probably  usually  prove 
that  the  assumption  is  a  safe  one. 

Losses  of  heat  in  this  manner  by  external  conduction  and 
radiation  have,  however,  been  rarely  measured  at  the  engine ; 
but  the  following  data  (p.  485)  from  the  trials  of  agricultural 
engines  at  the  Royal  (G.  B.)  Society's  competition,  by  Sir 
Frederick  Bramwell  and  Mr.  Anderson,  will  illustrate  the 
method  and  extent  of  this  waste  with  varying  temperatures.* 

The  total  waste  from  engines  and  boilers  was  thus  from  3^- 
to  i6£  per  cent  of  all  heat  of  combustion.  Larger  engines  and 
boilers  are  less  subject  to  this  waste  ;  since  the  area  of  surface 
is  less  in  proportion  to  weight  and  to  quantity  of  steam  and 
work.  As,  in  the  cases  cited,  the  total  waste,  from  engine  and 
boiler,  is,  in  the  best  example,  reduced  to  3^  per  cent,  it  is 
evident  that  the  loss  from  the  steam-cylinder  of  the  engine 
must  be  very  slight,  and,  in  large  engines,  may  be  made,  by 
careful  protection,  insignificant. 

The  Rate  of  Cooling  is  not  uniform,  but  decreases  as  the 
temperatures  and  pressures  of  steam  and  metal  fall,  as  shown 
by  the  line  cO,  in  Fig.  143,  and  increases  observably  with 
increasing  pressures,  thus  indicating  an  increasing  loss  which 
tends  to  set  a  limit  to  the  gain  otherwise  attainable  by  this 
progression.  The  curve,  c  O,  of  waste  gives  the  total  loss  in 
British  thermal  units  for  the  given  temperatures  and  corre- 

*  Jour.  Roy.  Ag.  Soc.;  vol.  xxiu;  1887. 


THERMODYNAMICS  OF   THE   STEAM-ENGINE.          48$ 


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486 


A    MANUAL    OF   THE   STEAM-ENGINE. 


spending  pressures.  The  line,  cB,  tangent  to  the  curve  at  its 
upper  extremity,  indicates  the  length  of  time,  measured  by 
its  ordinate,  A  B,  which  would  have  been  required  for  cooling 
down  to  the  minimum  had  the  rate  of  cooling  been  constant, 
The  actual  time  was  nearly  twice  as  great. 


\ 


FIG.  143. — RATE  OF  COOLING  OF  ENGINES. 

The  zero-point  is  here  taken  at  the  minimum  reading.  The 
ordinates  measure  the  total  quantities  of  heat  at  each  pressure 
and  temperature  and  time  indicated  on  the  curve,  in  excess  of 
that  remaining  at  the  end  of  the  period  of  observation  (364,600 
B.  T.  U.). 

It  was  observed,  in  these  experiments,  that  the  rate  of  cool-- 
ing was  very  variable,  ranging  from  about  2200  up  to  above 
10,000  units  per  dynamometric,  or  brake,  horse-power,  on  the 
"  ten  and  twenty  horse  engines  "  compared  ;  and  that  a  com- 
pound engine  wasted  heat  at  a  rate  exceeding,  by  28  per  cent, 
that  of  its  companion  simple  engine,  similarly  covered.  These 
cases  show  clearly  that,  with  small  engines  and  ineffective  lag- 
ging and  clothing,  this  waste  may  be  found,  especially  at  high 
pressures,  and  with  multiple-cylinder  engines,  a  very  observable 
tax  upon  efficiency.  Wastes  of  from  3  to  5  pounds  of  steam, 
the  ordinary  range  of  this  waste,  per  horse-power  and  per  hour, 


THERMODYNAMICS  OF   THE  STEAM-ENGIXE.          487 

for  the  compound,  and  of  2£  pounds  and  upward  for  simple 
engines,  constitute  very  considerable  percentages  of  the  total 
consumption  of  steam. 

The  waste  of  heat  by  radiation  from  well  clothed,  lagged, 
and  felted,  engine-cylinders  may  be  taken,,  as  an  average,  at 
about  one  half  a  British  thermal  unit  per  square  foot  of  surface 
and  per  degree  of  difference  of  temperature,  internal  and  ex- 
ternal. About  five  times  as  much  is  lost  from  polished  heads, 
and  probably  some  more  from  that  portion  of  the  piston-rod 
exposed  to  the  air  and  to  the  steam  alternately.  In  large  en- 
gines, well  clothed,  this  loss  often  constitutes  less  than  2  per 
cent  of  the  heat  supplied. 

127.  The  Methods  of  Reduction  of  Losses  of  Heat  by 
conduction  and  radiation  externally,  as  commonly  practised, 
consist  simply  in  carefully  covering  all  external  surfaces,  where 
it  can  well  be  done,  with  hair-felt,  asbestos,  preparations  of 
magnesia,  or  other  non-conducting  substances,  and  adding  a 
surface-covering  of  painted  canvas,  of  well-finished  wooden,  or 
Russia  iron,  lagging,  which  protects  the  clothing  beneath  it 
from  injury.  Cylinder-heads  are  sometimes  similarly  covered, 
but  are  often  left  bare,  and  are  then  very  carefully  polished,  as 
should  be  all  such  exposed  heated  parts. 

Conduction  and  radiation  from  piston-rods  and  valve-rods 
can  only  be  reduced  by  a  good  polish  and  such  effective  pack- 
ing as  will  insure  their  working  dry.  Conduction  to  the 
frame  and  other  parts  of  the  structure  connected  to  the  heated 
cylinder  is  checked  by  any  packing  or  "joint"  between  the 
two  members  of  the  machine ;  but  it  is  not  usual  to  attempt  to 
effect  such  an  economy  by  any  special  device.  In  this  respect, 
those  engines  in  which  the  cylinder  is  attached  to  the  frame 
only  by  its  front  head  probably  have  some  advantage. 

A  gain  by  improved  efficiency  of  engine  may  usually  be 
expected  to  give  still  greater  gain  in  economy  at  the  boiler.  A 
reduction  in  steam-consumption  results  in  the  increase  of  the 
ratio  of  area  of  heating  surface  to  weight  of  steam  required,  and 
this,  in  turn,  effects  an  increase  in  the  quantity  of  water  evapo- 
rated per  unit  weight  of  fuel.  Thus,  a  reported  gain  of  25  per 


488  A    MANUAL   OF   THE   STEAM-ENGINE. 

cent  in  a  small  engine,  by  compounding,  was,  in  a  case  observed 
by  the  Author,  reported,  also,  to  be  accompanied  by  a  gain  of 
above  35  per  cent  in  fuel  required  per  horse-power  per  hour. 

128.  Cylinder-condensation,  or  loss  by  internal  conduc- 
tion and  radiation,  is,  in  the  best  engines,  next  to  the  thermo- 
dynamic  waste,  the  most  serious  and  difficult  of  reduction.  In 
ordinary  cases,  this  is  far  in  excess  of  the  thermodynamic 
waste. 

Steam-engines,  as  already  seen,  are  impelled  by  a  fluid  which 
is  a  vastly  better  receiver  and  transmitter  of  heat  than  the 
permanent  gases.  Steam  takes  up  and  loses  heat,  in  the  process 
of  formation  and  of  condensation,  with  extreme  rapidity.  The 
working  fluid,  in  all  steam-engines,  is  readily  condensable,  and 
exchanges  heat  with  the  metallic  surfaces  of  the  working  cylin- 
der with  the  greatest  freedom.  It  is  usually  more  or  less  wet, 
and  its  humidity  is  subject  to  rapid  and  extreme  variation  in 
the  course  of  the  movement  of  the  piston.  Condensation  also 
occurs  in  another  way:  Suppose  steam  to  enter  the  steam- 
cylinder  perfectly  dry,  and  to  expand  adiabatically.  As  expan- 
sion progresses,  after  the  closing  of  the  steam-valve  by  the 
expansion-gear,  the  work  done  by  the  working  fluid  results  in 
the  transformation  of  so  much  heat  into  mechanical  energy — 
which  heat  can  now  only  be  obtained  by  drawing  upon  the  stock 
contained  in  the  steam  itself — that  a  part  of  the  steam  becomes 
liquefied.* 

This  fact  was  shown  by  Rankine  and  by  Clausius,  by  the 
study  of  the  thermodynamics  of  the  case ;  it  had,  a  generation 
earlier,  been  perceived  by  Carnot,t  and  by  Combes  as  early  as 
1843. 

The  liquefaction  of  the  steam,  in  consequence  of  trans- 
formation of  heat  into  work,  probably  aggravates  this  evil, 
although,  as  was  stated  by  Rankine,  not  itself  a  waste :  % 


*  On  the  Ratio  of  Expansion  at  Maximum  Efficiency;  R.  H.Thurston ;  Trans. 
Am.  Society  M.  E.,  1881. 

f  Reflections,  etc.;  Thurston's  Trans.;  p.  255. 

\  Steam-engine  and  other  Prime  Movers,  1859;  pp.  395-396. 


THERMODYNAMICS  OF   THE   STEAM-ENGINE.          489 

"  That  liquefaction  does  not,  when  it  first  takes  place, 
directly  constitute  a  waste  of  heat  or  of  energy;  for  it  is  accom- 
panied by  a  corresponding  performance  of  work.  It  does, 
however,  afterwards,  by  an  indirect  process,  diminish  the  effi- 
ciency of  the  engine ;  for  the  water  which  becomes  liquid  in 
the  cylinder,  probably  in  the  form  of  mist  and  spray,  acts  as 
a  distributor  of  heat,  and  equalizer  of  temperature,  abstracting 
heat  from  the  hot  and  dense  steam  during  its  admission  into 
the  cylinder,  and  communicating  that  heat  to  the  cool  and 
rarefied  steam  which  is  on  the  point  of  being  discharged,  and 
thus  lowering  the  initial  pressure,  and  increasing  the  final 
pressure,  of  the  steam,  but  lowering  the  initial  pressure  much 
more  than  the  final  pressure  is  increased ;  and  so  producing  a 
loss  of  energy,  which  cannot  be  estimated  theoretically." 

The  same  phenomenon  is  described  by  Professor  Cotterill, 
thus: 

"When  the  expansion-curve  drawn  by  an  indicator  is 
examined,  it  is  almost  always  found,  even  when  the  greatest 
care  has  been  taken  to  eliminate  the  disturbing  causes,  to  show 
that  evaporation  takes  place  during  expansion.  Now  these 
unquestionable  facts  can  only  be  explained  by  supposing  that 
liquefaction  takes  place  during  the  admission  of  the  steam  to 
the  cylinder,  and  evaporation  during  expansion  and  exhaust. 
This  alternate  liquefaction  and  evaporation  is  chiefly  due  to 
the  action  of  the  sides  of  the  cylinder,  in  many  cases  combined 
with  the  effect  of  water  remaining  in  the  cylinder  after  exhaust 
is  completed." 

The  surfaces  affected  by  this  action  are  of  varying  activity 
and  efficacy  in  the  production  of  wastes.  The  cylinder-heads, 
the  sides  of  the  piston,  the  surfaces  of  the  port-  and  steam-pas- 
sages, the  surfaces  of  the  clearance  or  "  dead  "  spaces,  often 
of  very  considerable  area,  and  the  extreme  portions  of  the 
internal  cylindrical  surfaces,  which  are  all  exposed  to  the  full 
range  of  temperature  from  boiler-steam  to  condenser,  produce 
the  main  portion  of  this  serious  loss.  Between  the  points  of 
mean  cut-off  at  the  two  ends  of  the  cylinder,  this  range  is  less. 
It  is  a  minimum  at  the  middle  of  the  cylinder ;  at  which  point 


490 


A    MANUAL    OF   THE   STEAM-ENGINE. 


the  inner  surfaces  are  exposed  to  the  least  variation  of  pressure. 
Whatever  treatment  may  be  adopted  to  evade  this  waste  will 
be  most  effective  on  those  parts  which  are  thus  exposed  to 
the  maximum  variation  of  temperature  and  pressure  of  the 
enclosed  steam. 

Of  the  absolute  magnitude  of  this  waste,  some  idea  may 
be  obtained  from  the  reported  results  of  experiment ;  some  of 
which  are  as  follows: 

Mr.  Clark  deduces  from  his  experiments  with  locomotives 
the  following  figures  for  usual  percentages  of  condensation  at 
various  points  of  cut-off  in  outside  connected  engines.  Engines 
with  inside  cylinders  are  observably  less  seriously  affected  ;  as 
the  heat  of  the  adjacent  smoke-box  and  boiler,  and  their  pro- 
tection against  the  cooling  action  of  the  passing  air,  exert  a 
favorable  effect.* 

CYLINDER-CONDENSATION  IN  LOCOMOTIVES. 


Per  cent  Condensation. 

Cut-off. 

Actual  r. 

Parts  of  Initial  Steam, 

Parts  of  Initial  Steam 

per  cent. 

and  Water. 

0.10 

4 

8o.O 

44.0 

0.15 

3-40 

57-0 

36.0 

O.2O 

2.85 

41.0 

29.0 

0.25 

2.50 

31-0 

23-6 

O.3O 

2.  2O 

23.0 

18.7 

0-35 

2.OO 

17-5 

15.0 

0.40 

1.83 

II.  O 

10.0 

0.50 

1.  60 

4.5 

4-3 

0.70 

1-25 

2.75 

2.7 

I.OO 

I.OO 

2.0 

2.0 

The  results  of  Isherwood's  investigation,  as  summed  up  by 
himself,  give  the  following  average  data:f 


*  Proceedings  Brit.  Inst.  C.  E.,  No.  1910;  1882-3. 

f  Experimental  Researches  in  Steam-engineering;  vol.  II.  p.  xxxiii. 


THERMODYNAMICS  OF  THE   STEAM-ENGINE. 
CYLINDER-CONDENSATION  IN  MARINE  ENGINE. 

STEAM  40   LBS.  BY    GAUGE. 


49 * 


Cut-off. 

Actual  r. 

Lbs.  Steam  per 
I.  H.  P.  per  hour. 

Relative  Cost 
in  Steam. 

Internal 
Condensation, 
per  cent. 

100 

46.86 

-397 

10.90 

90 

.11 

41-57 

.239 

12.43 

80 

•25 

37.85 

.128 

M-45 

70 

00 

•43 
.66 

35-54 
34-16 

•059 
.018 

16.95 
20.02 

50 

2.00 

33-55 

.000 

23-94 

40 

2.50 

33-59 

.OOI 

28.50 

30 

3-33 

34-52 

.029 

33-56 

20 

5.00 

36.88 

.099 

38.87 

10 

IO.OO 

42.83 

1.277 

44.46 

The  figures  of  the  last  columns  in  each  of  these  tables 
show  well  how  rapidly  internal  waste  increases  with  increasing 
expansion. 

CONDENSATION  IN  STEAM-CYLINDERS. 

Case.  I.  II.  III.  IV.  V. 

Cut-off 0.95         0.67  0.40  0.354  O-25 

Fraction  condensation  in  Ideal  Case..  0.004      0.026  0.056  0.061  0.081 

"  Actual  Case.  0.150      0.284  0.459  °-554  0.601 

Ratio  of  Real  to  Ideal 37.5  10.7  8.2  9.1  7.4 

The  above  table  presents  a  comparison  of  the  actual  con- 
densations occurring  in  the  unjacketed  engine  of  the  U.  S.  S. 
Michigan,  with  the  condensations,  resulting  from  the  work  of 
expansion,  which  would  have  taken  place  had  the  work  been 
done  in  a  non-conducting  cylinder,  as  computed  by  Professor 
Rankine* 

Hirn's  experimental  work  furnishes  some  exceedingly 
valuable  data,  as  may  be  seen  in  the  accompanying  table, 
abstracted  from  Ledieu.f  The  method  of  loss  and  its  distri- 
bution are  here  well  exhibited. 


*  Trans.  Inst.  Engrs.  of  Scotland;  Feb.  5,  1862. 

f  Him:    Theorie   Mecanique   de   la  Cbaleur;    1876.     Ledieu:    Machines 
Feu;  1882;  p.  383. 


492 


MANUAL   OF   THE  STEAM-ENGINE. 


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THEKMODYXAJtICS  OF   THE   STEAM-EXGIXE.          493 

These  great  wastes  by  internal  transfer  of  heat,  without 
transformation  into  mechanical  energy,  are  evidently  due  to 
precisely  those  conditions  which  make  the  steam-boiler  efficient. 
That  rapidity  of  conduction  which  causes  a  small  area  of  iron 
in  the  boiler  to  transfer  a  large  amount  of  energy,  in  the  form 
of  heat,  for  useful  application,  is  the  quality  which  causes  a 
small  area  of  iron  in  the  engine-cylinder  to  store  and  waste  a 
considerable  part  of  the  heat  entering  it. 

The  thickness  of  the  metallic  film  affected  by  the  phe- 
nomenon here  studied  is  probably  slight.  Mr.  A.  A.  Wilson, 
in  experiments  on  a  large  pumping-engine.  found  the  mean 
temperature  of  the  metal  nearly  equal  that  of  the  entering 
steam  at  a  point  as  near  the  inner  surface  of  the  cylinder  as  he 
could  safely  place  his  thermometer-bulb;  and  Mr.  Dixwell 
estimates,  as  a  deduction  from  his  own  tests,  that  the  mean 
variation  of  cylinder-temperature  does  not  exceed  30"  F.  He 
thus  takes,  in  the  discussion  of  one  of  his  engine-trials,  a  case 
in  which  920,000  pounds  of  steam  passed  through  the  engine, 
while  it  made  223,000  strokes :  giving  4. 12  pounds  per  stroke 
at  the  point  of  cut-off.  Taking  the  specific  heat  of  steam  at 
01475,  and  of  iron  at  0.1 14,  the  loss  of  temperature  of  the  steam 
having  been  found  to  be  200°  F.. 

4.12  X  200  X  0475  =  j:  X  30  X  0.114, 
when  JT  is  the  weight  of  iron  :  then 

jr  =  1 14-4  Ibs. 

of  iron  varying  in  temperature  the  specified  amount,  30°  F. 
The  area  of  surface  was  56.59  square  feet;  and  the  thickness, 
to  weigh  1 14^  Ibs^  would  be  but  0.054  inch,  or  less  than  one 
sixteenth. 

In  the  course  of  experiments  in  the  Sibley  College  labora- 
tory, Mr.  W.  W.  Churchill  being  the  observer,  the  thickness  of 
metal  of  cylinder-wall  was  reduced  to  0.2385  inch,  and  the 
temperature  of  its  outer  surface  observed  by  means  of  the 


494  A  MANUAL    OF   THE   STEAM-ENGINE. 

instantaneous  action  of  a  balanced  Wheatstone  bridge  and  a 
platinum-wire  conductor,  and  without  change  being  detected, 
the  temperature  of  the  entering  steam  being  300°  FM  and  up- 
ward, the  engine  non-condensing,  and  the  revolutions  308  per 
minute.  The  load  was  light,  however,  and  compression  heavy. 
The  conductor  indicated  a  constant  temperature  averaging  six 
degrees  lower  than  that  of  the  steam  at  entrance.  In  another 
series,  the  same  general  results  were  obtained ;  but  the  tem- 
perature recorded  was  less  constant. 

Reducing  the  thickness  of  wall  to  0.115  inch,  another  series 
of  trials  showed  slight  variation  of  temperature  and  a  reduc- 
tion from  that  of  the  steam  of  about  25  degrees.  Still  further 
reducing  the  wall  to  0.0426  inch,  a  fluctuation  of  17  degrees 
became  observable.  These  were  all  tentative  experiments, 
however,  and  are  not  considered  as  giving  reliable  quantitative 
values. 

Mr.  Willans,  as  a  result  of  his  own  experience  and  research, 
concludes  that  a  large  proportion  of  the  "  missing  quantity," 
due  cylinder-condensation,  must  be  ascribed  to  the  action  -of 
water  in  the  engine,  and  that  "water  is  likely  to  prove  a  more 
important  factor  than  surface  at  such  speeds  as  400  revolutions 
per  minute,"  and  that,  as  in  some  of  his  own  experiments, 
when  this  condensation  occurs  in  one  thirtieth  of  a  second,  the 
presence  of  a  small  constant  weight  of  water  in  the  cylinder 
may  account  for  substantially  all  this  waste,  and  that  its 
generally  observed  variations  of  magnitude  may  be  due  to 
changing  quantities  of  water  in  the  engine.  His  engines  were 
therefore  so  designed  as  to  avoid  giving  opportunity  for  water 
to  lodge  in  the  cylinder ;  any  collecting  on  the  piston-surface, 
the  only  place  available,  is  swept  off  by  the  exhaust-current. 
A  thickness  of  film  of  only  about  0.008  inch  of  water  would 
account  for  all  the  waste  thus  produced  in  his  observed  case. 

The  diagram  opposite  is  given  by  Mr.  Porter,  as  taken  from 
the  high-service  pumping-engines  at  Providence,  R.  I.,  now 


*  Porter  on  the  Indicator;  p.  172. 


THERMODYNAMICS  OF   THE   STEAM-ENGINE.          495 

The  speed  of  the  engine  was  10  revolutions  per  minute ;  at 
one  revolution,  this  action  was  still  further,  and  enormously, 
exaggerated.* 

The  problem  of  the  engineer  is,  evidently,  either  to  render  the 
internal  surfaces  as  thoroughly  non-conducting,  and  as  incapable 
of  heat-storage,  as  possible,  or  to  secure  similar  properties  for 
the  working  fluid  exposed  to  contact  with  them  ;  thus,  by  either 


FIG.  144. — CYLINDER-WASTE. 

or  both  methods  combined,  reducing  the  condensing  power  of 
the  cylinder  to  a  minimum.t 

The  cost  of  steam  and  power  in  engines  of  various  sizes 
has  been  ascertained,  by  the  researches  of  many  investigators, 
to  be  largely  dependent  upon  size  of  engine  and  power  de- 

*  The  higher  the  speed  the  more  superficial  the  action;  and,  at  very  high 
speeds  of  rotation,  a  limit  may  be  approached  at  which  the  wastes  by  variation  of 
temperature  of  the  metal  of  cylinder  become  insensible. 

The  more  effective  the  jacket  action,  also,  the  thinner  this  film  of  varying 
temperature. 

f  The  Westinghouse  Co.,  about  1885,  conducted  a  series  of  experiments  jto 
determine  the  possible  gain  in  fuel  economy  to  be  realized  from  the  use  of  non 
conducting  surfaces  in  steam-engine  cylinders,  as  far  as  possible.  The  non-con- 
ductor found  to  be  best  was  porcelain.  The  pistons  and  the  cylinder-heads  were 
coated,  but  the  difference  in  the  fuel  economy  was  so  small  as  "  not  to  be  wonh 
consideration,  commercially  speaking." 

A  device  proposed  by  the  Author  consists  in  converting  the  inner  surfaces 
into  a  graphitic  sponge,  filling  it  with  non-conducting  substances. 


496 


A    MANUAL    OF   THE   STEAM-ENGINE. 


manded.  The  accompanying  diagrams,  prepared  by  Mr. 
Emery,  and  the  corresponding  data  may  be  taken  to  exhibit 
this  cost  for  engines  of  the  design.*  Curves  in  group  No.  i  ex- 
hibit the  results  of  experiments  at  the  Novelty  Works,  N.  Y. 
City,  under  the  joint  supervision  of  that  establishment  and  the 
U.  S.  Navy  Department.  The  curves,  A,  B,  C,  D,  E,  refer  re- 
spectively to  steam-pressures  of  25,  40,  60,  80,  and  100  pounds. 


FIG.  145.— ACTUAL  WATER  E 


FIG.  146.— COMPUTED  EXPENDITURES. 


Curve  H  of  the  series  designated  No.  2  represents  the  cal- 
culated quantity  of  water  required  per  indicated  horse-power 
per  hour  in  a  non-condensing  engine.  The  calculations  take 
into  consideration  the  weight  of  steam  required  to  fill  the  cylin- 
der to  the  point  of  cut-off  and  to  supply  the  heat  transmuted 

*  Trans.  Am.  Soc.  M.  E.;   1888;  No.  cccxxi. 


THERMODYNAMICS  OF   THE  STEAM-ENGINE.          497 

into  work,  but  make  no  allowance  for  cylinder-condensation, 
for  losses  by  clearance,  or  for  deficiency  in  work  due  to  insuf- 
ficient area  of  passages,  or  to  back-pressure. 

Curve  G  is  a  similar  curve  based  on  the  additional  condi- 
tion that  the  clearances  and  ports  equal  one  twentieth  of  the 
cylinder  volume. 

Curve  Dis  D  in  series  No.  I,  and  shows  the  relative  extent 
of  the  losses  at  different  points  of  cut-off  due  to  cylinder-con- 
densation and  other  causes  not  included  in  the  calculated  re- 
sults for  an  engine  of  5  horse  power. 

The  curve  F  was  originally  interpolated  in  the  position 
shown  from  such  information  as  was  available  at  the  time  to 
show  the  probable  cost  of  using  steam  at  80  pounds  pressure 
in  an  engine  developing  about  100  horse -power.  Later  ex- 
periments show  that  for  conditions  stated  the  curve  should 
more  nearly  approach  the  curve  G. 

By  means  of  empirical  expressions  conforming  to  the  curves 
obtained  by  experiment,  Mr.  Emery  computed  probable  ap- 
proximate values  for  a  somewhat  wide  range  of  conditions  of 
operation  of  non-condensing  engines,  and  tabulated  them  as 
shown  on  page  49$. 

The  table  shows  that  equal  economy  should  be  secured  in 
non-condensing  engines  at  somewhat  higher  pressures  than 
with  condensing  engines.  It  would,  however,  require  the  use 
of  compound,  triple,  and  quadruple  expansion  engines,  to  se- 
cure best  results.  Mr.  Emery  would  restrict  the  expansion 
ratio  in  each  cylinder  to  2£,  in  such  engines. 

The  parallelism  of  Emery's  curves  indicates  that  we  are 
usually  safe  in  assuming  that  the  probable  cylinder-condensation 
in  the  regular  working  of  ordinary  unjacketed  non-condensing 
engines  is  sensibly  constant ;  and  at  moderate  speeds  Mr.  Buel 
takes  its  amount  as  1 5  pounds  per  hour  on  each  square  foot  of 
total  internal  surface  of  the  engine,  including  internal  super- 
fices  of  cylinder,  of  heads,  both  sides  of  the  piston,  the  surface 
of  its  rod,  and  the  internal  surfaces  of  the  steam -passages. 
The  condensation,  in  ordinary  forms  of  engine,  is  found,  on  this 
basis  of  computation,  to  vary  somewhat  on  both  sides  the  as- 


A    MANUAL    OF    THE   STEAM-ENGINE. 
STEAM-CONSUMPTION. 


I 

• 

3 

4 

5 

* 

7               8 

9 

IO 

it 

POUNDS  OF  WATER  PE 

R  INDICATED  HORSE-POWER  PER  HOUR. 

Engine  of  proper  size  to  develop  100  H.-P.    f=  100. 

Gauge  Pressure. 

Experimental  results  at  full 
stroke  in  small  engine,  ex- 
tended to  the  higher  pres- 
sures by  formula. 

Required  to  fill 
Cylinder. 

Required  to  supply  heat  for 
mechanical  work. 

nder-con- 
miscella- 

§ 
1 

i 

•a 

J_ 

5  for  N 
min. 

Required  at  full  stroke. 

Required  with  cut-off  at  0.6 
stroke. 

Required  with  cut-off  at  0.3 
stroke. 

Required  at  most  economi- 
cal cut-off. 

Approximate. 

J 

1 
M 

Required  for  cyli 
densation  and 
neous  losses. 

P 

•3 

60 
So 
100 

WS 

150 

400 

500 

E 

C, 

CM 

Ct 

Calc'd. 

C3  +  C4 

C 

l—C=l 

C 
i  —  c=o.4 

C 

I-<T=0.70 

C 

1—C= 

h.  min. 

74.80 
62.99 
52.29 

£* 
45-96 
44.38 
42-35 
40.25 

38.52 

57-75 
47-44 
41.99 
39-33 

57-75 
47-25 
41-49 
38-56 
36.32 
35-24 
34-19 
32.79 

1 
^58 

:P 

•55 
•53 

.16 

:687 
.48 
•41 

.22 

•15 

:3 

8.80 
14.81 
16.72 
17.82 
18.57 
19.  t6 
19.60 

62.54 
51-83 
45-77 
42.62 
40.30 
39.02 
37-89 
36.37 

53-74 
43-03 
36.97 
33-82 
31  -5° 
30.22 
29.09 
27-57 

30.37 
27.22 
24.90 
23.62 
22.49 
20.97 
19.30 

|a 

50.44 

29.05 
24.80 
21.73 
19.86 
18.29 
16.23 
13-95 
12.70 
11.35 

85 

29.65 

2.49 
2.47 

ii 

21.03 
22.33 

33-78 
33-08 

24.93 
24.28 

sumed  figure,  for  non-condensing  engines,  and  to  be  somewhat 
greater  for  condensing  engines ;  sometimes,  in  the  latter  case, 
exceeding  25  pounds,  accordingly  as  the  interior  surface  of  the 
cylinder  is  a  better  or  a  worse  heat-reservoir. 

The  performance  of  the  best  class  of  modern  engines  in  this 
respect  is  illustrated  by  the  following  tables  of  data  obtained 
by  Professor  Reynolds  from  the  triple-expansion  experimental 
engine  of  Owens  College.*  (§44;  Chap.  II.) 

In  the  first  three  cases,  in  the  first  table,  the  steam-jackets 
were  in  use  ;  in  the  last  three,  they  were  disconnected.  The 
difference  in  result  is  due  to  the  greater  cylinder-condensation 
in  the  latter  case  ;  the  total  amounts  of  which  are  given  in  the 


Minutes  of  Proceedings  of  the  Inst.  of  C.  E.;   1889;  No.  2407. 


THERMODYNAMICS  OF   THE   STEAM-ENGIXE. 


499 


AREAS  OF  DIAGRAMS  PER  POUND  OF  STEAM  AND  THERMAL 
EFFICIENCIES  OF  ENGINES. 


44 
*3«.645 
[88,096 

79-o 

S:f 

79-4 

33 
=  55.5-15 
192,067 
82.0 
23-2 
19.2 

82.6 

56 
228,420 
192,000 
84.6 
22.7 
19.4 

83-1 

4X 
235,500 
127,545 
54-0 
23-3 
14.1 

60.4 

35 
233,000 
139.546 
60.0 
23.2 
15-3 

65.9 

40 

221,360 

144,350 

65.0 
23.3 
15.5 

66.4 

Theoretical  area,  ft.  and  Ibs  
Measured  area,  ft.  and  Ibs.  

Percentage  of  theoretical  area.  . 
Theoretical  efficiency,  p.  c.  

Percentage    of    theoretical  effi- 
ciency   

CONDENSATION   WITHOUT  JACKETS. 


Xum 
ber  of 

Rerolnuons 

Ratio 

Propor 

c 

ion  of  Tot: 

ondenseds 

d  Steam 

t 

per 

of 

the 
Trial 

MiMte. 

Expansion. 

Mid- 

C»tK»ff. 

stroke. 

R.  -  .t-^e. 

Engine  No   I           •< 

41 

*e 

146 

2-7 
2   a 

0.40 

O  2Q 

0-39 

0.30 

O*22 

jj 

40 

322 

*«  3 
2.0 

"**V 
0.22 

0.21 

0.17 

Engine  No.  II  \ 

41 

35 

127 
215 

2-4 
2-4 

0-41 

•;  .  5  5 

0-35 
0.34 

0.29 
0.26 

1 

40 

320 

2.2 

0.30 

0.27 

0.14 

Engine  No.  III....} 

41 

35 

109 

184 

2-7 
3.05 

0.51 
0.48 

0.48 
0-47 

0-37 
0-33 

( 

40 

276 

2.6 

0.32 

0.36 

0.23 

second  table ;  in  which  the  proportion  thus  noted  ranges  from 
about  one  fourth  to  about  one  half  and  is  always  greatest  in 
the  high-pressure  and  least  in  the  low  pressure  cylinder.  These 
variations  from  the  ideal  case  are  well  shown  by  the  diagram  in 
Fig.  147,  in  which  the  actual  diagram  is  the  inner  and  the  ideal 
the  outer,  in  each  case :  the  departure  from  the  curve  for  sat- 
urated steam  and  the  modified  shape  of  the  diagram  exhibiting 
the  effect  of  introduction  of  the  essential  practical  conditions 
of  design  and  operation. 

129.  The  Laws  of  Variation  of  Losses,  internally,  are  not 
fully  ascertained.  The  experiments  of  Clark,  Hirn,  Isherwood, 
and  their  successors,  exhibit  the  general  method  of  variation 
already  indicated  ;  but  the  exact  law  remains  to  be  determined. 


5oo 


A   MANUAL    OF    THE    STEAM-ENGINE. 


The  Author  has  usually  taken  the  magnitude  of  this  loss  in  any 
given  engine,  other  conditions  invariable,  to  be  sensibly  pro- 
portional to  the  square-root  of  the  ratio  of  expansion,  and  to  be 
ordinarily  measured,  in  engines  of  moderate  size,  as  a  percentage 


FIG.  147.— REAL 


IDEAL  DIAGRAM. 


of  the  quantity  of  steam  or  of  fuel  demanded  by  the  perfect, 
ideal,  engine  under  similar  conditions,  by  from  one  tenth  to 
one  fifth  that  quantity,  accordingly  as  this  waste  is  more  or  less 
well  provided  against. 

In  experiments  directed  by  the  Author,  the  weight  of  steam 
condensed  per  square  foot  of  surface  exposed,  up  to  the  point 
of  "  cut-off,"  and  per  degree  Fahrenheit,  per  hour,  ranged  from 
0.015  to  0.020  pound,  corresponding  to  from  14  to  18  British 
thermal  units.*  For  ordinary  single-cylinder,  unjacketed 
engines,  it  may  be  taken,  under  usual  conditions,  at  the  higher 


*  Cylinder-condensation    in  Steam-engines  ;    R.  H.  Thurston  ;  Trans.  Am. 
Assoc.  for  Advancement  of  Science;  1885.     Journal  Franklin  Inst.;    Oct.  1885. 


THERMODYNAMICS  OF   THE   STEAM-ENGI\E.          5OI 

figure ;  assuming  the   law  to  be  capable  of   expression  by  a 
direct  and  simple  function. 

The  experiments  above  referred  to  were  made  by  Messrs. 
Gately  and  Kletsch,  upon  an  un jacketed,  simple,  engine  of  18 
inches  diameter  of  cylinder,  42  inches  stroke  of  piston,  both 
with  and  without  condensation.  The  valve-gear  was  of  the 
Corliss  variety,  and  its  action  such  as  to  secure  a  quick  and 
accurate  cut-off  at  the  desired  point.  Four  series  of  experi- 
ments were  undertaken,  in  each  of  which  two  conditions  were 
made  variable,  one  independent,  the  other  dependent ;  all 
others  being  for  the  time  kept  constant ;  thus  ascertaining : 

(1)  The  variation  of  condensation  with  varying  ratios  of  ex- 
pansion ; 

(2)  Varying  pressures,  the  condenser  being  in  use ; 

(3)  The  same,  without  condenser; 

(4)  Variation  with  changing  speeds  of  engine. 

The  results  obtained  and  the  deductions  therefrom  must  be 
accepted  as  only  approximate.  Some  irregularities  will  be  de- 
tected in  all  such  experimental  work  to  date,  which  are  prob- 
ably mainly  due  to  inevitable  variations  in  the  amount  of 
priming  and  quality  of  steam  used. 

(i)  To  determine  the  amount  of  condensation  in  the  steam- 
cylinder,  up  to  the  point  of  cut-off,  the  difference  was  taken 
between  the  amount  of  water  pumped  into  the  boiler  as  deter- 
mined from  weir  measurement  and  the  amount  shown  by  the 
indicator.  The 'ratio  of  this  quantity  to  the  true  amount  is  the 
fraction  of  cylinder-condensation  up  to  the  point  of  cut-off. 
The  per  cent  of  condensation,  as  determined,  increases  as  the 
ratio  of  expansion  increases. 

Fig.  148  shows  the  final  results  clearly,  the  ordinates  repre- 
senting cut-off,  and  the  abscissae  the  condensation  expressed  in 
per  cent  of  the  total  amount  of  steam  furnished  to  the  engine, 
thus: 

Cut-off  .589;         cylinder-condensation  =  22.73  per  cent. 
"443;  «  27.08    "       " 

"       .330;  "  "  =33-87    "       " 

"       .131  ;  "  "  =  50.07    "       " 


502 


A    MANUAL   OF   THE   STEAM-ENGINE. 


Thus  the  condensation  increases  rapidly  with  expansion  of 
steam  ;  or,  in  other  words,  with  longer  exposure  of  the  sides  of 
cylinder,  cylinder-head,  and  piston,  to  the  decreasing  tempera- 
tures of  the  expanding  steam  and  the  exhaust. 

Plotting  these  results,  we  obtain  the  curve  as  represented  in 
Fig.  148.  As  will  be  seen  later,  it  is  very  probable  that  this 


y» 


r 


\ 


>       -25       -3°       -35 
Condensation. 


FIG.  i48.-Cc 


curve  is  just  as  well  taken,  as  by  Professor  Cotterill,  as  loga- 
rithmic. It  is,  however,  closely  represented  by  the  hyperbola 
having  the  equation 

(x  +  0.12)  (y  -f  0.44)  —  0.2472  ; 

where  x  is  the  condensation  and  y  the  ratio  of  expansion  ;  or, 
referring  the  curve  to  its  asymptotes, 

x'y'  =  0.2472. 

At  full  stroke,  y  =  I,  and  x  =  0.12.  and  the  condensation  here 
becomes  twelve  per  cent ;  a  result  closely  corresponding  with 


THERMODYNAMICS  OF  THE   STEAM-EXGME,          JOg 

the  earlier  figures  obtained  by  Isherwood  on  the  U.  S.  S. 
Michigan.  When  we  approach  the  limit,  y  =  o :  .r  =  0.68, 
two  thirds  the  steam  is  condensed :  for  these  extreme  cases, 
however,  these  equations  cannot  be  expected  to  be  accurate. 

In  this  engine,  the  area  of  internal  surface  exposed,  up  to 
the  point  of  cut-off,  and  of  which  the  increments  are  constant, 
with  uniform  variation  of  the  cut-off,  is  measured  by 

^  =  3.96+16.5*. 

in  square  feet ;  and  the  variation  of  condensation  with  this 
varying  area  is  shown  in  the  next  figure. 


The  equation  of  the  curve  is 

(*  —  4-77)  (A  -  1-0266)  =  21647. 

Ike  Author  has  been  accustomed  to  assume  that  the  curve  may 
be  taken  as  parabolic,  and  to  use  the  more  manageable  ex- 
pression for  the  first  case,  above, 


=  a  \ '  r 


-VJ- 


504  A    MANUAL    OF    THE    STEAM-ENGINE. 

in  which  the  condensation  is  expressed  in  terms  of  the  recipro- 
cal of  the  cut-off,  —  =  r,  the  ratio  of  expansion,  a,  being  a  co- 
efficient having  a  constant  value  in  the  same  engine,  the  value 
of  r  only  varying.  From  the  data  just  given,  and  for  this 
engine, 

when  r  =  6.66    -f,        a  —  0.187; 

r  =  4.00,  a  =  0.1987; 

r  =  2.857,  a  =  0-1923  ; 

r  =  2.222  -f-,        a  =  0.1812; 

r  =  1.82,  a  =  0.174. 

From  which  it  will  be  seen  that  the  value  of  a  is  one  fifth 
approximately,  and  the  results  of  this  investigation  very  closely 
coincide  with  those  of  earlier  experiments  and  deduced  by  the 
Author  previously  to  this  investigation. 

The  hyperbolic  equations  give  the  following  figures : 

A  =  13.86 ;  x  =  cylinder-condensation  =  22.01  ;  error  —  0.39 

"      12.21;  "           "                                     25.00;  "     ±0.000 

"      10.56;  "           "               "                   28.50;  "     ±0.000 

;           "        8.91;  33-50;  "     —2.50 

"        7.26;  "           "                                    41.06  ;  "     —  2.94 

Also: 

y  =  cut-off  =  0.13  ;  x  =  cylinder-condensation  =  0.499  ;  error  —  o.oor 

=   .225;  "          "                              =0.410;  "         o.ooo 

=    -33  ;  "           "                               =  0.338 ;  "     —  0.002 

=    .45;  "           "                               =0.274;  "     +0.004 

=     .59;  "  "  "  =0.222;  "      -(-O.OO2 

These  equations  thus  so  closely  satisfy  the  record  obtained 
by  direct  observation  that  they  may  be  taken  sensibly  to 
represent  the  law  of  condensation,  as  a  function  of  the  ratio  of 
expansion  for  this  engine  under  the  conditions  described,  and 
show  that  the  weight  of  steam  condensed  is  sensibly  constant 
at  all  ratios  of  expansion  within  these  limits. 

The  magnitude  of  the  coefficient,  a,  in  the  expression  last 
given  above,  is  obviously  different  with  different  engines,  de- 
creasing as  the  size  of  engine  and  its  speed  increase.  The 
value,  O.2O,  above  found  will  only  apply  to  engines  similar  to 


THERMODYNAMICS  OF   THE   STEAM-ENGINE.  $0$ 

that  here  described,  in  size,  speed,  and  structure,  as  will  be 
seen  later,  when  deducing  the  more  general  expression. 

Taken  as  a  function  of  area  of  surfaces  producing  waste, 
these  data  show  the  condensation  to  be  directly  proportional 
to  that  area. 

(2)  The   variation  of   internal   condensation   with   varying 
steam-pressures,  all  other  conditions  being  as  usual  and  retained 
constant,  was  as  follows,  the  expansion  ratio  being  5  : 

Gauge-pressure  80       pounds  ;  condensation   35.24  per  cent. 

"        66.85       "  "  47-83    "      " 

52-33       "  36-84    "      " 

37-0        "  41-43    "      " 

22.3  41.19    "      •• 

The  engine  was  here  worked  condensing.  The  equation  of 
the  curve  for  this  case  is 

-r  =  45  —0.12667; 

in  which  x  is  the  steam-presssure  and  y  the  fraction  of  total 
steam  condensed.  Then 

y  =  pressure  =  80.0    ;  x  =  cylinder-condensation  =  34.88  ;  error  —    .036 

=  52.33;  "         "                 "              =38.3*:  +1-54 

=  37-o   ;  "        "                               =40.32;  —i. ii 

=  22.3    ;  "        "                "             =42.27;  -f- 1 .08 

And  the  equation  evidently  closely  represents  the  facts  for  this 
case.  It  indicates  that  condensation  would  become  unimpor- 
tant at  very  high  pressures  ;  the  expression  giving  x  =  o  for 
y=  355  Ibs.  by  gauge. 

(3)  The  non-condensing  engine  appears,  in  this  case,  to  have 
a  different  method   of   variation;    for,  throwing  off  the  con- 
denser, the  data  obtained  give,  with  the  point  of  cut-off  at  04, 
or  a  ratio  of  expansion  r  =  2.5,  very  much  less  condensation, 
and  it  is  not,  apparently,  as  before,  directly  variable  with  the 
variation    of   steam-pressure.     Only   three   trials   were   made, 
owing  to  the  impossibility  of  getting  steam  steadily  for  the 


5o6 


A    MANUAL   OF   THE   STEAM-ENGINE. 


highest  pressure  attempted  and  the  form  of  the  curve  for  this 
case  is  unknown  ;  but  the  figure  shows  the  lines  for  both  cases: 


1 


.05  .10  .15  .20  .25  .30  .35  .40  .45          .50  .55          .60 

Condensation. 
FIG.  150.— CONDENSATION  WITH  VARYING  PRESSURES. 

(4)  The  effect  of  variation  in  speed  of  engine,  or  time  of 
action  of  the  acting  surface  of  the  cylinder,  is  the  final  subject 
of  test.  Starting  with  an  average  boiler-pressure  of  19.67 
pounds  and  a  cut-off  of  .98  of  the  length  of  stroke  and  the  en- 
gine  running  at  an  average  of  33.74  revolutions  per  minute, 
three  trials  were  made,  concluding  with  an  average  speed  of 
62.977  revolutions  per  minute;  the  greatest  variation  in  the 
point  of  cut-off  being  .05  of  the  stroke,  and  in  the  pressure  .63 
of  a  pound.  Differences  in  the  condensation  occurring  can 
here  be  attributed  purely  to  the  variation  of  speed. 


THERMODYNAMICS  OF   THE   STEAM-EXGINE.          5OJ 

Difficulty  was  found  in  getting  the  engine  to  run  smoothly 
lower  than  thirty-three  revolutions  per  minute,  and  oppor- 
tunity was  not  given  to  make  a  fourth  test  at  a  higher  speed 
than  sixty-three  revolutions,  the  engine  being  needed  for  its 
regular  work.  But  it  will  be  seen  by  reference  to  the  figure  that 
the  three  points  of  the  curve  given  by  these  three  trials  are  so 
nearly  in  line  that  a  fourth  test  is  hardly  necessary. 

The  conditions  under  which  the  trials  were  made  were  so 
strictly  adhered  to,  and  the  results  obtained  varied  so  slightly, 
that  an  expression  from  these  results  determining  the  amount 
of  condensation  as  a  function  of  the  speed  may  be  taken  as 
strictly  representing  the  losses  occurring  by  condensation  in 
this  engine.  The  greatest  variation  in  the  range  of  pressure 
for  the  three  tests  was  three  and  one  half  per  cent,  and  the 
greatest  variation  in  the  cut-off  amounted  to  but  one  half  of 
one  per  cent. 

The  per  cent  of  condensation  was  : 

Revolutions  per  minute,  62.977;     per  cent  of  condensation,  24.37 
50.3;          "      "     "  "  28.75 

33-74;  33.506 

From  which  it  is  seen  that  the  condensation  varies  in  this  case 
sensibly  inversely  as  the  speed. 
Algebraically  expressed, 

jr  =  45  —0.33.7, 
and  we  have,  as  seen  in  Fig.  151, 

y  =  Revolutions  per  nain.  =  62.977;      *  =  Cjl  Con.  =  24.22;      error  -  0.15 
"  "      "          50.3;  "       "  28.41;          "     —0.34 

.    *  "      ••         33.74;  "      "          33-86;         "    +0.504 

Were  the  law  as  here  expressed  to  hold  good,  the  line  con- 
tinuing straight  to  its  intersection  with  the  coordinates,  the  loss 
of  steam  would  approach  0.45  as  the  speed  approached  the 
zero-limit,  and  would  itself  become  zero  as  the  engine-speed 
approximated  to  140  revolutions  per  minute. 


508  A    MANUAL    OF    THE   STEAM-ENGINE. 

Professor   Cotterill's   expression    for   this   limit   of   speed, 
N  =  ^fv,  d  taken  in  feet,  would   give   for   zero  condensation 

N  =  400,  nearly,  or  more  than  twice  the  former  figure. 

Professor  Marks  has  gone  over  this  work  to  determine  the 


\ 


.05      .10      .15      .ao      .25      .30      .35      .40      .45      .50      .55      .6 

Condensation. 
FIG.  151. — CONDENSATION  WITH  VARYING  SPEED. 

value  of  the  so-called  "  condensation-constant "  C,  in  the  ex- 
pression for  waste, 

W=ACt(Tl-  T3), 

for  this  engine,  under  the  various  conditions  of  its  operation, 
accepting  the  assumption  that  wastes  are  proportional  directly 
to  time  of  exposure  to  the  exhaust  steam,  rather  than  to  the 
square-root  of  that  quantity.  Here  A,  t,  J", ,  Tt,  represent 
area  of  exposed  surface ;  time  of  exposure,  and  temperatures. 
The  following  are  his  results  for  the  non-condensing  engine 
here  studied : 


THERMODYNAMICS  OF    THE   STEAM-ENGINE. 


509 


CYLINDER-CONDENSATION. 

SIMPLE,    NON-CONDENSING   ENGINE. 
(Experiments  of  Messrs.  Gately  &  Kletzsch,  Sandy  Hook,  1884.) 


1 

1-8 

f          CJ 

i 

| 

I 

1     X 

£ 

u 

«s 

1 

| 

Condensa- 
tion 

& 

^J 

«  1 

i 

S          |<5 

1  1_ 

0 

« 

<2 

I. 

" 

1   . 

Constant. 

cference  Number  of 
ment. 

uration  of  Rxperimeni 

roke  of  Cylinder  in  fei 

iameter  of  Cylinder  Ir 

eciprocal  of  True  Nu 
Expansions. 

umber  of  Strokes  per  i 

gS 

11 

•s 
1 

bsolute  Pressure  in  poi 
square  inch  at  Cut- 

bsolute  Steam-pressur 
Imust  at  Mid.  stroke, 
per  square  inch. 

smperature  of  Cylinde 
off  (Kafir.). 

smpcrature  of  Cylinde 
huust. 

cu 

|j 
1 

*tio  of  Actual  to  I 
Steam  at  Cut-off 

i  Ibb.  of  Steam. 

British  Units  of 
Heat. 

K 

Q 

m 

Q    tt 

Z 

c»       < 

* 

H         H 

w 

at       1     5 

- 

k  m 

i 

w 

•  5 
(9) 

1.40 

2.00 

i  -55 

3.5 

;-  = 

i-s 

-50.589 
50.443 
.50.330 

136.52  Dry  Sat.  6..54 
.35.9     "       "     68.34 
.34.64    "       "     62.10 

4-aa 

3-9' 
4-48 

294.2  [155.2    430 
30..  .4:152.  15;  390.13 
294.80(157.561426.35 

.294  0.0,576  i4.ao. 
.371  0.01929  18.00 
.5.2  0.0.909  17.31 

(10)  2.00 

3-3 

1.50.131 

137-9 

"     149-  « 

365 

279.84  .49.4    530-9 

.003  o-oi   ^ 

'5.15 

1-3 

.5  0.208 

.38.03    "        "      78.80    3  24    3.i.02'.44.  58  342.2 

.5440.oi544JI3.82 

::• 

2.00    3.5    .50.244.43.46!"       "      53.21     3.24  1284.95  144.58  492.1 

(?)    .917  0.025631 
.583  0.0.4.6, 

»-y 

'14' 
ti 

2.00     3.5!     .50.2.0 
2.00      3.5       .50.242 

.37-82 
«35.85 

:;  :: 

39-83    36. 
26.74    3  46 

266.741.49-02 
244.261.47.2. 

642.9 
936.6 

.7070.0.52814-16 
.7000.0.37212.94 

•  :-: 

•::: 

3.00  3.5   .50.4.2 
2.30  3.5!  .5^0.420 

.35-96 
»37-i4 

:;  :: 

65.36  .4  7° 
50.42   .4.82 

298..6L2 

281.30  212.4 

407-5 

(?)     .I22!0.00884 

(?)  .307  0.02288  1 

(?) 

(is 

3.00  3.5!  .50.466 

133-04 

"  •• 

28.40  .4-84 

247.56212.49 

886.6 

(?)  .376  0.04090 

3  -  -  - 

(?) 

•I) 

'•30  (3-5 

2-00     3.5 

1-45  '3-5 

•50.938 
.50.961 
.50.981! 

125.95 

I  00.60 
67-48 

"  " 

37-38    3-'5  1245.561.46.3. 
28.35     3-86    247-4oji5i.57 
28.53    4-96  1247.811161.94 

9.6.2 
886.8 
88t.6 

.322  0.014041x2.23 
.403  0.0.528  14.36 
.504  0.0.449113.68 

Average. 


Numbers  7-10  illustrate  varying  expansion  ;  11-15,  varying 
steam-pressures,  condensing;  16-19,  varying  pressure,  non-con- 
densing ;  20-22,  varying  speed  of  engine. 

Major  English,  computing  the  wastes  in  simple  marine  un- 
jacketed  condensing  engines,  obtains  just  double  the  above- 
given  constants ;  and  both  sets  of  results  correspond  fairly  with 
the  experience  of  various  other  investigators.*  For  jacketed 
condensing  engines  he  obtains  nearly  the  mean  of  the  two,  and 
not  far  from  two  thirds  the  higher  figure. 


*  Proceedings  Inst.  Mech.  Engrs.;  1887. 


510  A   MANUAL   OF  THE   STEAM-ENGINE. 

Fourier's   expression   for   heat-absorption,  taking  /  as  the 
symbol  for  time, 


shows  that,  as  the  period  of  exposure  to  the  higher  temperature 
diminishes,  the  amount  of  heat-absorption  is  reduced,  and  varies 
inversely  as  the  square-root  of  the  speed  of  engine,  a  conclusion 
independently  derived  by  Escher  *  from  direct  experiment,  and 
by  the  Author  by  observation  of  the  results  of  various  engine- 
trials,  although  not  apparently  confirmed  by  those  just  quoted. 

Professor  C.  A.  Smith,  in  1880,  found  a  variation  of  120°  F. 
in  the  internal  temperature  of  the  metal  in  a  locomotive  cylin- 
der, the  magnitude  of  the  change  varying  inversely  as  the 
speed  of  the  engine.f  Escher  found  this  waste  to  be  propor- 
tional, very  nearly,  other  things  equal,  to  the  square-root  of  the 
absolute  pressure  of  entering  steam. 

The  rate  of  transfer  of  heat  by  this  condensation,  in  en- 
gines of  large  range  of  expansion,  is  very  great  ;  in  average 
practice  a  dozen  times  as  rapid  as  the  transfer  across  the  heat- 
ing surfaces  of  the  steam-boiler.  A  flow  of  6000  B.  T.  U.  per 
hour  in  the  latter  case  and  of  60,000  units  in  the  former  are  not 
exceptional  values  for  transfer  on  an  area  of  one  square  foot. 
This  difference  is  accounted  for  by  the  fact  that  this  case  of 
the  boiler,  like  that  of  a  steam-jacket,  is  one  of  steady  flow  and 
affected  only  by  conductivity  of  the  metal  and  thermal  resist- 
ance of  surface  ;  while  cylinder-condensation  is  a  process  of 
storage,  and  is  a  function  of  specific  heat  per  unit  of  volume  as 
well  as  of  conductivity. 

Major  English  finds,  as  previously  taken  by  the  Author,:}:  and 
still  earlier  by  Professor  Cotterill,§  that  internal,  or  cylinder, 
condensation  varies,  at  least  approximately,  as  the  square-root 

*  Engineer;  1882. 
f  Engineering;  1880;  p.  460. 

\  President's  Annual  Address;   Am.  Soc.  M.E.;    1880.     Efficiencies  of  the 
Steam-engine;  Trans.  Am.  Soc.  M.  E.;  1880. 
§  Proc.  Inst.  M.  E.;  1871;   p.  516. 


THERMODYNAMICS  OF   THE   STEAM-ENGINE.  $11 

of  the  time  of  action,  or  as  — ,  where  A7"  is  the  number  of  revo- 
lutions per  minute  and  s  the  area  of  surface  effecting  the  cool- 
ing the  entering  steam.*  This  result  has  been  also  experi- 
mentally confirmed  by  Escher.  He  proposes  the  formula 


in  which  C  is  the  initial  condensation  in  British  thermal  units, 
per  pound  of  steam,  worked  in  an  unjacketed  cylinder  ;  W'vs>  the 
weight  of  feed-water  in  pounds  per  stroke ;  s,  the  exposed  sur- 
face of  metal  at  the  beginning  of  the  stroke ;  and  7*,  and  Tm 
are  the  initial  temperature  of  steam,  and  the  mean  temperature 
of  the  cylinder-walls,  at  a  minimum,  both  on  the  absolute  scale. 
Pj  is  the  density  of  the  entering  steam.  A  is  a  constant,  which 
he  finds  to  be,  for  cases  studied  by  him,  80  in  British  units. 
For  jacketed  engines,  he  takes  Tt  =  Tm  and  adopts 


in  which  A  becomes  56,  indicating  a  gain  of  about  30  per  cent 
in  the  reduction  of  this  waste,  by  the  use  of  the  jacket,  for  the 
cases  examined. 

Major  English  finds,  for  re-evaporation,  the  following  ex- 
pression : 


where  the  total  surface  exposed  to  the  point  assumed  is  s  ;  Tm 
and  T^  are  the  mean  absolute  temperatures  and  the  final  abso- 
lute temperature  of  the  steam  up  to  and  at  that  point  ;  «//- 


*  Proc.  Inst.  M.  E.;  Oct.  1889. 


512  A    MANUAL    OF    THE   STEAM-ENGINE. 

jacketed  cylinders  being  assumed.     For  jacketed  engines,  Tm  is 
made  T,  ,  and  then 


"  Initial  condensation  and  corresponding  transfer  of  heat  to 
the  metal  will  of  course  go  on  upon  each  fresh  surface  exposed 
during  the  stroke  ;  but  the  supply  of  heat  to  effect  this  is  drawn 
by  re-evaporation  from  that  stored  up  in  the  surface  already 
exposed;"  so  that  the  effect  is  simply  "to  distribute  it  over  a 
larger  area." 

Thus  the  excess  of  re-evaporation  over  condensation  will 
become,  for  any  elementary  movement  of  the  piston, 


or 


accordingly  as  the  unjacketed  or  the  jacketed  engine  is  taken  ; 
B  having  the  value  80  or  56,  as  the  case  may  be.  The  net  con- 
densation, up  to  any  given  point,  becomes 


for  unjacketed  and  for  jacketed  cylinders,  respectively. 
The  total  weights  of  steam  per  stroke  become 

W  = 


in  which  A  is  80  or  56,  as  the  case  may  be,  and  X  is  volume 
swept  through,  to  point  of  cut-off,  in  cubic  feet ;  c  is  the  clear- 


THERMODYNAMICS  OF   THE   STEAM-ENGINE.  513 

ance-ratio  to  that  volume ;  »  is  the  ratio  of  cushion  to  total 
steam  per  stroke  ;  and  the  other  quantities  as  already  given.  A 
comparison  of  these  expressions  with  the  results  of  test  of  the 
\Villans  engine,  which  happens  to  give  the  needed  data,  shows 
remarkably  close  correspondence. 

It  is  obvious,  on  comparison  of  the  data  now  available,  and 
the  varying  conditions  under  which  they  are  produced,  that  the 
precise  form  of  the  expression  for  this  waste  will  be  determined, 
as  well  as,  probably,  the  magnitudes  of  its  constants,  both  by 
the  condition  of  the  surfaces  acting,  and  by  that  of  the  steam 
supplied,  as  well  as  by  the  variable  conditions  of  operation  of 
the  engine  itself. 

The  indications  are,  as  deduced  from  a  study  of  representa- 
tive indicator-diagrams,  that  in  about  one  second,  were  the  time 
allowed,  the  process  of  absorption  of  heat  would  be  practically, 
in  such  cases,  complete ;  while  for  shorter  periods  the  total  ab- 
sorption would  be  sufficient  to  condense  steam  in  proportion  to 
the  square-root  of  the  time  of  exposure ;  i.e.,  one  half  as  much, 
for  example,  in  one-fourth  second. 

Experiment,  as  shown  by  Hirn,  proves  the  initial  condensa- 
tion to  be  progressive,  as  the  piston  advances,  up  to  the  point 
of  cut-off,  ordinarily ;  in  cases  cited  by  him,  increasing  from  I 
per  cent  water  at  the  beginning  to  31  per  cent  at  the  end  of 
the  admission-period,  and  in  some  cases  attaining  very  much 
higher  proportions.  Hirn  has  shown  that,  when  superheated 
steam  is  used,  there  may  exist  condensation  on  the  interior 
surfaces  of  the  cylinder  and  superheated  steam  in  the  midst  of 
the  charge,  the  cylinder  containing  at  the  same  time  water 
and  wet,  dry,  and  superheated,  steam. 

Careful  discrimination  should  be  made  between  the  wastes 
produced  by  heat-transfer  between  metal  and  steam  during  the 
expansion-period  and  those  occurring  during  the  exhaust- 
stroke.  The  latter  are  losses  of  the  whole  quantity  so  trans- 
ferred ;  while  the  former  are  the  differences  between  the  effi- 
ciencies of  transformation  with  maximum  range  of  expansion 
and  with  the  lesser  actual  ranges  for  the  successive  decrements 
of  heat  and  temperature  during  transfer.  If  possible,  in  all 


514  A  MANUAL    OF    THE    STEAM-ENGINE. 

calorimetric  investigations  the  two  quantities  of  rejected  heat 
should  be  separately  recorded.  The  condensation  at  the  point 
of  cut-off  is  often  20  or  30  per  cent;  where  it  is  reduced  to  12 
or  15  at  the  end  of  the  expansion,  and  the  waste  by  surrender 
of  heat  by  the  metal  during  the  exhaust  period  is  10  to  20  per 
cent. 

The  advantage  possessed  by  a  valve-gear  and  system  by 
which  separate  steam  and  exhaust  ports  are  provided,  in  reduc- 
tion of  internal  wastes,  is  obvious,  and  is  practically  found  to 
be  very  considerable  ;  especially  when,  as  is  usual,  the  valves 
are  so  placed  at  each  end  of  the  cylinder  as  to  reduce  the  "  dead 
spaces  "  to  minimum  volume.  Large  marine  engines  are  now 
designed,  in  some  instances,  with  separate  steam  and  exhaust 
valves  and  ports  ;  the  valves  being  of  the  piston  variety  and 
double-ported. 

Re-evaporation  taking  place  during  expansion  gives  rise  to 
a  real  gain  of  efficiency ;  yet  evidently  a  loss  occurs  if  a  com- 
parison is  made  with  the  case  in  which  the  same  steam,  instead 
of  being  initially  condensed,  is  worked  from  initial,  maximum 
pressure  and  temperature. 

While,  other  conditions  being  equal,  increase  of  engine-speed 
decreases  wastes,  there  will  always  be  found  a  practical  limit, 
if  nowhere  earlier,  at  the  point  at  which  the  resulting  decreased 
mean  forward-pressure  and  increased  back-pressure  give  rise  to 
overbalancing  loss.  This  limit  is  set  farther  away  as  ports  are 
enlarged  ;  but,  again,  in  a  new  compensation,  enlarged  ports 
increase  the  cost,  in  work,  of  the  operation  of  the  valves  and 
gear. 

While  the  theory  of  heat-engines  can  only  give  a  general 
knowledge  of  practical  and  of  applicable  principles  in  their 
design  and  operation,  it  may  point  the  way  to  further  improve- 
ment, may  serve  as  a  guide  and  check  in  novel  constructions, 
and,  coupled  with  experimental  knowledge,  may  even,  in  some 
cases,  enable  a  computation  to  be  made  of  probable  efficiencies 
that  may  be  useful,  if  not  substantially  exact.  In  all  cases, 
however,  the  engineer  checks  his  work  by  reference  to  the  ex- 
perience already  had  with  engines  of  as  nearly  as  possible  sim- 


THERMODYNAMICS  OF   THE   STEAM-EXGIXE.  $1$ 

ilar  kind  and  under  similar  conditions  of  operation.  Expe- 
rience, after  the  machine  has  been  built  and  set  at  work,  finally 
enables  him  to  make  precise  adjustment,  where  his  preliminary 
estimates  had  given  him  approximations. 

The  following  table,  computed  by  Mr.  Thompson,  exhibits 
the  probable  water-consumptions  and  the  mean  effective  pres- 
sures for  ideal  cases,  with  a  correction  for  initial  condensation 
and  leakage,  the  engines  being  assumed  to  be  of  good  con- 
struction and  of  fairly  large  size. 

These  allowances  for  internal  wastes  amount  to  about 
0.12  \'r  and  0.15  Vr,  for  non-condensing  and  for  condensing 
engines  respectively.  The  Author  would  allow  one  half  greater 
loss  in  engines  of  common  form  and  of  one  or  two  hundred 
horse-power.  The  figures  should  obviously  diminish  with  in- 
creasing sizes  and  speeds,  and  should  increase  as  the  engines  are 
smaller  and  speeds  lower,  as  elsewhere  shown. 

In  conclusion  :  The  variation  of  condensation,  with  changes 
of  pressure  and  temperature,  under  usual  conditions  of  prac- 
tice, is  thus  found  to  be  very  moderate,  and  to  follow  a  very 
simple  law,  so  far  as  it  can  be  traced.  The  waste  with  varying 
speed  of  engine  is  found,  also,  to  be  nearly  as  previously  indi- 
cated by  the  Author ;  but  the  law  is  less  exactly  determined 
than  in  the  case  of  varying  expansion.  Since,  however,  in  all 
ordinary  cases,  in  practice,  the  speed  of  engine  and  the  boiler- 
pressure  are  practically  constant,  in  the  regular  operation  of 
the  engine,  the  most  important  part  of  the  investigation  is 
that  relating  to  the  ratio  of  expansion.  The  next  most  im- 
portant matter  is  the  determination  of  the  variation  of  loss 
with  varying  speed  of  engine,  and  the  results  here  reached  are 
sufficiently  exact  to  be  very  useful,  both  to  the  designer  and 
the  owner  of  engines,  although  the  precise  method  of  varia- 
tion and  its  exact  algebraic  expression  still  remain  subjects 
for  investigation.  The  last  investigation,  relating  to  variation 
with  change  of  pressures,  is  interesting  as  bearing  upon  the 
future  of  the  continually  progressing  advance  in  the  direction 
of  increasing  pressures.  The  last  two  lines  of  research  de- 
mand still  further  exploration.  The  results  here  reached  must 


516 


A    MANUAL   OF    THE   STEAM-ENGINE. 


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THERMODYNAMICS  OF   THE   STEAM-EXG1XE.  $17 

be  regarded,  at  present,  as  applicable,  in  the  theory  of  the 
steam-engine,  only  provisionally,  and  as  to  be  accepted  finally, 
only  after  repeated  experiment. 

Collating  the  facts,  so  far  as  known,  the  Author  has  con- 
tinued to  employ  the  expressions,  based  on  Fourier's  work  and 
on  experiment, 


=  b  — 


in  which  x  is  the  fraction  of  steam  condensed  ;  a  a  constant  to 
be  determined  for  each  engine,  or  class  of  engines,  of  similar 
size,  speed,  and  stenm-pressure  ;  b  a  constant  for  the  general 
expression:  /IT  the  range  of  temperature  worked  through; 
d  the  diameter  of  the  engine-cylinder  in  feet  ;  r  the  real 
ratio  of  expansion,  and  X  the  revolutions  per  minute. 

130.  The  Theory  of  Internal  Condensation  and  Waste 
is  obviously  one  of  exceeding  difficulty  ;  and  an  exact  and 
rational  theory  must  include  so  many  variable  and  mutually 
interacting  conditions  that  it  cannot  be  expected,  even  if  fully 
developed,  to  find  application,  in  all  cases,  in  the  engineer's,  or 
the  designer's,  work. 

It  is  commonly  assumed  that  cylinder-condensation  will  be 
proportional  to  the  range  of  temperature  between  that  of  the 
entering  steam  and  the  exhaust  ;  to  the  time  of  exposure  to 
the  exhaust,  or  inversely  as  the  speed  of  engine,  and  to  the  area 
of  internal  surface  affected,  up  to  the  point  of  cut-off.  On  this 
basis  Professor  Marks  has  made  comparisons  of  data  derived 
from  a  considerable  number  of  experiments,  mainly  on 
non-condensing  Corliss  mill-engines,  and  has  obtained,  as 
already  seen  (§  129),  as  a  mean  for  ordinary  work,  a  value  of  C, 
the  number  of  pounds  of  steam  condensed  on  the  square  foot 
of  internal  cylinder-surface,  per  hour,  and  per  degree  range  of 
temperature,  C  =  0.02047.  equivalent  to  18.13  British  thermal 
units.*  The  experiments  of  Messrs.  Gately  and  Kletsch, 
already  described,  give  from  0.016  to  0.019  pound,  or  14.5  to 

*  Relative  Proportions  of  the  Steam-engine  ;  pp.  206-7. 


5l8  A    MANUAL    OF   THE   STEAM-ENGINE. 

17.4  B.  T.  U.,  with  ratios  of  expansion  varying  from  2  to  7,  and 
an  average  of  0.0165,  nearly,  equivalent  to  15  B.  T.  U.  for  the 
whole  series  of  trials.  The  first-given  values  may  probably 
be  found  sufficiently  approximate  for  use  in  estimating  the 
waste  in  any  similar  engines. 

The  value  of  this  constant  being  determined,  the  total  cyl- 
inder-condensation is,  approximately,  in  pounds  of  steam,  per 
hour, 

W=CA(Tl-  T;)/; (i) 

where  C  is  that  constant,  say  0.02,  A  the  area  of  internal  sur- 
face covered  by  the  steam  up  to  the  point  of  cut-off,  in  square 
feet ;  while  t,  the  time  of  exposure  of  heat  and  steam  observed 
in  experiment,  is  generally  nearly  constant,  at  any  given 
speed  of  engine,  and  range  of  pressure  and  temperature, 
irrespective  of  the  magnitude  of  the  varying  ratio  of  expansion, 
and,  as  in  the  Sandy  Hook  experiments,  a  nearly  constant 
product  can  be  obtained  for  the  product  of  the  "  cut-off " 
and  percentage  of  waste.  The  same  investigation  and  Professor 
Marks's  deductions  from  the  reported  data  show  that  it  is  most 
likely  to  be  the  time  of  either  expansion  or  of  exposure  to  the 
exhaust,  more  probably  to  their  sum,  which  should  be  taken  for 
/  while  it  is  not  yet  ascertained  whether  the  function  to  be  ac- 
cepted is  the  square-root  of  that  quantity,  its  first  power,  or 
some  intermediate  function.  It  is  probable  that  the  several  ex- 
pressions  of  Professors  Cotterill  and  Marks  and  of  the  Author 
will  find  use,  as  at  least  approximate,  each  in  its  appropriate 
place. 

In  producing  an  expression  for  the  magnitude  of  internal 
heat-wastes  by  condensation  and  later  evaporation,  we  may 
adopt,  as  already  seen,  either  of  several  methods,  which  are 
more  or  less  closely  approximate.  Following  Fourier,  we  find 
that  the  quantity  of  heat  thus  stored  and  wastefully  restored 
may  be  taken  as  proportional  to  the  area  of  surface  acting,  the 
temperature  range,  or  temperature  head,  and  the  square-root 
of  the  time  of  action.  All  these  proposed  expressions  are 
based  upon  these  assumptions  or  upon  experimental  data  con- 


THERMODYNAMICS  OF   THE   STEAM-ENGINE.  519 

firming  them  ;  except  that  it  remains  questionable  whether  this 
function  of  the  time  is  of  either  constant  form  or  value. 

That  the  time  to  be  taken  is  not  that  of  exposure  to  the 
entering  steam,  up  to  the  point  of  cut-off,  is  certain,  from  the 
fact  that  the  total  loss  is  never  so  proportional. 

Experiment  has  indicated,  however,  that  the  waste  often 
varies  more  nearly  as  the  square-root  of  the  time  of  action,  and 
the  Author  has  been  accustomed  so  to  take  it.*  It  is  more 
convenient,  usually,  to  take  this  loss  as  a  function  of  the  ratio 
of  expansion,  as  seen  later,  and  experiment  has  been  found  to 
indicate  this  function  to  be  the  square-root,  approximately,  of 
that  ratio.  It  has,  as  yet,  been  impossible  to  ascertain  by  ex- 
periment precisely  how  the  waste  varies  with  range  of  temper- 
ature. It  seems  extremely  probable  that  the  condition,  the 
quality,  of  the  steam  from  the  boiler  may  so  seriously  modify 
the  working  of  an  engine  as  to  make  it  difficult  to  analyze  the 
total  variation  into  the  factors  due  all  these  constantly  varying 
complications  of  physical  conditions. 

It  will  often  be  sufficient,  in  the  solution  of  special  prob- 
lems, to  assume  approximate  data.  Thus,  the  Marks  coeffi- 
cient will  answer  all  purposes  in  the  comparison  of  engines  of 
different  sizes  working  under  otherwise  similar  conditions.  The 
expression 


may  be  used  in  computing  the  probable  weight  of  steam 
needed  to  supply  cylinder-wastes  ;  when  W^  is  the  weight 
needed,  for  the  representative  ideal  case,  no  initial  condensa- 
tion occurring  ;  a  is  the  constant  determined  as  already  indi- 
cated, and  which  may  be  taken  as  not  far  from  4  for  unjack- 
eted  and  3  for  well-jacketed  cylinders,  for  average  cases.  D 
is  the  diameter  of  cylinder  in  inches,  r  is  the  ratio  of  expan- 
sion, and  /  is  the  time  of  one  stroke,  in  seconds.  In  the  Gately 

Q 

and  Kletsch  experiments,  ^  =  0.2,  approximately,  and  /  =  I. 
very  nearly. 

*  Trans.  Am.  Soc.  M.  E.  ;  May  1881.     Jour.  Franklin  Inst.  ;  May  1881. 


52O  A    MANUAL   OF   THE   STEAM-ENGINE. 

The  value  of  the  constants  a  and  c  in  the  expression  for 
waste, 


may,  with  superheating,  or  better  thermodynamic  conditions 
in  other  respects,  be  reduced  considerably  below  the  values 
here  assumed  as  representing  ordinarily  good  average  practice. 
Mr.  Barrus  gives  data  from  trials  conducted  by  him  in  which 
they  fall  to,  in  some  cases,  two  thirds,  and  in  other  seven  to 
one  half,  those  obtained  in  earlier  work  by  the  Author.  The 
range  would  seem  to  be  from,  approximately, 

a  =  2          to     a  =  3, 
c  =  o.io    to     c  =  0.15  ; 

where  steam  is  used  without  superheating,  and  to  as  low  as 
a  =  i      and      c  =  0.05, 

or  less,  with  steam  effectively  superheated  ;  d  being  taken  as 
the  diameter  of  the  cylinder  in  inches.* 

The  assumption,  in  our  equations,  that  heat-transfer,  in 
cylinder-condensation,  is  sensibly  proportional  to  the  range  of 
temperature,  in  ordinary  cases,  seems  justified  by  experiment. 
This  conclusion  of  Rankine  and  later  engineers  is  confirmed, 
not  only  by  the  cases  earlier  studied  by  the  Author,  but  also 
by  later  investigations.  Mr.  Bodmer  finds  this  fact  illustrated 
by  the  engine-trials  both  of  Willans  and  of  Major  English. 
His  conclusions  are  usually  substantially  in  accord  with  those 
previously  reached.  He  finds  the  quantity  of  heat  transferred, 
and  of  steam  condensed  wastefully,  proportional  to  the  total 
area  of  the  walls  of  the  clearance  and  port  spaces,  as  already 
seen.f  In  the  expression,  for  simple  engines,  taken  by  Bod- 
mer, 

Q=  C(T-t)S-i-N*, 


*  Trans.  Am.  Society  Mech.  Engrs. ;  vol.  xi;  1890;  pp.  170,  175;  tables. 
f  Industries;  Oct.  17,  1890;  p.  385. 


THERMODYNAMICS  OF   THE  STEAM-ENGIXE.  521 

Q  is  the  heat  transferred  in  B.  T.  U. ;  T  —  t  the  temperature- 
range  ;  ^'  the  area  of  clearance  and  port  surfaces,  in  square 
feet ;  and  N  the  number  of  revolutions  per  minute.  The  value 
of  C  varies  from  about  o.i  B.  T.  U.  in  simple,  unjacketed, 
engines,  to  0.5  for  good  jacketed  cylinders,  and  appears  to  be 
fairly  constant. 

With  well-clothed  cylinders,  it  seems,  according  to  the 
experiments  of  Mr.  Buel,  that  the  amount  of  steam  unac- 
counted for  depends  mainly  upon  the  area  of  internal  surface ; 
and,  in  ordinary'  practice,  in  the  case  of  non-condensing  engines, 
with  unjacketed  simple  engines,  but  with  well-clothed  cylinders, 
the  condensation  per  hour  will  be  between  20  and  30  pounds  per 
square  foot  of  total  internal  surface,  from  10  to  20  pounds  per 
square  foot  of  internal  surface,  for  similar  engines,  condensing, 
and  about  these  amounts  for  the  former  class  with  steam-jack- 
eted cylinders,  and  one  half  the  latter  figure  for  jacketed  con- 
densing engines.  In  case  it  be  assumed  that  the  cylinder-con- 
densation is  15  pounds  per  hour,  per  square  foot  of  internal 
surface,  including  the  ports,  the  two  sides  of  the  piston,  and 
the  surface  of  the  rod,  supposing  the  interior  surface  to  be 
about  as  follows : 

Ports , ,    12.0  sq.  ft. 

Sides  of  cylinder 3 1 .4  "     " 

Cylinder-heads  and  sides  of  piston 12.6  "     " 

Piston-rod 4.6  "     " 


Total 60.6"     " 

— we  have  as  steam  unaccounted  for  by  the  indicator 
60.6  x  15  =  909  pounds  per  hour. 

It  would  perhaps  be  more  correct  to  take  the  areas  of 
heads,  piston  and  steam-passages,  and  a  variable  fraction  of  the 
cylinder-surface,  and  the  condensations  as  a  constant  function 
of  that  total  area.  This  total,  in  many  marine  engines,  is  as 
much  as  twice  the  combined  areas  of  piston  and  cylinder 
heads,  and  all  these  areas  are  in  action  twice  as  long  as  the 
average  for  the  cylindrical  surfaces. 


522  A    MANUAL   OF   THE  STEAM-ENGINE. 

Professor  C.  A.  Smith  concluded,  after  studying  the  work 
of  Isherwood  and  other  early  investigators,  that,  as  the  Author 
has  elsewhere  indicated,  "  the  whole  excess  of  water  used  over 
that  required  in  a  non-conducting  cylinder  is  rudely  propor- 
tional to  the  difference  of  temperature  between  the  incoming 
and  outgoing  steam,  and  to  the  diameter  of  piston  ;"  and  such 
excess  is  nearly  constant,  and  is  independent  of  the  ratio  of 
expansion  for  ordinary  cases,  a  conclusion  which  has  been  seen 
to  be  confirmed  by  both  experiment  and  computation  based  on 
theory. 

There  are  thus  available  several  more  or  less  closely  ap- 
proximate methods  of  computation  that  will  answer  the  pur- 
poses of  the  engineer  and  give  fairly  accurate  measures  of 
these  wastes.  Of  the  several  expressions  on  which  they  are 
based,  one  or  another  will  be  employed  as  they  are  found  more 
or  less  suitable  to  the  purpose  and  conditions  of  the  case  in 
hand. 

That  the  assumption  of  approximately  constant  wastes  by 
internal  cylinder-condensation,  as  already  indicated  in  several 
ways  and  by  reference  to  experiments,  may  be  ordinarily 
adopted  in  provisional  computations  of  efficiency  and  steam- 
consumption  is  also  evident  from  .an  inspection  of  the  curves 
given  by  Mr.  Emery  and  by  the  results  of  computation  by  the 
other  methods  presented  in  this  work,  notably  those  relating  to 
the  compound  engine.  Mr.  Buel  has  computed,  in  great  de- 
tail, the  probable  demand  of  steam  in  an  engine  of  about  150 
horse-power,  having  found  for  such  engines,  by  experiment,  a 
nearly  constant  condensation,  with  varying  expansion,  of  about 
15  pounds  of  steam  per  square  foot  of  internal  surface  per 
hour.* 

A  tabular  resume  of  this  work  will  be  found  in  the  appen- 
dix with  the  nomenclature,  the  formulas,  and  the  results  for  a 
wide  range  of  values  of  the  ratio  of  expansion. 

The  proportions  of  the  cylinder  affect  greatly  the  magni- 
tude of  this  waste.  Thus, 


*  Am.  Machinist;  June  30,  1888. 


THERMODYNAMICS  OF   THE  STEAM-ENGINE.  523 

Let  d  =  the  diameter  of  cylinder ; 
/  =  the  length  of  stroke ; 

e  =  the  proportion  of  total  area  of  surfaces  of  dead- 
spaces  to  those  of  the  clearance  proper ; 
r  =  ratio  of  expansion ; 
V=  volumes  of  cylinder ; 
S  =  surfaces. 

Neglecting  the  cushion-steam,  the  area  in  contact  with  steam 
at  cut-off  is 


the  volume  of  steam  enclosed  is 
and  the  ratio  of  S  to  Vis 


The  cylinder-condensation  would  be  proportional,  all  parts 
being  equally  wasteful,  to  the  value  of  this  ratio.  The  ratio 
of  active  surface  to  total  volume  of  cylinder  is 

5,         St 


and  the  values  of  r  and  of  the  volume,  F,  ,  being  constant, 
yt  =  \xd*l,  nearly,  =  const., 


and  it  becomes  evident  that  this  waste  is  influenced  greatly  by 
changing  values  of  d  and  /,  increasing  rapidly  as  the  diameter 


524  A    MANUAL    OF    THE    STEAM-ENGINE. 

is  increased  and  the  stroke  diminished.     With  similar  propor- 
tions and  varying  size  of  cylinder, 


and  the  waste  thus  varies  inversely,  as  already  elsewhere  taken, 
inversely  as  the  linear  dimension  of  the  cylinder,  and  values  of 
the  percentage  of  condensation  obtained  from  any  one  engine 
by  experiment  must  be  multiplied  by  the  inverse  ratio  of  such 
dimension  to  obtain  correct  values  of  this  proportion  of  waste 
for  other  sizes. 

The  value  of  e,  above,  is  given  by  Cotterill  as  from  i.i  in 
the  best  cases  of  four-valve  engine,  as  the  Corliss,  to  about  2 
for  single  slide-valve  engines. 

The  time  of  exposure  is  only  the  same,  however,  for  the 
surfaces  of  heads,  piston,  and  passages,  and  is  there  a  maxi- 
mum. As  already  noted,  the  effect  of  the  varying  exposure  of 
the  cylindrical  surfaces  may  often  probably  be  neglected  with- 
out important  error,  and  the  whole  loss  taken  as  that  of  those 
parts  alone. 

Where  the  ratio  of  expansion  is  not  great,  the  presence 
of  "  entrained "  water  in  the  steam  may  not  produce  any- 
important  ill-effect.  For  the  ideal  case  of  the  non-conducting 
engine,  this  was  long  ago  shown  to  be  true,  by  Combes.*  This 
deduction  was  also  found  to  be  correct  in  practice,  by  Mon. 
Him.  With  large  ratios  of  expansion,  and  especially  with 
jacketed  engines,  the  opposite  is  probably  always  true. 

The  irregularities,  discrepancies,  and,  often,  apparent  con- 
tradictions observed  in  the  reported  results  of  experiments  on 
the  effect  of  the  steam-jacket,  and,  especially,  on  the  extent 
and  method  of  variation  of  cylinder-condensation  and  wastes 
are,  perhaps,  generally  due  to  unnoted  variations  in  quality  of 
steam,  and  also  possibly,  often,  to  inaccurate  observations. 

Professor  Cotterill,  observing  that  the  range  of  temperature 

*  Thfiorie  MScanique  de  la  Chaleur;  1863;  §  xxxv.  p.  157. 


THERMODYNAMICS  OF    THE  STEAM-ENGIXE. 


525 


is  approximately  proportional  to  log,  r,  adopts,  for  usual  ranges 
of  expansion  in  a  single  cylinder,  the  expression, 


in  which  y  =  condensation-ratio  ; 

r  =  expansion-ratio  ; 

d  =  diameter  of  cylinder,  in  feet  ; 
IV  '=  revolutions  per  minute; 

and  finds  the  value  of  the  coefficient  C  to  average  about  5  ; 
varying  from  4  to  7  with  the  nature  of  the  surfaces  character- 
istic of  the  engine.*  In  this,  as  in  all  the  preceding  cases,  the 
time-function  is  based  on  the  period  of  action  of  the  exhaust. 
It  is  nevertheless  obvious  that  the  time  of  action  of  the  pro- 


FIG.  152.— HKAT-TRAJ.-SFKR. 

gressive  cooling  during  expansion  must  modify  this  effect. 
Since  the  total  initial  condensation,  which  is  usually  principally 
waste,  is  determined  by  the  extent  of  the  antecedent  cooling, 
it  would  seem  that  these  functions  of  time,  which  actually  de- 
termine this  waste,  can  be  only  approximately  proportional  to 
Nt  or  to  its  functions  as  taken. 

The  total  steam  demanded  is  obtained  by  multiplying  the 
ideal  quantity  by  I  -(- y,  the  "  liquefaction-factor." 

*  This  value  for  the  Author's  work  on  mill-engines  is  6,  nearly. 


526  A   MANUAL   OF    THE    STEAM-ENGINE. 

Hirn's  method  of  distinguishing  the  various  heat  and  work 
effects,  as  formulated  by  Professor  Dwelshauvers-Dery,  is  il- 
lustrated by  the  following  :  * 

The  indicator-diagram^  Fig.  151,  completed  by  marking  on  a 
proper  scale  the  volume  of  the  clearance,  v,  shows  the  quanti- 
ties which  the  diagram  and  the  data  ought  to  furnish. 

The  following  volumes,  expressed  in  cubic  feet,  are  taken 
directly  from  the  engine  : 

v,  volume  of  the  clearance  space. 

Vt,      "        occupied  by  the  steam  at  the  point  of  cut-off. 

V^     "  "  "         "        end  of  expansion. 

F2,      "  "  "  "         "  "      exhaust. 

F3,     "  "  "  "         "  "   the  compression. 

Vt,     "  "  "  "         "  "       "  stroke. 

Va  =  (F3  —  v)  -|-  (F0  —  v}  is  the  volume  swept  through  during 
admission. 

Vd  =  F,  —  F0  is  the  volume  swept  through  during  expansion. 

Ve  =  (Vt  —  FJ  -f  (Vt  —  F4)  is  the  volume  swept  through  dur- 
ing exhaust. 

Ve  =  Fa  —  Fs  is  the  volume  swept  through  during  the  com- 
pression. 

Vf  •=.  V^  —  v  \s  the  volume  swept  through  during  a  stroke. 

On  the  diagram  the  pressures  are  measured  in  Ibs.  per 
square  foot : 

Pt,  pressure  at  the  end  of  admission. 
Pt,         "  "  "      expansion. 

Pv         "  "  "      exhaust. 

P%,         "  "       the  compression. 

Ta"  =  area  bBAab  is  the  work  in  thermal  units  during  the  ad- 
mission before  the  beginning  of  the  stroke. 

T^  —  area  bBDdb  is  the  work  in  thermal  units  during  the  ad- 
mission forward  stroke. 

Ta  =  Ta"  —  Ta  is  the  work  in  thermal  units  during  the  ad- 
mission. 

*  Trans.  Am.  Society  Mech.  Engrs. ;  No.  CCLIX;  vol.  xi;  1889. 


THERMODYNAMICS  OF   THE  STEAM-ENGINE.  $2/ 

Td  =  area  dDEed  is  the  work  in  thermal  units  during  the  ex- 

pansion. 
TV  =  area  eEFfe  is  the  work  in  thermal  units  during  the  ex- 

haust  before  the  end  of  the  forward  stroke. 
Te"  =  area.  fFCcf  is  the  work  in  thermal  units  during  the  ex- 

haust, backward  stroke. 
Te  =  Te"  —  7y  is  the  work  in  thermal  units  during  the  ex- 

haust. 
T,  =  area  cCAac  is  the  work  in  thermal  units  during  the  com- 

pression. 
7}  =  area  bBDEFfb  =  Ta'  -f  Td  -f-  TV  is  the  work  in  ther- 

mal units  during  the  forward  stroke. 
Tn  =  vteifFCABbf  =  Te"  +  Te  +  TV'  is  the  work  in  ther- 

mal units  during  the  backward  stroke. 

T'=  Tf—Tn  =  ABDEFCA    is  the  indicated  work  in  ther- 

mal units  corresponding  to  a  stroke  of  the  piston. 

The  steam  has  also  done  work  not  indicated  on  the  diagram, 

represented  by  the  area  aAKka,  which  is  necessary  to  accom- 

plish the  compression  of  the  steam  into  the  clearance  in  order 

to^give  it  a  pressure  equal  to  that  of  the  steam  entering  the 

cylinder.     Since  the  magnitude  of  this  work  is  not  known,  it 

will  be  reckoned  in  the  heat  exchanged  between  the  steam  and 

the  metal  during  the  admission. 

Uncertainty  exists  as  to  the  composition  of  the  mixture  of 
steam  and  water  in  the  cylinder  when  exhaust  ceases  and  com- 
pression begins.  M.  Hirn  has  shown  that  in  general  it  may  be 
assumed  that  the  mixture  contains  only  steam,  all  the  water 
which  covered  the  walls  having  been  vaporized  and  expelled 
into  the  condenser  during  the  exhaust,  and  hence  our  calcula- 
tion gives  the  weight  Mc  pounds  of  steam  during  compression. 
The  volume  F,  of  steam  and  its  pressure  Pt  can  be  ascertained 
from  the  diagram,  at  this  instant.  From  the  tables  the  value  of 
tf,  is  deduced,  the  weight  in  pounds  per  cubic  foot,  and 


Experiment  must  supply  the  weight  Ma  pounds  of  steam 
which  passes  into  the  cylinder  at  each  stroke  of  the  piston  and 


528  A    MANUAL    OF   THE   STEAM-ENGINE. 

its  quality  x,  or  the  weight  m  of  pure  steam  contained  therein 
at  the  boiler-pressure.  This  will  be  called  Q  thermal  units. 
From  what  precedes,  its  value  will  be 


in  which  A.  and  q  are  the  latent  heat  of  the  steam  and  the  heat 
of  the  water  at  the  given  pressure. 

During  expansion  the  weight  of  the  mixture  in  the  cylinder 
is,  therefore, 


and  during  compression,  Mc. 

Hence  if  the  steam  is  saturated,  its  internal  heat  will  be  as 
follows  :  During  the  expansion 


mp. 
During  the  compression 

U= 


If  there  is  a  steam-jacket,  the  water  which  comes  from  the 
condensation  is  weighed,  and  its  weight  ascertained  per  stroke 
of  piston.  Let  it  be  called  Mj  pounds.  This  steam  is  con- 
densed under  the  mean  pressure  of  the  boiler.  For  each 
pound,  the  jacket  will  have  furnished  r  thermal  units.  The 
jacket  has  then  furnished  <2'  'thermal  units,  and 

Q=Mjr. 

Part  of  the  heat  brought  in  by  the  jacket  will  have  reached 
the  steam  ;  another  part  is  lost  by  radiation.  The  radiation  per 
stroke  should  be  evaluated  experimentally.  It  will  be  called  E 
thermal  units. 

When  the  engine  is  condensing,  the  weight  of  water  which 
leaves  the  condenser  is  measured,  and  from  this  is  deduced  the 
weight  of  cold  water,  Me  pounds,  introduced  into  the  condenser 
for  each  stroke.  Its  initial  temperature  /,  is  measured  and  its 
final  temperature  tf.  The  steam-tables  give  the  heats  of  the 


THERMODYNAMICS  OF   THE  STEA31-EXGIXE.          $29 

water  qt  and  qf  which  correspond.    Hence  the  heat  rejected  per 
stroke  by  the  cold  water  is  ascertained  by  means  of  the  equation 


Finally  the  weight  Aff  pounds  of  water  comes  from  the  con- 
densed steam  and  is  at  the  temperature  tf  if  the  condensation 
is  effectuated  by  injection,  and  at  the  temperature  //  if  by  a 
surface  condenser.  It  follows  that  a  second  part  of  the  heat  re- 
jected into  the  condenser,  which  may  be  called  c  thermal  units, 
will  be  determined  by  one  of  these  two  formulae, 


or    c  — 

The  heat  rejected  in  the  condenser  will  be  the  sum,  or 
(C+c). 

When  there  is  no  condensation,  this  heat,  rejected  into  the 
atmosphere,  cannot  be  evaluated. 

The  vapor  in  the  cylinder  carries  there  Q  thermal  units  at 
each  stroke.  It  receives  from  the  jacket  Q'  —  E  thermal  units. 
It  loses  T  thermal  units  to  overcome  the  exterior  work,  and  it 
carries  into  the  condenser  (C  -\-  c)  thermal  units.  As  the 
regime  is  reached,  the  sum  of  all  these  quantities  of  heat  is 
zero. 

Hence  follows  the  first  fundamental  equation  : 


Q  +  &=T+(C+c)  +  E..    .....    (I) 

With  condensation,  all  the  quantities  are  given  experiment- 
ally. This  equation  can  only  serve  in  this  case  as  a  check.  If 
the  second  member  should  differ  sensibly  from  the  first,  it 
would  mean  that  the  trial  had  been  badly  conducted.  Without 
condensation  this  equation  may  serve  to  determine  the  value 
of  the  rejected  heat  (C  -\-  c\ 

The  quantities  of  heat  received  or  given  up  by  the  metal, 
exchanged  between  the  metal  and  the  steam,  will  be  designated 


53O  A    MANUAL   OF   THE    STEAM-ENGINE. 

by  R  when  expressed  in  thermal  units.    The  subscript  indicates 
the  phase  during  which  the  exchange  is  measured.     Hence  : 
^thermal  units  is  the  quantity  of  heat  exchanged  between 

the  metal  and  the  steam  during  admission  ; 
Rd  thermal  units  is  the  quantity  of  heat  exchanged  between 

the  metal  and  the  steam  during  expansion  ; 
Re  thermal  units  is  the  quantity  of  heat  exchanged  between 

the  metal  and  the  steam  during  exhaust  ; 
Rc  thermal  units  is  the  quantity  of  heat  exchanged  between 

the  metal  and  the  steam  during  compression. 
Ra  ,  Rd  ,  Rc  will  have  positive   signs  when  the  heat  passes 
from  the  steam  to  the  metal.   Re,  on  the  other  hand,  is  positive 
when  the  heat  passes  from  the  metal  to  the  steam. 

In  general,  Rc  and  Ra  are  positive,  and  Rd  is  negative  ;  that 
is  to  say,  that,  generally,  the  steam  warms  the  metal  during  the 
compression  and  admission,  and  the  metal  gives  up  its  heat  to 
the  steam  during  the  expansion.  The  exchange  which  takes 
place  while  the  cylinder  has  no  communication  with  the  con- 
denser will  be  called  R.  It  follows  that 


The  total  exchange  for  one  stroke  of  the  piston  can  be 
called  R,  and 

R  =  Rf—  Re  =  Rc  4-  Ra  +  Rd  -  Re. 

This  total  would  be  zero  if  there  were  no  heat  denoted  by 
E  lost  by  radiation.  R  =  E.  When  the  jacket  furnishes  Q 
thermal  units,  Q'  =  E  +  (—  R). 

The  second  equation  can  then  be  written  as  follows  : 

R  =  E-Q',     or     Rf+Q  =  E  +  Rt\ 
or,  again, 

Re  +  Ra  +  Rd  =  Rt+(E-Qt)  .....     (II) 

The  quantities  designated  by  R  are  not  given  directly  by 
experiment  ;  they  must  be  computed  ;  which  requires  four  new 
equations,  in  which  Rc,  Ra,  Rd,  Re  will  be  the  unknown  quanti- 


THERMODYNAMICS  OF    THE   STEAM-EXGIXE.  53! 

ties.  The  equations  of  the  expansion  and  the  compression  are 
easy  to  write,  since  the  weight  of  fluid  in  action  is  constant. 
The  fluid  is  enclosed  in  the  cylinder,  and  cannot  exchange  heat 
except  with  the  metal  of  the  cylinder.  When  U0  and  £/,  rep- 
resent the  internal  heat  of  the  steam  at  the  commencement 
and  at  the  end  of  expansion,  we  shall  have 


Similarly,  the  internal  heat  of  the  fluid  at  the  commence- 
ment of  compression  was  b\.  The  heat  Te  resulting  from  the 
work  of  compression  is  added  to  this,  and  this  sum  ought  to 
preserve  for  the  steam  the  heat  denoted  by  £/,  ,  and  also  to 
give  Re  thermal  units  to  the  metal  ;  whence 


In  the  periods  of  admission  and  exhaust,  the  problem  is 
complicated  by  the  fact  that  the  steam,  in  coming  into  the 
cylinder,  carries  thither  Q  thermal  units,  and,  in  leaving  the 
cylinder,  it  carries  out  (C-\-c)  thermal  units  to  the  condenser 
or  the  outer  air.  Whence,  for  the  admission, 

U.+  Q=U.+  T.+R.-t 
and  for  the  exhaust, 


These  last  equations  can  be  written  as  below,  and,  adding 
those  preceding,  we  have 


(I) 

-Q';      .     .       (li 
R*=U9+Q-U0-Ta;  ......     (Ill, 

Rd=  u.-U.-T^..    .......     (IV) 

R.=  Ut  +  (C+c)-Ul-T.-,    ....      (V) 

R<=  U.-  U,+  Te  ........     (VI) 

The  quantity  Ra  does  not  represent  solely  the  exchange  of 
heat  between  the  vapor  and  the  metal.  There  is  heat  given 
out  by  the  steam  to  compress  that  which,  under  low  pressure^ 


532  A    MANUAL   OF   THE    STEAM-ENGINE. 

filled  the  waste  spaces  at  the  end  of  the  exhaust.  This  heat, 
not  shown  by  the  indicator,  is  an  integral  part  of  Ra,  U^  has 
been  obtained  on  the  hypothesis  that,  at  the  commencement  of 
compression,  there  the  steam  is  dry  and  saturated. 

The  object  of  the  computations  is  to  obtain  the  values  of 
JRC,  Ra,  Rd,  Re,  Rf,  and  to  represent  these  values  graphically. 
For  this  purpose  the  same  scale  is  adopted  for  the  exchange  of 
heat  as  for  the  diagrams  of  pressure,  and  in  the  following  man- 
ner: Ta  represents  a  certain  number  of  thermal  units  lost  by 
the  steam  while  the  piston  is  generating  the  volume  Va  cubic 
feet.  In  like  manner,  Ra  represents  the  thermal  units  lost  by 
the  steam  while  the  piston  sweeps  through  the  same  volume. 
The  value  of  Ta  is  represented  on  the  diagram  by  a  surface 
whose  length,  representing  Va,  is  the  base.  If  the  pressure 
during  admission  was  constant  and  equal  to/a,  this  diagram 
would  be  a  horizontal  line  at  the  height  which  is  represented 
by  pa,  and  the  area  would  be  rectangular  and  equal  \.o  paVa. 
l( pa  is  counted  in  pounds  per  square  foot,  then/aFa  =  772 Ta\ 

772T 
whence  pa  =  ^77—. 

V  a 

Similarly,  a  height  ra  can  be  calculated  such  that 

raVa 
whence 


also,  in  like  manner, 


r-  =  -?. 


If  the  exchanges   are  positive— that  is  to  say,  if  it  is  the 
steam  which  furnishes  heat  to  the  metal — the  ordinates  r  will  be 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


533 


carried  above  the  axis  in  the  forward  stroke,  and  below  in  the 
backward  stroke.  If  the  exchanges  are  negative — that  is  to  say, 
if  it  is  the  metal  which  furnishes  heat  to  the  steam — the  ordi- 
nates  r  are  carried  below  the  axis  for  the  forward,  and  above  it 
for  the  backward  stroke.  In  a  trial,  to  be  considered  later,  Ra 
has  been  found  positive ;  Rd  negative ;  Rt  negative ;  and  Re 
positive.  Then  the  diagram  of  exchanges  is  shown  in  Fig.  153. 


FIG.  153 — HEAT- EXCHANGES. 

The  area  aKLABda  represents  Ra\ 
"     dCDed  "          Rd; 

"     eEFGHce         "  Re- 

"     cljac  "  Rc. 

Positive  exchange  is  represented  by  hatchings  from  left  to 
right ;  negative  transfer  by  hatchings  from  right  to  left.  The 
difference  of  these  two  surfaces  would  be  zero  if  there  were  no 
heat  lost  by  external  radiation,  or  received  from  a  jacket.  In 
the  example  there  was  a  loss.  On  the  diagram  is  a  line  MN,  at 
a  height  such  that  the  surface  OMNfO  represents  Rf=' 


534  A  MANUAL    OF   THE   STEAM-ENGINE. 

Ra-\-Rd.  This  is  the  loss  due  to  the  action  of  the  cylinder- 
walls.  The  straight  line  PQ  is  at  such  a  height  that,  on  the 
same  scale,  the  surface,  OPQfO,  of  which  the  contour  is  edged 
by  hatchings,  represents  the  positive  work  7}  of  the  steam. 

We  refer  all  the  quantities  to  one  pound  of  steam  em- 
ployed. We  shall  give  an  example  of  application  in  the  chap- 
ter on  Engine-trials  ;  which  see. 

Hirn  and  Hallauer  have  shown  that,  in  ordinary  cases,  at 
least,  in  the  computation  of  the  efficiencies  of  steam-engines,  it 
may  be  safely  assumed  :  (i)  that  the  weight  of  vapor  remain- 
ing in  the  clearance-spaces  may  be  neglected ;  (2)  that  this 
vapor,  in  compression,  may  be  considered,  if  at  all,  as  dry  and 
saturated.  It  is  only  when  the  cylinder  is  so  constructed  as  to 
hold  precipitated  water  in  its  hollows  that  the  presence  of  the 
liquid  affects  in  this  manner  the  economical  working  of  the 
engine. 

The  rate  at  which  the  metal  surface  may  condense  the 
entering  steam  is  probably,  however,  greatly  modified  by  the 
extent  to  which  water  adheres  to  it  and  obstructs  the  entrance 
of  heat,  and  by  the  rapidity  and  thoroughness  with  which 
water  at  any  time  precipitated  on  those  surfaces  is  removed 
during  that  or  earlier  stages. 

131.  The  Restriction  of  Cylinder-condensation  may  be 
effected,  to  a  limited  extent,  by  proper  precautions. 

This  loss,  as  previously  stated,  is  greater  as  the  range  of 
temperature  during  expansion  is  greater ;  is  increased  by  slow 
speed  of  engine,  by  reduction  of  back-pressure,  by  increase  in 
size  of  engine  for  a  given  amount  of  work  done,  by  increase  in 
conductivity  of  the  surfaces  of  the  working  cylinder,  and  by 
wetness  of  steam.  It  is  reduced  by  low  ratios  of  expansion, 
by  increasing  back-pressures,  by  reducing  initial  pressures,  by 
increasing  speed  of  engine,  and  by  special  expedients,  as  steam- 
jacketing,  superheating,  and  the  division  of  the  expansion 
between  two  or  more  cylinders,  in  "  compound  "  or  multiple- 
cylinder  engines. 

This  waste  becomes  the  less  when  the  sides  of  the  cylinders 
only  are  jacketed,  the  smaller  their  diameter;  it  is  lessened, 


THERMODYNAMICS  OF  THE    STEAM-EXGIXE.  535 

when  both  heads  and  pistons  are  jacketed,  by  increasing  diame- 
ters, volumes  being  in  both  cases  equal.  With  superheated 
steam,  and  whenever  there  is  little  initial  condensation  to  be 
anticipated,  the  shape  of  cylinder  is  determined  by  the  mini- 
mum ratio  of  volume  to  internal  superfices,  Le.,  . =  -  • 

length       2' 

unless — as  is  often  the  case — it  is  controlled  by  commercial  con- 
siderations. The  surfaces  of  the  piston  must  evidently  be 
here  included,  since  the  principal  losses  occur  largely  on  those 
surfaces. 

In  general,  we  may  say  that  the  efficiency  of  an  engine  is 
some  function  of  differences  of  temperature,  speed  of  engine, 
and  areas  exposed  to  contact  with  steam :  but  the  difference 
of  temperature  is  a  varying  function  of  pressures  and  times  of 
exposure ;  the  speed  determines  time  and  exposure,  and  the 
area  of  surface  exposed  is  a  function  of  volume  per  unit  of 
weight  of  steam,  and  of  shape  of  cylinder.  All  these  condi- 
tions are  involved  and  interdependent,  and  simple  approximate 
expressions  will  be  found  preferable  to  any  exact  formula. 

Again,  there  may  be  noted,  as  already  stated,  some  com- 
pensations. The  difference  in  back-pressure  between  non- 
condensing  and  condensing  engines  is  productive  of  such  a 
wide  difference  in  the  range  of  temperatures  worked  through 
as  possibly  often  to  justify  the  assumption  that  condensation 
may  be  assumed  to  be  independent  of  the  actual  back-press- 
ure, and  to  be  determined  solely  by  other  conditions  above 
noted.  In  steam-jacketed  engines  the  value  of  the  steam- 
jacket  is  reduced  by  high  speed;  since  the  losses  that  it  is 
designed  to  check  are  rendered  less  by  the  same  cause.  The 
internal  friction  of  engine,  due  to  the  pressure  and  rubbing 
of  the  piston  and  its  rings,  produces  an  equivalent  amount  of 
heat,  and  this  aids,  by  thus  drying  the  steam,  in  reducing 
waste. 

The  proper  methods  of  prevention  of  such  wastes  are,  evi- 
dently, those  reducing:  (i)  the  heat-transferring  power  of  the 
fluid ;  (2)  the  heat  receiving  and  storing  power  of  the  surfaces  in 
contact  with  it ;  (3)  the  time  of  exposure ;  and  (4)  the  range  of 


536  A    MANUAL    OF   THE   STEAM-ENGINE. 

temperature  worked  through.     The  methods  actually  practised 
or  proposed  are  : 

(1)  Effectively  drying  the   steam,  as    by  superheating,  by 
compression  ;  by  steam-jacketing,  and  by  admixture  of  air  or 
gas. 

(2)  Lining  the  cylinder  with  non-conductors,  or  bathing  it 
with  oil,  or  other  non-volatile  and  slowly-conducting  substance. 

(3)  Increasing  the  speed  of  engine. 

(4)  "  Compounding." 

Superheating  is  found  to  be  most  effective ;  but  it  is  limited 
in  the  extent  to  which  it  may  be  carried ;  and,  practically,  up 
to  the  present  time,  it  has  been  found  undesirable  to  attempt 
much  more  than  to  thoroughly  dry  the  steam  before  its 
entrance  into  the  engine. 

One  hundred  degrees  Fahrenheit  (55^°  Cent.)  is  usually 
considered  a  fair  and  safe  limit  for  superheating  at  the  boiler ; 
and,  with  steam  as  ordinarily  supplied,  this  merely  secures  dry 
steam  at  the  engine,  thus  greatly  reducing  its  conductivity. 
The  chilling  taking  place  at  its  entrance  probably  even  then 
invariably  produces  more  or  less  moisture.  To  carry  super- 
heating so  far  as  to  enable  the  steam  to  be  worked  wholly  in 
the  superheated  condition  would  usually  compel  an  increase  of 
temperature  to  several  hundred  degrees  above  the  normal. 

Steam-jacketing  is  frequently  practised  with  compound  en- 
gines, and  sometimes  with  the  simple  engine  when  intended  to 
work  at  high  ratios  of  expansion. 

The  introduction  of  air,  by  reducing  the  conductivity  of  the 
fluid,  has  been  found  by  Warsop,  experimenting  on  locomo- 
tives,* and  by  others,  to  produce,  in  some  cases,  a  gain  of 
about  ten  per  cent.  This  last  is  not  a  common  practice;  but 
the  other  methods  are  in  common  use,  and  are  found  to  effect 
an  economy  which  increases  with  decrease  of  efficiency  in 
other  respects ;  an  economy  which  may  probably  average,  in 
successful  practice,  about  twenty  per  cent. 

Lining  the  cylinder  with   a    non-conductor,  if   practicable, 

*  London  Engineering;  1873. 


THERMODYNAMICS  OF   THE   STEASf-EXGIXE.          537 

would  considerably  reduce  this  form  of  waste.  Smeaton,  a 
century  ago,  so  lined  his  cylinder-heads,  using  wood  for  the 
purpose,  and  Emery  has  attempted,  though  without  permanent 
success,  to  line  the  whole  interior  with  glass  or  porcelain,*  and 
the  Author  has  reduced  the  heat-absorbing  power  of  such  sur- 
faces, in  experimental  investigations.  40  and  60  per  cent.+  The 
free  use  of  oil  in  the  cylinder  has  been  usually  found  to  pro- 
duce sensible,  but  costly,  gain  in  efficiency.  A  well-polished 
internal  surface,  especially  if  bathed  in  oil,  is  hardly  less  effec- 
tive in  reducing  wastes  than  is  well-dried  steam.  Old  and 
carefully  handled  engines  are  apt  to  show  a  decided  advantage 
over  new,  and  probably  for  this  reason. 

High  spffds  of  engine,  other  things  being  equal,  have  been 
found  to  give  very  decided  gains,  as  compared  with  low  speeds  ; 
and,  both  for  this  reason  and  on  account  of  the  gain  in  power 
also  to  be  thus  secured,  speeds  have  been  increasing  steadily, 
since  the  time  of  Watt,  from  his  standard  maximum  velocity, 

F=  128  I  7~. 

— where  s  is  the  stroke  of  piston  in  feet, — to  several  times 
that  figure ;  to  more  than 

F=8oo  V~s 

in  some  cases,  in  locomotive  engineering  practice.  Speeds  of 
rotation  have  thus  been  brought  up  to  100,  in  even  very  large 
marine  engines,  and  to  300  and  upward  in  small  stationary 

engines.     At  speeds  exceeding  about  JT=e  ~~ ,   those  wastes 

become  unimportant.  This  expedient,  as  affecting  a  good 
type  of  simple  engine,  has  been  found  quite  as  effective, 
on  the  average,  as  jacketing  or  moderate  superheating  in 
common  practice,  and  even  to  give  a  close  competition  in 

*  Trans.  Am.  Soc.  Mech.  Engis.:  iSSi. 

f  Ibid.;  1889.  See  papers  by  Carpenter  and  Horse,  also  by  the  Author,  in 
Trans.  Am.  Soc.  C.  E.;  iS39-91. 


538  A    MANUAL   OF   THE   STEAM-ENGINE. 

many  cases  with  the  compound  engine  operated  at  low  speeds. 
Usual  values  of  the  factor  first  given  above  are  about  1 50  to 
200  for  pumping-engines,  300  to  400  for  common  mill-engines, 
and  500  to  600  for  "  high-speed  "  engines,  and  equally  high 
speeds  for  the  fastest  engines, 

"  Compounding"  or  the  use  of  two  or  more  cylinders  "  in 
series,"  in  which  the  ratio  of  expansion  is  restricted,  in  each,  to 
a  practically  economical  limit,  is  the  now  usual  system,  espe- 
cially in  marine-engine  construction,  is  becoming  daily  more 
common  with  stationary  engines,  and  is  also  coming  into  use  in 
locomotives.  By  the  adoption  of  this  plan,  steam-pressures 
and  total  ratios  of  expansion  for  maximum  economy  have 
been  increased  very  greatly  over  those  admissible  with  the 
single-cylinder  engine.  While  the  latter  has  been  found,  with 
steam  at  60  pounds  pressure,  by  gauge,  to  demand,  ordinarily, 
3  °r  3i  pounds  of  coal,  or  25  to  30  pounds  of  steam,  per 
indicated  horse-power  per  hour,  the  former,  under  similar 
circumstances,  requires  but  2  or  2^  pounds  of  coal,  17  to  20 
pounds  of  feed-water,  per  I.  H.  P.  per  hour;  and  the  "  triple- 
expansion,"  at  150  pounds,  or  ten  atmospheres,  takes  \\  to  if 
pounds  of  coal,  14  to  18  pounds  of  steam  ;  while  the  "  quad- 
ruple-expansion "  engine,  at  12  to  15  atmospheres  (180  to  225 
Ibs.  per  square  inch)  is  said  to  demand  only  13  to  15  pounds 
of  feed-water,  or  i^  to  I  £  pounds  of  good  fuel,  figures  probably 
never  yet  reached  by  simple  engines. 

The  ratios  of  expansion,  which,  with  the  simple  engine,  have 
not  been  usually  successfully  carried  beyond  5  or  7,  are  thus 
increased  to  8  or  10  in  the  "compound,"  to  12  or  15  with  the 
"triple,"  and  to  15  or  20,  or  even  more,  with  the  "  quadruple- 
expansion  "  engine.  The  terminal  pressure  is  usually  between 
%  and  f  atmosphere  (7^  or  10  Ibs.  per  square  inch),  absolute 
pressure,  in  the  best  forms  of  engine. 

Compression  of  the  exhaust  as  nearly  to  boiler-pressure  as 
is  possible,  as  already  remarked,  is  decidedly  advantageous — 
and  especially  with  the  non-condensing  engine — not  only  as  a 
means  of  filling  the  clearance  and  port  spaces,  and  thus  saving 
some  steam,  but  also,  and  possibly  in  some  cases  to  a  still  more 


THERMODYNAMICS  OF   THE   STEAM-ENGINE.  539 

important  extent,  by  transforming  a  certain  amount  of  energy 
into  heat  and  communicating  this  heat  to  the  cooled  surfaces 
of  the  cylinder ;  warming  them  up  to  approximately  the  tem- 
perature of  the  entering  steam,  thus  checking  initial  condensa- 
tion to  an  extent  which  may  much  more  than  compensate  the, 
apparent,  added  waste  of  power  in  compression.  With  a  "  link- 
motion"  valve-gear^  an  increase  of  the  ratio  of  expansion  is 
accompanied  by  increased  compression,  and  thus  the  exaggera- 
tion, by  increased  expansion,  of  the  evil  here  considered  is 
partly  checked  by  the  coincident  increase  of  compression.  The 
locomotive  is  probably  an  illustration  of  marked  gain  occurring 
in  this  manner. 

Practical  limitations  of  the  principal  methods  of  restricting 
exhaust-wastes  and  of  enhancing  efficiency  are  now  familiar 
to  engineers.  Drying  steam  is  always  advantageous,  by  what- 
ever method  practised ;  but,  at  the  pressures  now  common,  of 
ten  atmospheres  (150  pounds  per  square  inch)  and  upward,  the 
temperature  of  the  steam  is  already  not  far  from  that  at  which 
ordinary  lubricants  are  liable  to  decomposition  ;  and  any  con- 
siderable superheat  inside  the  engine-icylinder  is  therefore 
usually  thought  unsafe. 

Jacketing  is  not  always  considered  sufficiently  advantageous 
to  compensate  added  cost  and  risks  at  moderate  expansion- 
ratios,  and  at  such  speeds  as  are  now  standard ;  and  many 
engineers  leave  even  the  high-pressure  cylinders  of  slow-mov- 
ing compound  engines  unjacketed.  No  practicable  method  of 
lining  with  non-conductors  has  yet  been  found,  although  the 
experiments  of  the  Author  seem  to  indicate  that  this  is  a 
promising  direction  for  investigation;  and  speeds  of  engines 
are  now  but  slowly,  if  at  all,  increasing.  The  dangers  of  heat- 
ing journals,  and  of  breakage,  introduced  with  excessive  ve- 
locities, have  become  already  appreciable. 

Compounding  to  a  greater  extent  than  now  practised  is 
only  advisable  with  very  considerable  increase  of  steam-pres- 
sures, and  this  advance  is  impeded  by  the  difficulty  of  obtain- 
ing thoroughly  safe,  economical,  and  otherwise  satisfactory, 
steam-generators. 


540  A    MANUAL    OF   THE   STEAM-ENGINE. 

The  subjects  of  compounding,  jacketing,  and  superheating 
are  of  such  importance  as  to  demand  their  consideration  in  a 
separate  chapter. 

132.  The  Friction  of  the  Engine  itself,  the  "  Internal 
Friction  ';  of  the  machine,  is  usually  a  considerable  quantity, 
and  is  a  source  of  loss  of  energy  by  reduction  of  the  efficiency 
of  the  engine  as  a  machine.  Since  the  efficiency  of  any  train 
of  mechanism,  as  a  machine  purely,  is  the  ratio  of  the  quantity 
of  work  delivered  by  it  to  whatever  it  may  drive,  or  of  work 
done  by  it  upon  the  next  element  in  order  to  the  work  which 
it  receives,  or  the  energy  applied  to  its  propulsion,  the  internal 
losses  of  mechanical  energy  become,  to  the  engineer,  subjects 
of  real  importance.  As  "  Friction  is  thus  the  principal  cause, 
and  usually  the  only  cause,  of  loss  of  energy  and  waste  of  work 
in  machinery,"  *  "  a  given  amount  of  energy  being  expended 
upon  a  driving-point  in  any  machine,  that  amount  will,  in  ac- 
cordance with  the  principle  of  persistence  of  energy,  be  trans- 
mitted from  piece  to  piece,  from  element  to  element,  of  the 
machine  or  train  of  mechanism,  without  diminution,  if  no  per- 
manent distortion  takes  place  and  no  friction  occurs  between 
the  several  elements  of  the  train,  or  between  those  parts  and 
the  frame  or  adjacent  parts.  Temporary  distortion,  within  the 
limit  of  perfect  elasticity,  causes  no  waste  of  energy ;  per- 
manent distortion  causes  a  loss  of  energy  equal  to  the  total 
work  performed  in  producing  it ;  but  permanent  distortion  is 
due  to  deficiency  of  strength,  and  to  defective  elasticity,  and 
is  never  permitted,  in  well-designed  machinery,  properly  oper- 
ated. Hence  the  important  principle  : 

"  The  only  cause  of  lost  work  in  mechanism  which  is  to  be 
anticipated  in  design,  and  calculated  upon  in  deducing  the 
theory  of  any  special  machine,  is  the  friction  necessarily  con- 
sequent upon  the  relative  motion  of  parts  in  contact  and  under 
pressure."f 

The  compound  friction  of  lubricated  surfaces,  as  it  may 

*  Friction  and   Lost  Work  in    Machinery  and  Mill-work;  R.    H.    Thurston; 
N.  Y.,  J.  Wiley  &  Sons,  1885;  p.  n;  §  12. 
f  Ibid.,  pp.  II,  12. 


THERMODYNAMICS  OF   THE   STEAM-ENGINE.  $4! 

be  termed,  or  friction  due  to  the  action  of  surfaces  of  solids 
partly  separated  by  a  fluid,  is  observed  in  all  cases  in  which 
the  rubbing  surfaces  are  lubricated.  In  such  instances  the 
solids  are  usually  not  completely  separated  by  the  liquid  film 
interposed  between  them,  but  partly  rub  on  each  other,  and 
are  partly  supported  by  the  layer  of  lubricant  which  is  retained 
in  place  by  adhesion  and  by  capillary  action.  The  rubbing 
together  of  the  two  solids  produces  wear,  the  amount  of  which 
is  indicated  by  the  rate  at  which  the  lubricant  becomes  dis- 
colored and  charged  with  abraded  metal.  The  work  of  friction, 
both  of  solid  and  of  liquid,  is  transformed  into  heat  and  is  dis- 
posed of  as  the  bearing  heats,  principally  by  radiation  and 
conduction  to  adjacent  parts,  and  partly  by  the  heating  of  the 
lubricant.  In  all  cases  some  abrasion  is  indicated  by  the 
change  produced  in  the  lubricant,  and  some  heating  is  usually 
perceived  in  the  bearing. 

With  very  heavy  pressures  and  slow  speeds,  the  journal  and 
bearing  are  forced  into  close  contact,  as  is  shown  by  their  worn 
and  often  abraded  wearing  surfaces ;  while  with  very  light 
pressures  and  high  velocities  the  journal  floats  on  the  film  of 
fluid  which  is  continually  interposed  between  it  and  the  bearing. 
In  this  case  the  friction  occurs  between  two  fluid  layers,  one 
moving  with  each  surface.  There  are  thus  evidently  two  limit- 
ing cases  between  which  all  examples  of  satisfactorily  lubricated 
surfaces  fall :  the  one  limit  is  that  of  purely  solid  friction, 
which  limit  being  passed,  and  sometimes  before,  abrasion 
ensues ;  the  other  limit  is  that  at  which  the  resistance  is  en- 
tirely that  due  to  the  friction  of  the  film  of  fluid  which  sepa- 
rates the  surfaces  of  the  solids  completely. 

The  laws  governing  the  friction  of  lubricated  surfaces  are 
evidently  neither  those  of  solid  friction  nor  those  of  fluid  fric- 
tion, but  will  approximate  to  the  one  or  the  other  as  the  limits 
just  described  are  approached.  The  value  of  the  coefficient  of 
friction  varies  with  every  change  of  velocity,  of  pressure,  and 
of  temperature,  as  well  as  with  change  of  character  of  the  sur- 
faces in  contact. 

Where  mixed  friction  is  met  with,  it  will  usually  be  found 


542  A   MANUAL   OF    THE   STEAM-ENGINE. 

that  its  laws  approximate  to  those  of  solid  friction  as  the  jour- 
nal is  run  dry,  and  to  those  of  fluid  friction  as  it  is  the  more 
effectively  flooded  with  oil.  Thus  a  journal  or  bearing  surface 
fed  with  oil  by  an  oil-cup,  and  where  no  oil-grooves  are  used 
to  distribute  the  oil,  will  exhibit  a  total  friction  in  some  cases 
nearly  proportional  to  the  total  pressure,  the  latter  being 
varied  ;  while  similar  surfaces  flooded  with  oil,  as  by  the  oil- 
bath,  offer  a  resistance  sometimes  nearly  independent  of  the 
pressure,  and  but  little,  if  appreciably  any,  greater  with  heavy 
than  with  light  loads.  A  perfectly  lubricated  bearing  should 
follow  the  laws  of  fluid  friction,  and  its  friction  should  be  inde- 
pendent of  the  intensity  of  pressure  produced  by  the  load, 
varying  as  the  square  of  the  speed  of  rubbing.  Such  perfect 
lubrication  has  never  yet  been  attained. 

For  perfect  lubrication,  assuming  it  practicable  with  com- 
plete separation  of  the  surfaces,  the  laws  of  friction  would  be- 
come : 

(1)  The  coefficient  is  inversely  as  the  intensity  of  the  press- 
ure, and  the  resistance  is  independent  of  the  load. 

(2)  The  friction  coefficient  varies    as   the   square   of  the 
speed. 

(3)  The  resistance  varies  directly  as  the  area  of  journal  and 
bearing. 

(4)  The  friction  is  reduced  as  temperature  rises,  and  as  the 
viscosity  of  the  lubricant  is  thus  decreased. 

These  laws  will  probably  hold,  even  with  the  greases,  which 
all  become  fluid  when  introduced  between  the  rubbing  surfaces. 

It  is  found  by  experiment,  as  stated  later,  that  the  perfec- 
tion of  this  form  of  lubrication  depends  upon  the  amount  of 
fluid-pressure  produced  between  the  surfaces  by  forcing  in  the 
lubricant  between  them.  This  separation  occurs  to  an  impor- 
tant extent  at  high  speed  and  less  at  low  velocities.  Hence, 
the  friction  of  lubricated  parts  is  often  found  to  decrease  at 
low  speed  with  increase  of  velocity,  while  increasing  at  high 
speeds  as  velocity  increases. 

The  limits  of  pressure  for  lubricated  surfaces  are  determined 
by  the  nature  of  the  materials  composing  them,  and  by  their 


THERMODYNAMICS  OF   THE   STEAM-ENGINE.  $43 

smoothness  and  exactness  of  fit,  as  well  as  by  the  speed  of 
rubbing,  the  character  of  the  lubricant,  and  the  methods  of  its 
application.  A  higher  pressure  is  usually  permissible  on  hard 
than  on  soft  material  ;  although  when  the  soft  materials,  as  for 
example  common  white  alloys  for  bearings,  are  well  sustained 
by  a  harder  metal,  the  heaviest  pressures  allowed  by  the  lubri- 
cant may  be  carried. 

The  more  viscous  the  lubricating  substance,  and  the  stronger 
the  capillary  action  taking  it  into  the  space  between  the  jour- 
nal and  the  bearing,  the  higher  the  pressure  safely  carried. 
With  increase  of  speed  the  maximum  pressure  is  lessened,  and 
it  is  usual  to  take  the  intensity  of  pressure  as  inversely  as  the 
velocity  of  rubbing. 

The  magnitude  of  the  waste  of  energy  by  friction  is 
measured  in  horse-power  by  the  expressions  (British  measure): 

(I)  Flat  surfaces,  HP  = 


(2)  Cylindrical  surfaces,  HP=          ~', 


when  f,  P,  and  V  are  the  coefficient  of  friction,  the  load  and 
the  speed  of  rubbing  in  feet,  and  R  and  d  are  the  revolutions 
per  minute  and  diameter  of  journal  in  inches. 

The  methods  of  reducing  waste  of  energy  by  friction  in 
mechanism  are  based  upon  very  simple  principles.  It  is  evi- 
dent that  to  make  the  work  and  power  so  lost  a  minimum  it  is 
necessary  to  adopt  the  following  precautions  : 

(i)  Make  the  coefficient  of  friction  the  least  by  proper 
choice  of  rubbing  surfaces  and  by  the  best  lubrication.  To  do 
this  we  should  have  at  least  one  of  the  rubbing  surfaces  of  a 
granular  metal,  and  if  possible  both  —  that  one  which  it  is  easier 
to  replace  being  of  the  softer  metal.  The  surfaces  should  not 
be  subjected  to  a  normal  pressure  beyond  which  the  lubricating 
matter  will  be  expelled.  For  slides,  a  much  less  pressure 
should  be  taken  than  for  journals,  as  they  have  not  as  free  a 
lubrication  as  well-arranged  cylindrical  journals  ;  but  this  limit 


544  A    MANUAL    OF   THE   STEAM-ENGINE. 

is  best  determined  by  reference  to  the  speed    of  rubbing  and 
the  nature  of  the  lubricant. 

(2)  Make  the  space  through  which  the  friction   is  to  act  a 
minimum  by  reducing  the  diameters  of  all  journals  to  the  least 
compatible  with  safety  under  the  stresses  they  are  expected  to 
sustain.     The  work  done  is  independent  of  the  length  of  the 
journal,  except  as  it   may  modify  pressures,  and  thus  the  co- 
efficient of  friction. 

(3)  Properly  fitting  the  bearing  surfaces,  removing  that  por- 
tion of  the  bearing  near  the  jaws,  and  transferring  the  bearing 
surface  to  the  bottom,  one  sixth  of  the  circumference  of  the 
journal  may  be  thus  removed.     A  journal  well  fitted   cold  is 
not  necessarily  a  good  fit  after  it  becomes  heated  by  friction, 
owing  partly  to  the  want  of  homogeneousness  of  the  metal  of 
the  journal  and  bearing;  a  worn  journal  has  less  friction  than 
when  new.     It  is  a  question  whether  all  journals  should  not  be 
brought  to  a  proper  bearing  and  given  a  high   polish  before 
they  are  considered  fit  to  perform  their  office.     It  is  now  usual 
carefully  to  grind  all  cylindrical  journals,  and  to  secure  a  very 
perfect  fit  in  the  bearing  before  setting  the  machinery  at  work. 

(4)  Giving  the   journals  such  forms  and   such  size   as   will 
allow  them  to  convey  away  the  heat   generated,  either   by 
radiation  from   their  surfaces   or  by  conduction   through  the 
mass  of  metal,  to  circulating  water,  to  lubricating  matter,  or  to 
adjacent  masses. 

•   (5)  Securing  an  efficient  system  of  supply  of  the  lubricant. 

Since  lubrication  has  for  its  objects  both  the  reduction  of 
friction  and  the  prevention  of  excessive  development  of  heat, 
the  engineer  resorts  to  the  expedient  of  interposing  between 
the  rubbing  surfaces  a  substance  having  the  lowest  possible 
coefficient  of  friction  and  the  greatest  capacity  for  preventing 
or  reducing  the  development  of  heat.  It  is  evident  that  in 
order  that  any  substance  may  be  efficient  as  a  lubricating 
material  it  must  possess  the  following  characteristics : 

(i)  Enough  "  body"  or  combined  capillarity  and  viscosity 
to  keep  the  surfaces  between  which  it  is  interposed  from  com- 
ing in  contact  under  maximum  pressure. 


THERMODYNAMICS  OF   THE   STEAM-ENGINE.  545 

(2)  The  greatest  fluidity  consistent  with  the  preceding  re- 
quirements, i.e.,  the  least  fluid-friction  allowable. 

(3)  The   lowest  possible  coefficient    of    friction  under  the 
conditions  of  actual  use,  i.e.,  the  sum  of  the  two  components, 
solid  and  fluid  friction,  should  be  a  minimum. 

(4)  A  maximum  capacity  for  receiving,  transmitting,  stor- 
ing, and  carrying  away  heat. 

(5)  Freedom  from  tendency  to  decompose  or  to  change  in 
composition  by  gumming  or  otherwise,  on  exposure  to  the  air 
or  while  in  use. 

(6)  Entire  absence  of  acid  or  other  properties  liable  to  pro- 
duce injury  of  materials  or  metals  with  which  they  may  be 
brought  in  contact. 

(7)  A  high  temperature  of  vaporization  and  of  decompo- 
sition, and  a  low  temperature  of  solidification. 

(8)  Special  adaptation  to  the  conditions,  as  to  speed  and 
pressure  of  rubbing  surfaces,  under  which  the  unguent  is  to  be 
used. 

(9)  It  must  be  free  from  grit  and  from  all  foreign  matter. 

Oils  must  be  used  with  some  caution  when  applied  to  jour- 
nals upon  which  other  lubricants  have  been  employed.  It 
sometimes  happens  that  two  oils  are  entirely  incapable  of 
working  together,  and  this  incompatibility  may  cause  trouble 
when  they  are  used  together,  or  even  successively.  A  minor 
good  quality  possessed  by  some  lubricants  in  greater  degree 

'than  others  is  that  of  being  readily  removed,  and  allowing  the 
bearing  surfaces  to  be  easily  cleansed  when  they  have  become 
soiled  and  gummed  by  alteration  of  the  unguent,  and  by  the 
gathering  of  dust  and  abraded  metal  upon  them. 

Oils  should  not  be  liable  to  decomposition  by  heat  or  wear, 
or  to  separation  when  mixed,  either  in  use  or  by  long  stand- 
ing, or  by  alteration  of  temperature.  They  should,  if  mixed, 
always  have  the  same  specified  composition.  Uniformity  in 
this  respect  is  as  important  as  excellence  of  quality  of  the  nor- 
mal mixture,  and  the  quality  of  the  oil  is  usually  of  more  im- 
portance than  the  quantity.  The  adhesiveness  of  the  oil  to  the 
metal,  and  the  ease  of  flow,  with  minimum  fluid-friction,  are 


546  A   MANUAL    OF   THE   STEAM-ENGINE. 

the  essential  characteristics  of  a  good  combination  of  materials 
in  bearings  and  lubricant.  Cast-iron  is  somewhat  spongy  in 
texture,  and  is  therefore  an  exceptionally  good  metal  for  bear- 
ing surfaces,  when  of  ample  area. 

Bearing  surfaces  are  of  bronze  or  other  alloys,  of  cast-iron 
or  other  metal,  or  of  wood,  according  to  location,  intensity  of 
pressure,  velocity  of  rubbing,  and  nature  of  the  material  of  the 
journal.  Ordnance  bronze  wears  well  under  heavy  pressures 
and  at  high  speeds  if  not  subjected  to  intense  localized  pres- 
sures by  the  springing  or  misfitting  of  parts  ;  cast-iron  has  an 
advantage,  if  used  under  moderate  pressures  and  in  ample  ex- 
tent of  surface,  in  its  porosity  and  absorptive  power  and  the 
persistence  with  which  oil  and  grease  adhere  to  it ;  wrought- 
iron  and  steel  sustain  heavy  loads,  if  free  from  surface  defects ; 
"  mild  steel  "  is  peculiarly  valuable  for  journals,  and  hard  steel 
ground  to  shape  and  well  bedded  in  its  bearing  will  safely 
carry  pressures  of  enormous  intensity;  wood  is  only  used  in 
special  cases.  Too  high  a  polish  on  the  harder  surfaces  is  ob- 
jectionable where  thin  oils  and  heavy  pressures  are  adopted,  as 
the  lubricant  is  difficult  to  feed  between  the  metals  in  contact, 
or  to  keep  there  while  in  operation. 

It  is  nearly  always  advisable  to  make  the  bearing  of  the 
softer  metal,  since  its  renewal  is  a  matter  of  less  difficulty  and 
expense  than  that  of  the  journal,  and  since  the  journal  must 
usually  have  great  strength.  A  hard  bearing  cuts  the  softer 
journal,  and  gives  rise  often  to  serious  expense.  It  is  from 
this  consideration  that  bearings  are  often  "  babbitted"  or  lined 
with  the  soft  white  alloys. 

The  fitting  of  the  surfaces  in  contact  is  as  important  a 
matter  as  the  selection  of  the  material  of  which  they  are  com- 
posed. The  theory  of  friction  is  based  upon  the  assumption 
that  all  parts  are  accurately  made  to  correct  dimensions,  and 
exactly  fitted  ;  and  the  conclusions  derived  are  therefore  in- 
validated by  any  departure  from  such  assumed  conditions. 
Precision  and  stability  of  form — stiffness  of  all  loaded  parts — 
are  essential  elements  of  successful  working.  Stability  of  form 
is  dependent  upon  extent  of  surface  exposed  to  wear :  if  this 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


547 


area  is  ample,  so  that  the  two  rubbing  parts  nowhere  and  at 
no  time  come  into  unrelieved  metallic  contact,  no  appreciable 
wear  will  occur,  and  their  forms  will  be  permanent. 

Surfaces  of  similar  area  and  form,  even  when  well  fitted,  if 
of  different  materials  will  wear  very  differently.  Thus  the 
following  table  shows  the  comparative  wear  of  axle-bearings. 
Thoroughly  pure  bronzes,  like  those  fluxed  with  phosphorus, 
were  reported  as  wearing  very  much  less  than  ordinary  com- 
positions. 


Bearing. 

Composition. 

Cost 

PSL. 

ioo  Ibs.* 

Miles 
run 
per  Ib. 

Wear 
Per 

ioo  miles 
for  four 
bearings. 

Cop- 
per. 

Tin. 

Anti 
mony. 

83 

82 
3 

5 

17 

IS 

g 

7 

10 

$28  60 
28  68 
32  85 
32  27 

13  04 
28  68 

25,489 
27,918 
22,075 
24,857 

22,921 
2,576 

200  grs.f 
252      ' 
366       ' 
284      ' 

308      « 
274      ' 

White-metal             

Lead    composition:    lead, 
84'  antimony   16  

Gun-metal  on  brake-cars.  . 

82 

18 

•• 

In  many  cases  the  excessive  wear  of  a  bearing  is  due  to  a 
misfit.  The  Hopkins  bearing  is  a  bronze  bearing  lined  with  a 
thin  layer  of  lead,  which,  when  new  and  unfitted,  can  accom- 
modate itself  to  the  distorted  journal  and  permit  gradual  wear 
to  a  correct  fit  without  danger  of  injury,  such  as  occurs  often 
with  the  common  hard,  unlined  "  brass."  In  the  Defreest 
bearing  a  thin  bronze  bearing-piece  is  sustained  by  a  strong 
iron  backing-piece,  and  between  them  is  a  sheet-lead  filling. 
Journals  should  be  fitted  without  the  use  of  emery  or  other 
gritty  grinding  material,  which  may  adhere  to  its  surface  and 
thus  produce  injury. 

Bearing  surfaces  of  wood  are,  under  the  conditions  already- 
described  as  favorable  to  their  use,  exceedingly  durable,  and 
will  carry  enormous  loads  without  abrasion.  Thus  lignum-vitae 
will  sustain  pressures  exceeding  1000  Ibs.  per  square  inch  (70 
*  Including  melting  expenses,  loss,  etc.  These  figures  are  constantly  vary- 


ing. 


f  Seven  thousand  grains  per  pound. 


548  A  MANUAL   OF    THE   STEAM-ENGINE. 

kgs.  per  sq.  cm.),  where  brass  becomes  rapidly  abraded  and  de- 
stroyed under  but  little  more  than  one  fourth  of  that  load,  and 
will  run  continuously  under  4000  Ibs.  (281  kgs.  per  sq.  cm.) 
when  bronze  sets  fast  instantly.  Camwood  has  been  subjected 
to  pressures  exceeding  8000  Ibs.  per  square  inch  (562  kgs.  per 
sq.  cm.),  and  has  worked  without  injury;  snakewood  carries 
about  as  heavy  a  load  as  lignum-vitae. 

The  bearing  surfaces  of  watch-work  are  often  made  of  ruby, 
agate,  and  other  fine-grained  and  hard  stones,  and  of  gems. 

A  comparison  made  by  the  Author  between  surfaces  of 
gun-bronze,  of  "  Babbitt"-metal,  and  of  other  soft,  white  alloys, 
all  working  on  steel,  proved  all  to  have  substantially  the  same 
friction.  In  other  words,  the  coefficient  of  friction  was  deter- 
mined by  the  nature  of  the  unguent  and  not  by  that  of  the 
rubbing  surfaces,  when  the  latter  are  in  good  order.  The  soft 
metals,  however,  heated  more  than  the  bronze,  running  at 
temperatures  somewhat  higher  with  equally  free  or  even  freer 
feed.  To  retain  the  temperature  at  135°  F.  (57°  C.),  in  some 
cases  one  half  more  oil — over  300  grammes,  as  against  200 — 
was  needed  on  the  white  metal  than  on  the  bronze.  This 
probably  does  not,  however,  necessarily  indicate  a  serious  de- 
fect, but  simply  deficient  conductivity.  Lined  journals  may  be 
expected  to  run  normally  warmer  than  unlined  bronze  of  good 
quality.  The  following  are  the  results  of  experiment  with  a 
"  Babbitt"-metal,  which  was  compared  with  bronze  and  a  sec- 
ond white  alloy : 

Bronzes.  White  Metal. 

No.  i.  No.  2. 

Mean  temperature,  Fahr 133°  152°  137° 

Mean  coefficient  of  friction o.oi  o  0.013  o.oio 

Oil  used  per  hour,  ounces 7  17  12 

These  differences  prove  ordinary  lubricated  surfaces  to  have 
contact,  since  they  give  differences  in  the  values  of  /where 
none  could  exist  were  the  friction  fluid-friction  solely. 

Riveting,  in  steam-boilers  and  bridge-work,  or  other  con- 
structions, is  usually  taken  as  having  a  coefficient, /=  0.333  ; 
but  it  should  never  be  reckoned  upon  as  an  element  of  definite 


THERMODYNAMICS  OF   THE   STEAJf-EA'ClXE. 


549 


value,  although  the  enormous  pressure  produced  by  the  shrink- 
age of  heated  rivets,  while  cooling,  gives  it  some  importance. 
The  elastic  limit  of  common  iron  is  usually  not  far  from  25,000 
Ibs.  per  square  inch  (1757.5  kg5-  P61"  sq-  cm^»,  and  one  third 
this  amount,  above  8000  Ibs.  (562.4  legs.)  per  unit  of  section  of 
rivet,  is  a  quantity  of  real  value  as  an  element  of  safety. 

The  friction  of  belts  and  of  gearing  has  been  often  studied 
experimental!}7.  Morin  concluded  its  amount  for  belting  to 
be  proportional  to  the  angle  on  the  pulley  subtended  by  the 
belt,  to  the  logarithm  of  the  ratio  of  tensions,  and  to  be  inde- 
pendent of  the  width  of  belt  and  of  the  linear  measure  of  the 
arc  embraced  by  it  —  Le^  independent  of  the  area  of  contact. 
He  obtained  /=  0^8  to  /=  0.38,  the  value  varying  with  the 
condition  of  the  belt. 

Adopting  the  formula  of  Prony  for  flic  difference  of  tension 
on  the  two  parts  of  the  belt,  the  values  of  its  coefficient,  t, 
were  obtained  as  in  the  table. 

The  maximum  difference  of  tension  allowable  is 


The  minimum  tension  allowable  to  prevent  slip  is  taken  as 


r.+  z;    i*+ 


D. 


VALUE  OF  1  IN  FRONTS  FORMULA. 


O.2O 

OL40 

0.60 

0-SO 
I.OO 

1-50 

2.00 
2.30 


1.9 
3-5 
6.6 
is.3 


1.8 
3-3 


R::*  :-  V« 


1.6 
2.6 


6.8 
10.9 


«-9 
3-5 
6.6 

23.9 
ni-3 

:~    • 
*5T-4S 


1-5 
3-5 

1:1 

22.4 

:--    5 


5$O  A   MANUAL   OF   THE   STEAM-ENGINE. 

The  maximum  stress  allowable  on  the  leather  was  stated  at 
about  350  Ibs.  per  square  inch  of  cross-section. 
In  the  equations  * 

R  =  T,  -  Tt  =  r,(i  -  ef*} 


__ 
2R       ~  2(eS°  -  i)' 

/"varies  from  0.15  to  0.6,  the  former  value  being  found  only 
where  the  belt  is  actually  wet  with  -oil. 

Reuleaux  takes  f=  0.25,  and  the  experiments  of  Messrs. 
Towne  and  Briggs  f  indicate  that  this  value  is  exceeded,  under 
ordinary  working  conditions,  more  than  60  per  cent. 

Rubber  belting  has  greater  adhesion  than  leather,  and 
values  of  f  may  be  used  exceeding  very  greatly  those  adopted 
for  leather. 

The  angle  0  =  2nn,  where  n  is  the  number  of  turns  or  part 
of  turns  taken  by  the  belt  about  the  pulley.  Rankine  gives  \ 
the  following  values  of  the  coefficient  2.72887"  in  the  equation 
eS*  =  io2-7288/"  which  comes  into  use  in  the  application  of  these 
formulas,  as  seen  in  Chapter  II  : 

/=o.i5  0.25  0.42  0.56 

2.7288/  =  0.41  0.68  1.15  1.53 

and,  where  6  =  n  and  n  =  £,  as  is  usual, 


T, 
(7;  +  FJ 


T,=  1.603  2.188  3.758  5.821 

R  =  2.66  1.84  1.36  i.  21 

2R  =  2.16  1.34  0.86  0.71 


Usually  we  assume  T,—R;  T,  =  2R  ;  (T,  +  T9  -r-  2R  =  1.5 
and  /becomes  0.22. 

*  Friction  and  Lost  Work;  chapter  II.  §  31. 
f  Journal  of  the  Franklin  Institute;  1868. 
J  Machinery  and  Mill-work,  p.  352. 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


551 


Rankine*  gives  /  for  a  wire-rope  running  on  cast-iron  at 
0.15  and  on  gutta-percha  at  0.25. 

Rope-gearing  has  a  value  of  f  =  0.25  to  f  =  0.8,  and  the 
resistance  to  slipping  is  increased  in  proportion  to  the  cosecant 
of  the  half-angle  of  the  wedge-shaped  groove  of  the  carrying- 
wheel,  f 

The  method  of  supply  of  oil  should  be  carefully  looked  to, 
and  a  very  free  "  feed,"  with  a  system  of  collection  and  reap- 
plication  of  the  oil  leaving  the  bearing,  will  be  found  to  give 
by  far  the  greatest  economy  of  power  and  cost.  Experiments 
made  for  the  Institution  of  Mechanical  Engineers,  in  which 
oiling  by  a  pad  as  in  railway  work,  by  a  siphon  lubricator  or 
oil-cup,  and  by  a  bath,  which  keeps  the  surfaces  flooded  with 
oil,  gave  the  following  figures,  showing  an  enormous  advantage 
in  the  use  of  the  last  method : 

METHODS  OF  OILING  (RAPE-SEED  OIL). 

VELOCITY   OF    RUBBING,    157    FEET    (46    M.)    PER    MINUTE. 


Actual  Load. 

Coefficient 
of  Friction. 

Comparative 
Friction. 

KiJogs.  per 
sq.  cm. 

Lbs.  per 
sq.  in. 

Oil-bath     

I8.5 
17-7 
I9.I 

263 
252 
272 

0.00139 
0.00980 
0.00900 

I 
T.o6 
6.48 

Pad  under  journal  

Conclusions. — Specified  qualities  of  lubricant  may,  by  the 
processes  here  described,  be  secured  by  test.  If  an  unguent  is 
desired  for  heavy  pressures,  or  an  oil  for  very  light  work,  or 
for  high  or  low  speeds  of  rubbing  under  known  pressures,  the 
methods  of  study  of  the  available  lubricants  which  have  been 
described  will  enable  the  engineer  or  the  manufacturer  to 
select  that  which  is  best  suited  to  the  specified  purpose.  He 
may  go  still  further,  and,  by  repeated  mixing  and  test  gradu- 
ally improving  the  mixtures,  may  finally  secure  compounds 
having  the  best  possible  qualities  for  the  various  proposed 


*  Machinery  and  Mill-work,  p.  352. 

f  American  Machinist;  November  i,  1884. 


552  A    MANUAL    OF    THE    STEAM-ENGINE. 

applications.  The  Author  has  in  this  manner  sometimes  pro- 
duced lubricants  for  manufacturers  which  have  been  found 
peculiarly  well  suited  for  special  lines  of  trade. 

Studying  the  facts  here  stated,  and  the  data  acquired  by 
many  hundreds  of  other  experiments,  made  on  one  or  the  other 
of  these  last-described  machines  for  testing  lubricants,  we  may 
recapitulate  the  facts  and  figures  for  ordinary  use  in  machine- 
design  and  in  estimating  losses  of  power  by  friction  as  follows: 

(1)  The  great  cause  of  variation  with  well-cared-for  journals, 
since  they  must  work  at  ordinary  temperatures,  is  alteration 
of  pressure  and  variation  in  methods  of  supply;  and  it  is  seen 
that  the  higher  pressures  give  the  lowest  percentages  of  loss  of 
power  by  friction. 

(2)  The  value  of  the  coefficient  is  greatly  modified  by  the 
state  of  the  rubbing  surfaces ;  a  single  scratch  has  its  effect  in 
wasting  power.     A  good    journal  usually  has   its   surface   as 
smooth  and  as  absolutely  uniform  as  a  mirror.     Every  well- 
kept  journal  acquires  such  a  surface. 

(3)  For  general  purposes  and  for  heavy  work,  as  in  the  ex- 
periments of  the  Author,  and  at  considerable  speeds,  the  value 
of   the    coefficient  varies  nearly  inversely  as  the  square-root 
of  the  pressure,  for  pressures  ranging  from  50  to  500  Ibs.  per 
square  inch. 

(4)  The  coefficient   for  rest  or  starting   may  similarly  be 
taken  to  vary  nearly  as  the  cube-root   of   the  pressure.     For 
closer  estimates  and  other  conditions,  the  tables  just  given  can 
be  referred  to  directly. 

(5)  The  coefficient  for  the  instant  of  coming  to  rest,  under 
the  special  conditions  here  referred  to,  is  nearly  constant,  and 
may  be  taken  at  0.03. 

(6)  The  resistance  due  to  friction  varies  with  velocity,  de- 
creasing with  increasing  velocity  rapidly  at  very  low  speeds,  as 
from  i  to  10  feet  per  second,  and  slowly  as  higher  speeds  are 
reached,  until  the   law  changes  and  increase  at  ordinary  tem- 
peratures takes  place,  and  at  a  low  rate  throughout  the  whole 
range  of  usual  velocities  of  rubbing  met  with  in  machinery. 

Its  amount  and  the  law  vary  with  method  of  lubrication, 


THERMODYNAMICS  OF  THE  STEAM-EXGIXE.  553 

however.     With  oil-bath   lubrication  the  value  of  f  usually 
varies  more  nearly  as  the  square-root  of  the  velocity. 

(7)  With  pressure  and  velocity  varying,  we  may  take  the 
coefficient  as  varying  as  the  fifth  root  of  the  velocity,  divided 
by  the  square-root  of  the  pressure  for  such  work  as  is  repre- 
sented by  the  experiments  of  the  Author. 

(8)  The  effect  of  heating  journals  under  conditions  here  il- 
lustrated is  to  increase  the  friction  above  oxr  or  loo*  F.,  at  a 
speed  as  low  as  30  to   100  feet  per  minute,  while  at  higher 
speeds  and  low  pressures  the  opposite  effect  is  produced,  and 
the  coefficient  often  decreases  more  nearly  as  the  square-root 
of  the  rise  of  temperature. 

191  The  temperature  of  minimum  friction,  under  the  con- 
ditions of  the  experiments  here  referred  to,  varies  nearly  as  the 
cube-root  of  the  velocity,  for  a  pressure  of  about  200  Ibs.  per 
square  inch. 

no)  The  endurance  of  any  lubricant  should  be  determined 
by  actual  wear  upon  a  good  journal  under  the  pressures  and 
velocities  proposed  for  its  use. 

The  economy  with  which  it  can  be  used  will  be  dependent 
upon  its  natural  method  and  rate  of  flow,  and  upon  its  capillary 
qualities,  as  well  as  upon  its  intrinsic  wearing  power  and  the 
method  adopted  in  feeding  it.  Greases,  therefore,  are  usually 
more  economical  in  cost  than  oils,  even  if  having  less  wearing 
capacity. 

(i  i)  The  only  method  of  learning  the  true  value  of  a  lubri- 
cant and  its  applicability  in  the  arts  is  to  place  it  under  test, 
determining  its  friction-reducing  power,  and  its  other  valuable 
qualities,  not  only  at  a  standard  pressure  and  velocity,  and  at 
ordinary  temperatures,  but  measuring  its  friction  and  endurance 
as  affected  by  changing  temperatures,  speeds,  pressures,  and 
methods  of  application,  throughout  the  whole  range  of  usual 
practice,  and  its  wearing  effect. 

(12)  The  true  value  of  an  oil  to  the  consumer  is  not  propor- 
tional simply  to  its  friction-reducing  power  and  endurance, 
under  the  conditions  of  his  work ;  but  its  value  to  him  is  meas- 
ured by  the  difference  hi  value  of  power  expended,  when  using 


554  A    MANUAL   OF   THE   STEAM-ENGINE. 

the  different  lubricants,  less  the  difference  in  total  cost  of  oil 
or  grease  used  ;  but  for  commercial  purposes,  no  better  method 
of  grading  prices  seems  practicable  than  that  which  makes 
their  market  value  proportional  to  their  endurance,  divided  by 
their  coefficients  of  friction. 

The  consumer  will  usually  find  it  economical  to  use  that 
lubricant  which  is  shown  to  be  the  best  for  his  special  case, 
with  little  regard  to  price,  and  often  finds  real  economy  in 
using  the  better  material,  gaining  sufficient  to  repay  excess  in 
the  total  cost  very  many  times  over. 

(13)  To  secure  maximum  economy,  the  journal  should  be 
subjected  to  a  pressure  the  limit  of  which  is  determinable  by 
either  Rankine's  or  Thurston's  formula  ;*  the  most  efficient 
materials   should  be  chosen   for  the  rubbing  surfaces ;    they 
should  be  reduced  to  the  most  perfect  state  of  smoothness  and 
perfection  in  form  and  fit ;  a  lubricant  should  be  chosen  which 
is  best  adapted  for  use  under  the  precise  conditions  assumed  ; 
the  lubricant  should  be  supplied  precisely  as  needed,  and  by  a 
method  perfectly  adapted  to  the  special  unguent  chosen.    The 
real  problem  is  often,  not  what  oil  shall  be  used,  but  how  to 
secure  most  effective  lubrication. 

(14)  The  semi-fluid  lubricants,  when  equally  good  reducers 
of  friction,  are  usually  the  most  economical  for  heating  jour- 
nals, in  consequence  of  their  peculiar  self-regulating  flow,  as  the 
rubbing  parts  warm  or  cool  while  working.     They  are  usually 
too  viscous  for  economical  use  in  ordinary  work. 

The  loss  by  internal  friction  in  the  steam-engine  includes 
the  wastes  at  the  journals  of  the  shaft,  crank-pin,  and  cross- 
head-pin  or  "  wrist-pin,"  and  of  the  valve-motion  ;  of  the  sliding 
friction  of  cross-head  and  other  guides ;  of  the  piston-rods  and 
valve-stems  in  their  "  stuffing-boxes,"  and  of  the  rubbing  of 
pistons  and  valves  on  the  surfaces  over  which  they  glide,  and 
the  resistance  of  air-pumps  in  condensing  engines.  Its  total  is 
ordinarily  equivalent  to  from  one  pound  on  the  square  inch  of 
piston,  in  very  large  engines  in  good  order,  to  about  four  or 

*  Friction  and  Lost  Work;  §  127. 


THERMODYNAMICS  OF   THE   STEAM-ENGINE.  555 

five  pounds  in  small  engines  —  of  25  to  50  horse-power  —  and  be- 
comes very  much  greater  when  the  lubricants  used  are  ineffi- 
cient, the  rubbing  surfaces  in  bad  shape,  the  stuffing-boxes  too 
tightly  packed,  or  the  packing-rings  set  out  too  much.  These 
figures  ordinarily  correspond  to  from  five  to  as  much  as  ten  per 
cent  of  the  total  indicated  power  of  the  engine,  in  the  best 
cases  and  to  from  ten  per  cent  upward,  indefinitely,  in  worse 
cases. 

Studying  these  losses  in  detail,  it  is  found  that  the  friction 
of  the  journals,  when  properly,  uniformly,  and  effectively  lubri- 
cated, is  relatively  less,  though  absolutely  somewhat  greater, 
as  the  pressures  on  them,  and  work  transmitted  across  them. 
increase  ;  *  that  the  friction  of  guides  follows  the  same  law  ; 
that  the  work  lost  in  the  stuffing-boxes  is  probably  independent 
of  the  work  of  the  engine  ;  and  that  the  friction  of  the  piston 
and  of  the  valve  may  usually  be  taken  as  also  independent  of 
the  engine-load,  though  probably  .always  affected  by  the  in- 
tensity of  the  steam-pressure. 

Experiments  made  by  the  Author  lead  to  the  conclusion  + 
that  the  method  of  variation  of  the  internal  friction  of  the 
steam-engine  is  not  usually  exactly  that  stated  by  early  writers 
on  the  subject.  It  has  been  customary  among  engineers  con- 
versant with  the  operation  of  the  steam-engine  to  take  the 
"  friction-card  "  obtained  by  applying  the  indicator  to  the  un- 
loaded engine  as  a  measure  of  the  friction  of  the  engine  at  all 
times,  whether  loaded  or  unloaded  ;  while  it  has  been  usual,  in 
theory,  to  accept  the  formula  of  De  Pambour,  which  is  unques- 
tionably accurate  in  form, 


in  which  R  is  the  total  resistance,  R,  is  that  of  the  net  work  of 
the  engine,  its  "  useful  "  load,  and  Rt  is  the  work  of  friction  of 
the  parts  of  the  machine  itself,  and  /a  coefficient  of  friction. 

*  Where  this  is  not  true,  the  deduction  follows,  inevitably,  that  the  friction 
is  thai  of  solids,  not,  as  it  should  be,  "  mediate,"  as  Him  calls  it,  and  that  the 
lubrication  is  not  effective. 

f  Trans.  Am.  Soc.  Mech.  Engineers;  1886;  vol.  viil. 


556  A    MANUAL    OF    THE    STEAM-ENGINE. 

This  formula  is  based  upon  the  very  reasonable  assumption 
that  the  total  friction  must  be  a  minimum  in  the  unloaded  en- 
gine, and  that  the  imposition  of  external  work  upon  it  must, 
by  increasing  the  pressure  on  its  running  parts,  add  to  the  total 
by  the  amount  of  friction  so  arising.  But  whether  this  increase 
of  waste  energy  amounts  to  so  much  as  to  become  observable, 
or  to  be  practically  important  in  the  operation  of  the  engine ; 
whether  the  engineer  is  right  in  theory,  or  correct  in  his  practice, 
in  usual  cases,  is  not  wholly  certain.  The  friction  of  engine,  as 
has  been  seen,  consists  of  the  resistances  due  to  the  motion  of 
the  various  piston,  valve,  and  other  elements  through  stuffing- 
boxes  and  in  guides,  the  friction  of  the  piston-rings  on  the 
cylinder  surface,  the  friction  of  eccentrics,  and,  often,  of  other 
parts  which  are  independent  of  the  magnitude  of  the  load 
thrown  upon  the  engine  by  the  useful  resistance,  in  addition  to 
the  friction  of  the  journals  transmitting  the  effort  of  the  steam 
to  the  exterior  resisting  work,  and  of  other  parts  directly  and 
indirectly  affected  by  its  variation.  It  thus  happens  that  the 
resistance  due  to  the  friction  of  the  latter  may  be,  and  prob- 
ably often  is,  but  a  small  proportion  of  the  whole  friction  of 
engine.  The  total  friction  of  engine,  as  has  been  seen,  in  good 
engines  of  ordinary  kinds,  amounts  to  from  5  to  10  per  cent  of 
the  total  power  developed  when  fully  loaded ;  but  the  coeffi- 
cient of  friction  of  any  one  journal,  if  well  lubricated,  has  often 
been  found  by  the  Author,  under  such  pressures  as  are  usual 
on  the  main  journals  of  the  steam-engine,  to  fall  to  a  low  fig- 
ure, and  the  absorption  of  work  and  energy  may  thus  be  even 
a  still  lower  proportion  of  the  work  of  the  steam  as  the  speed 
of  rubbing  is  less  than  that  of  the  piston.  The  loss  of  power 
along  the  line  of  connection  is  probably  always  small.  Again  : 
the  coefficient  of  friction,  with  really  good  lubrication,  within 
the  usual  range  of  pressures  on  journals  and  guides,  increases 
as  pressures  fall,  and  decreases  when  the  pressures  increase 
with  variation  of  engine-power  and  load  ;  and  this  compensa- 
tion often  occurs  to  such  an  extent  that  the  total  frictional  re- 
sistance, on  these  parts  even,  varies  slowly  with  variation  of 
load  ;  while  the  friction  of  the  other  portions  of  the  engine  re- 


THERMODYNAMICS  OF   THE   STEAM-ENGINE.  557 

mains  constant.*  The  resultant  effect  is  often  a  practically 
constant  friction  of  engine  under  all  loads,  the  speed  and 
steam-pressure  being  constant.  In  condensing  engines  this 
friction  is  subject  to  similar  conditions  ;  but  the  work  of  the 
air-pump  should  decrease  with  the  reduction  of  the  load. 

Among  the  most  excellent  illustrations  of  thorough  lubri- 
cation are  those  of  Tower,  f  in  which  a  near  approach  to  per- 
fect fluid-friction  was  attained,  the  total  resistance  thus  becom- 
ing nearly  constant  at  all  pressures,  and,  nearly, 


in  which,  as  given  by  Kennedy,*  c  depends  on  the  lubricant,  and 
is  about  0.0014  for  sperm  oil,  0.0015  for  rapeseed,  and  0.0018 
for  good  mineral  oils  ;  v  is  the  speed  of  rubbing  in  feet  per 
minute;  and/  is  the  pressure  per  square  inch.  At  i1  =  250 
and/  =  310,  f  •=•  c,  nearly. 

It  will  be  observed  that  the  variation  of  fp,  which  is  here  a 
constant  for  a  given  velocity,  is  a  gauge  of  the  efficiency  of  the 
lubrication  ;  since  f  is  constant  when  the  two  solids  are  in 
actual  contact. 

The  Efficiency  of  Machine,  as  distinguished  from  the  effi- 
ciency of  its  thermodynamic  operation,  the  efficiency  of  the 
mechanism,  is  measured  by  the  ratio  of  the  quantity  of  work 
done  at  the  engine-shaft,  to  that  shown  at  the  piston  by  the 
indicator,  and  is  less  than  unity  as  the  lost  work  of  friction  re- 
duces the  former  quantity.  The  value  of  this  efficiency  is,  as 
a  maximum,  about  0.95  in  the  simplest  and  best  constructions 
of  non-condensing  engine,  and  ranges  from  about  0.90  down 
to  80  or  less  with  condensing  engines  ;  while  0.90  is  a  common 
value  of  the  former,  and  0.85  for  the  latter,  under  usual  con- 
ditions of  operation. 


*  Friction  and  Lost  Work;  chapter  VH. 
f  Trans.  Brit.  Inst.  Mcch.  Engrs. ;  1884. 
\  Mechanics  of  Machinery:  p.  573. 


558 


A    MANUAL    OF   THE   STEAM-ENGINE. 


Increasing  the  number  of  steam-cylinders,  other  things 
equal,  increases  the  friction  of  the  engine.  For : 

Let  n  =  number  of  small  cylinders  ; 

d  =  diameter  of  each  small  cylinder  ; 
D  =         "          "     "      large  cylinder; 
/  =  length  of  stroke  ; 

s  =  area  rubbing  surface  of  small  cylinder ; 
S=     "          "  "         "  large  " 

Then 

s  =  nrtdl ; 
5  =  n  D I  =  >fnndl\ 

and  the  friction  increases  as  the  square-root  of  the  number  of 
cylinders,  where  all  the  small  cylinders  are  of  equal  size. 
This  friction  in  a  double  engine  would  thus  exceed  by  40  per 
cent  that  of  a  simple  engine. 

133.  Investigations  of  Internal  Engine-friction  were 
made,  within  a  few  years,  to  determine  its  nature,  extent,  and 
method  of  variation,  and  the  conclusions  reached  have  been 
sustained  by  still  later  experiment.  Of  these  investigations, 
the  first,  made  under  the  supervision  of  the  Author,  was  con- 
ducted by  Messrs.  Aldrich  and  Mitchell,*  with  the  following 
results : 


Number  of 
Card. 

Revolutions. 

Steam-pres- 
sure. 

Brake  H.  P. 

Indicator 
H.  P. 

Diff. 

Friction  per 
cent. 

I 

232 

5° 

4.06 

7.41 

3-35 

45 

3 

230 

63 

6.00 

IO.OO 

4.00 

40 

5 

230 

73 

8.10 

11-75 

3-65 

32 

7 

230 

75 

IO.OO 

14.02 

4.02 

28 

9 

230 

80 

12.  OO 

15-17 

3-17 

21 

ii 

230 

75 

14,00 

16.86 

2.86 

17 

13 

231 

72 

20.1 

22.07 

2.06 

9 

IS 

229 

60 

29-55 

33-04 

3-i6 

9-5 

17 

229 

70 

39-85 

43-04 

3-19 

7-4 

19 

230 

90 

5O.OO 

52.60 

2.60 

4-9 

This  engine  was  rated  at  30  I.  H.  P.,  8  inches  in  diameter 
of  cylinder,  14  inches  stroke  of  piston,  having  a  rod  44  inches 


*  Trans.  Am.  Soc.  Mech.  Engrs.;   1886;  vol.  vm;  No.  ccxxviii. 


THERMODYNAMICS  OF   THE   STEAM-ENGIXE.  559 

long  between  centres,  a  balanced  valve  with  stroke  of  2  to  4 
inches,  according  to  position  or  governor  and  eccentric,  a  fly- 
wheel 50  inches  in  diameter,  weighing  2300  pounds,  the  steam 
and  exhaust  pipes  having  diameters  of  2^  and  4  inches,  re- 
spectively, and  the  whole  machine  weighing  2\  tons.  The 
space  occupied  by  the  engine  was  9  feet  4  inches  in  length,  by 
4  feet  8  inches  in  width,  and  3  feet  10  inches  in  height. 

Examining  the  above  table  of  powers,  it  is  seen  that  the 
difference  between  indicated  and  dynamometric  power,  the 
friction  of  the  engine,  varies  somewhat,  with  varying  steam- 
pressures  and  varying  total  power ;  but  in  such  manner  as  to 
indicate  the  controlling  cause  to  be  irregular  in  action,  and 
possibly  to  some  extent  due  to  errors  of  observation  and  to 
accident ;  and  we  are  probably  justified  in  taking  it  as  approxi- 
mately constant  under  all  ordinary  variations  of  load. 

The  repetition  of  the  experiment  upon  an  engine  of  another 
make,  having  a  cylinder  9  inches  in  diameter  and  a  stroke  of 
piston  of  12  inches,  which  would  naturally  give  a  somewhat  in- 
creased percentage  of  friction,  in  consequence  of  the  propor- 
tionally smaller  stroke,  at  20,  30,  50,  and  65  horse-power,  by 
brake,  and  running  free,  revolutions  300  per  minute — a  speed 
which  may  also  have  caused  some  increase  in  frictional  resist- 
ance, not  only  in  rubbing  parts,  but  by  increasing  back-pres- 
sure— gave  a  friction  of  engine  measuring  from  2.66  horse- 
power unloaded,  to  4  horse-power  at  2O  to  30  horse-power,  4.8 
horse-power  at  50,  and  5.3  at  65  horse-power,  the  total  friction 
increasing  perceptibly,  as  assumed  by  De  Pambour,  but  de- 
creasing in  percentage  of  load,  from  16  to  7.5,  between  20  and 
65  horse-power.  It  is  very  nearly  constant  throughout  the 
whole  range  of  power  that  the  engine  would  be  worked  under 
ordinary  circumstances,  and  may  be  so  taken  without  serious 
error.  At  their  rated  powers  these  two  engines  thus  exhibit 
efficiencies  of  mechanism  of  about  94  and  90  per  cent,  re- 
spectively. 

Another  series  of  experiments  was  made  by  Messrs.  Day 
and  Riley  during  the  year  1886,  confirming  the  deductions 
already  given.  The  engine  taken  for  test  was  built  for  pur- 


56o 


A  'MANUAL  OF  THE  STEAM-ENGINE. 


poses  of  experimental  investigation.     It  was  12  inches  stroke, 
and  6£  inches  in  diameter. 

The   conclusion  already  reached  is  thus   again  confirmed. 
The  following  are  the  data  obtained  : 


1 

2 

3 

4 

5 

6 

7                  8 

No.  of 
Card. 

Rev.  per 

Minute. 

Steam- 
pressure. 

Brake   Power. 
H.   P. 

Ind.  H.  P.P.I, 
per  card. 

Diff.   Frict. 
H.  P. 

Mean  F. 
Pres. 

Frict. 

per  cent. 

I 

282 

19 

0 

2.26 

2.26 

3-70 

IOO 

3 

286 

66 

7.6l 

10.95 

3-33 

5-25 

30 

5 

285 

71 

I3.IO 

15-99 

2.61 

4-25 

18 

7 

284 

74 

18.55 

20.73 

2.65 

4.18 

12 

9 

279 

65 

23.61 

25-95 

2-33 

3-73 

9 

ii 

280 

72 

29.03 

32.22 

3-i9 

5-15 

IO 

These  experiments  lead  to  the  discovery  of  the  fact  that  the 
engine-friction  varied,  at  constant  load  and  speed,  with  varia- 
tion of  steam-pressure.  In  order  to  determine  whether  this 
hitherto  unobserved  fact  were  true,  the  following  data  were 
obtained : 


No.  of 
Card. 

Rev. 

Steam- 
pressure. 

I.  H.  P. 

Mean 
Pressure. 

Mean  F. 
Press. 

Per  cent. 
Frict. 

I 

250 

25 

6.01 

10.84 

i-95 

18 

1 

3 

285 

42 

7-17 

"•35 

3.63 

32 

Ten 

5 

271 

58 

6.81 

11.28 

3-i6 

28 

}•  pounds  on 

7 

286 

68 

7-77 

12.25 

4.90 

40 

the  brake. 

9 

296 

82 

7.87 

12.  OO 

4.68 

39 

J 

ii 

279 

66^ 

1.995 

3-22 

3-22 

IOO 

1 

13 

275 

35 

1.71 

2.80 

2.80 

" 

1  No  load  on 

15 

272 

25 

i  .  876           3.11 

3-" 

"        1  fthe  brakes. 

17 

270 

15 

1.712     i       2.86 

2.86 

"          J 

In  the  first  set  of  experiments,  here  numbered  i  to  9,  in- 
clusive, the  weight  on  the  brake-arm  was  kept  constant  at  ten 
pounds ;  in  the  remaining  experiments  all  weight  was  removed. 
In  both  cases,  the  same  general  effect  is  seen.  As  the  steam- 
pressure  rises,  the  speed  being  the  same  and  the  resistance  the 
same,  the  friction  of  the  engine  increases ;  from  2  pounds,  at 
25  pounds'  pressure  in  the  steam-chest,  to  nearly  five  pounds 
per  square  inch  of  piston  at  the  maximum,  82  pounds  steam  in 
the  valve-chest.  As  the  steam-pressure  fell  from  this  point  to 


THR&MODYNAMKS  OF  THE  STEAM-EXGIXE. 


56l 


15  pounds,  in 


iments  9  to  17,  the  load  being  thrown  off 


entirely,  and  the  speed  being  nearly  constant,  the  mean  pressure 
measuring  the  friction  of  engine  falls  again  below  3  pounds  per 
square  inch  of  piston. 

The  accompanying  figure  illustrates  graphically  the  method 
of  variation  of  the  internal  resistance,,  in  per  cent  of  power  de- 
veloped, with  variation  of  work  done  by  the  engine,  as  illus- 


trated  in  the  first  series  of  trials.  The  curve  is.  evidently,  at 
least  approximately  hyperbolic. 

Similar  experiments  conducted,  for  the  Author,  by  Professor 
R.  C  Carpenter,  exhibited  the  same  facts  where  the  method  of 
steam-distribution  was  changed  from  the  "*  automatic  **  system 
of  regulation  and  adjustment  of  the  ratio  of  expansion  to  the 
"throttling"  system. 

A  series  of  trials  made  to  determine  the  effect  of  variation 


5^2  A    MANUAL    OF    THE    STEAM-ENGINE. 

of  speed  of  engine  showed  a  general  tendency  to  increase  of 
friction-resistance  as  the  speed  increased,  and  these  and  the  ex- 
periments and  data  already  obtained  serve  to  give  the  law  of 
variation  with  a  very  satisfactory  degree  of  accuracy.  The  line 
most  closely  corresponding  with  the  data  which  have  been 
found  most  reliable  has  very  exactly  the  equation 

y  —  o.ooS-r ; 

and  the  internal  friction  of  this  engine  in  horse-power  was  about 
O.8  per  cent  of  the  number  of  revolutions  per  minute. 

Referring  to  the  results  obtained  by  the  Author,  Mr.  D.  K. 
Clark  remarks:  "The  degree  of  nearness  to  uniformity  of  fric- 
tional  resistance  for  various  powers  of  the  same  engine,  at  the 
same  speed,  is  probably  dependent  upon  the  degree  of  nearness 
by  which  the  momentum  of  the  reciprocating  parts  is  balanced 
by  the  pressure  of  the  steam."* 

Earlier  experiments  have  incidentally  supplied  some  data 
relating  to  this  form  of  waste  of  energy,  thus  : 

A  Porter-Allen  engine,  16  inches  diameter  of  cylinder  and 
30  inches  stroke  of  piston,  in  trials  by  the  American  Institute 
in  1871  gave  : 

I.  H.  P 27          56          84  109          142 

Friction  H.  P 9.1         9.5         8.5  8.7         12.7 

A  pair  of  Westinghouse  single-acting  engines  12  inches  di- 
ameter and  1 1  inches  stroke  gave  the  following,f  at  300  revolu- 
tions : 

I.  H.  P.,  loaded 84     Friction  H.  P 7 

"        light 10  "  "     10 

A  "Buckeye"  engine,  7X14  inches,  at  280  revolutions, 
gave  : 

I.  H.  P.,  loaded 23.0     Friction  H.  P 5.0 

"         light 5.1  "  "      5.1 

*The  Steam-engine;  vol.  u.  p.  619. 
f  Trans.  Am.  Soc.  Mech.  Engrs. ;  1887. 


THERMODYNAMICS  OF   THE   STEAM-ENGINE.  $63 

MM.  Him  and  Hallauer  give  the  following  for  compounded 
engines,*  condensing : 

I.  H.  P.,  loaded 347  181     Friction 44  19 

reduced  I'd..  185   137  "      4025 

Indicating,  as  would  be  anticipated,  lessened  waste  energy  with 
lessened  load  and  correspondingly  reduced  air-pump  work. 

The  experiments  of  M.  Walther-Meunier  on  engines  of  a 
wide  range  of  power  show  an  average  of  efficiency  of  machine  of 
0.8815  for  the  compound  and  0.9115  for  the  simple  engine,  the 
difference  of  3  per  cent  being  in  favor  of  the  latter.  The  former 
had  the  advantage,  on  the  other  hand,  of  8  per  cent  in  con- 
sumption of  steam — a  small  gain,  however.f 

The  internal  friction  of  condensing  engines  has  been  the 
subject  of  an  investigation  by  MM.  Walther-Meunier  and  Lud- 
wig,*  a  compound  engine  of  some  300  indicated  horse-power 
being  used,  with  the  following  results : 

(l)      ENGINE  WORKING  COMPOUND. 

I.  H.  P.  D.  H.  P.  Frict.  H.  P.  Efficiency. 

28845  248.97  39.48  0.863 

222.73  188.68  34.05  0.847 

136.07  108.28  27-79  0.795 

(2)      H.  P.   CYLINDER  WITH   CONDENSATION. 

153.12  128.38  24.74  0.839 

108.96  88.19  20.77  0.809 

55-19  37-94  i7-25  0.689 

(3)      SAME  WITHOUT  CONDENSATION. 

145.87  128.38  1749  0-880 

103.93  88.19  15.74  0.848 

51-34 37-94 U-40 0-738 

*  Alsatian  Experiments;  1876. 

t  Congres  International  de  Mecanique  appliquee;  1889;  vol.  II.  p.  133. 
\  Bull,  de  la  Soc.  Ind.  de  Mulhouse;  1887;  p.  140.     Proc.  Inst.  C.  E.;  xc; 
1886-7:  part  iv.  p.  524. 


564 


A    MANUAL   OF   THE   STEAM-ENGINE. 


With  a  range  of  work  from  about  150  to  nearly  300  horse- 
power, the  friction-waste  was  thus,  as  expressed  by  the  formula 
of  De  Pambour, 

Pf=P0  +  o.07$Pe ,  nearly ; 

while,  when  the  high-pressure  engine  only  was  at  work,  giving 
55  to  150  H.  P., 

Pf=P0-\-o.iiPt 
with  condenser  in  action,  and 

Pf  =  P0  +  o.o6Pe 

working,  non-condensing,  at  about  the  same  power,  measured 
by  indicator.    The  air-pump  demanded  7.25  to  7.5  horse-power. 
Earlier  issues  of  the  journal  in  which  these  data  are  re- 
corded give,  from  various  sources,  the  following  figures  : 


Date. 

Engine. 

Builder. 

Best  H.  P. 

Max. 
Effic. 

1864 

Beam,  simple. 

G.  A.  Him. 

II5.OO 

90.8 

1867 

"       Woolf. 

Koechlin. 

191.44 

89.6 

1876 

Horizontal,  Woolf. 

Alsatian  Soc. 

174.46 

89.1 

1878 

Corliss. 

Berger-Andre. 

144.82 

9!-5 

1879 

Horizontal,  comp'd. 

Weyher  &  Richmond. 

6o.OO 

87.5 

1884 

Collman. 

Burghart  Bros. 

22.26 

87.8 

1884 
1885 

Hor.  portable. 
"     compound. 

Quid  &  Co. 
Alsatian  Soc. 

23-97 
59.26 

86.3 
89.1 

!2  cyls.  and  condens.  ) 

248.97 

86.3 

1886 

icyl.    "          "          I 

Bitschweiler-Thaun. 

128.38 

83-9 

i     "      "          "          i 

128.38 

88.0 

The  data  here  collated  show  plainly  the  increase  in  efficiency 
of  machine  as  the  power  demanded  increases;  but  the  last  table 
also  shows  that,  where  equally  well  proportioned  to  their  work, 
small  engines  may  have  practically  equal  efficiency,  as  machines, 
with  large  engines  ;  and  that  horizontal  and  beam  engines  may 
be  substantially  equal  in  this  respect.  Single-cylinder  engines 
but  slightly  excel  good  compound  engines  ;  and  the  triple- 
expansion  engine  with  three  equidistant  cranks  is  still  more 
satisfactory  in  its  operation. 


THERMODYNAMICS  OF   THE  STEAM-ENGINE.          565 

134.  The  Methods  of  Variation  and  of  Distribution  of 
Internal  Friction  of  Engine  are,  so  far  as  deducible  from 
these  data,  and  from  those  of  other  investigators,  evidently  as 
follows  : 

(1)  The  friction  of  the  non-condensing  engine,  of  the  better 
class  as  here  described,  is  sensibly  constant,  at  any  given  speed, 
at  all  loads;  and   at  different  speeds,  is  independent  of  the 
magnitude  of  the  load. 

(2)  The  friction  of  such  engines  is  variable  with  variation  of 
speed  of  engine  ;  increasing  as  speed  increases,  in  some  ratio 
as    yet  not   fully   determined,  but    probably  differing    with 
every  engine,  and,  for  the  same  engine,  with  every  change  of 
conditions  of  operation. 

Generally,  we  may  write 


(3)  The  friction  of  engines  increases  with  increase  of  steam- 
pressure,   in    such    cases,    in   a    probably  similarly  variable 
manner  with  that  observed  with  alteration  of  speed  ;  neither 
method  of  variation  being  ordinarily  capable  of  representation 
by  any  convenient  algebraic  expression. 

(4)  The  total  resistance  measured  at  the  piston  of  the  engine 
is  composed  of  two  parts,  the  one  sensibly  constant  at  the 
working  speed,  the  other  variable  with  external  load,  and  may 
be,  for  practical  purposes,  at  least,  represented  by  the  expres- 
sion 


in  which  R  is  the  total  resistance,  as  shown  on  the  indicator 
diagram,  Rt  the  resistance  due  to  the  external  load  —  e.g.,  as 
measured  by  a  Prony  brake,  —  and  R.  the  resistance  of  the  un- 
loaded engine. 

Here/  =  o  hi  the  cases  taken  in  §  133. 

(5)  In  engines  of  this  class,  the  internal  friction  varies  di- 
rectly with  the  speed,  or  sensibly  so,  other  things  being  equal  ; 


566  A   MANUAL   OF   THE   STEAM-ENGINE. 

is  directly  proportional  to  the  power  exerted,  and  may  be 
taken  as  a  constant  part  thereof,  whenever  other  conditions 
remain  unchanged  with  varying  speed. 

(6)  We  usually  find  confirmation  of  the  fact,  well  known  to 
engineers  of  experience,  that  the  operation  of  a  well-cared-for 
engine  will  continuously,  and  for  a  long  time,  appreciably  re- 
duce the  internal  friction  of  the  machine. 

In  Distribution,  experiment  shows  the  total  friction  of  engine 
to  be  composed,  in  most  cases,  mainly  of  main  shaft,  piston, 
and  valve-gear  resistances,  in  the  non-condensing  engine,  and 
of  air-pump  and  load  in  condensing  engines.  Investigations 
made  for  the  Author  by  Messrs.  Carpenter  and  Preston  give 
the  following  for  a  fast-running  engine  with  unbalanced  valve 
and  "  automatic "  valve-gear ;  the  total  amounts  to  ten  per 
cent  of  the  rated  power  of  the  engine — 20  I.  H.  P. 

Friction  H.  P.  Friction  per  cent. 

Main  shaft  and  eccentrics 0.867  42.4 

Three-ported  valve 0.560  27.4 

Piston  and  rod 0.328  16. 1 

Cross-head  and  pin 0.174  8.5 

Crank-pin 0.115  5.6 


Total 2.044  100.0 

The  following  distribution  was  found  for  a  similar  case 
with  a  balanced  valve,  the  total  being  about  7^  per  cent  of  the 
rated  power  : 

Friction  H.  P.     Friction  per  cent 

Main  shaft,  etc 0.867  56.9 

Valve 0.038  2.6 

Piston  and  rod 0.328  21.6 

Cross-head  and  pin 0.174  11.5 

Crank-pin o.  1 1 5  7.4 


Total 1.522  100.0 


THERMODYNAMICS  OF    THE  STEAM-ENGINE. 


567 


The  coefficient  of  friction  can  be  deduced  with  certainty 
only  for  the  main  journals  of  the  engine;  since  there  is  a 
variation  in  pressure  of  piston-rings,  stuffing  boxes,  and  in 
other  quantities,  which  is,  to  a  great  extent,  unknown. 

If  we  call  f  the  coefficient  of  friction,/  the  pressure  on  the 
bearings  in  pounds  for  engines  light,  and  plus  mean  pressure 
on  piston  for  engines  loaded,  c  the  circumference  of  the  bear- 
ings in  feet,  n  the  number  of  revolutions  per  minute,  fpcn 
will  thus  equal  the  "lost  work"  of  friction;  which  has  been 
determined  in  the  previous  experiments,  and  is  expressed  as 
horse-power ;  this  is  indicated  to  foot-pounds  by  multiplying 
by  33>ooa 

Hence  fpcn  =  33,000  H.  P. 

33,000  H.  P. 
pen. 


The  following  shows  the  value  of  this  coefficient  for  several 
engines,  and  the  next  table  is  a  summary  of  results. 

COEFFICIENT  OF  FRICTION  FOR  THE  MAIN  BEARINGS  OF 
STEAM-ENGINES. 


Engine. 

F.  H.  P.  due  to  Main 
journals. 

Weight  on  Journals 
in  pounds. 

u« 

1  Coefficient  of  Fric- 
tion, engine  loaded. 

Iw  g  «  to  Rcvolutionn  of  Jour- 
nal per  nvinutc. 

0.85 
3-70 
0.68 
3-30 

1500 

2DOO 
500 
4OOO 

u  is 

5*   -04 

*  This  engine  was  new,  and  gave  an  excessive  amount  of  friction  as  com- 
pared with  older  engines  of  the  same  class.  These  main-journal  frictions  seem 
to  the  Author  large;  especially  numbers  2  and  3. 


568 


A   MANUAL   OF   THE   STEAM-ENGINE. 


DISTRIBUTION  OF   FRICTION. 

SUMMARY    OF    RESULTS. 


Pans  of  Engine. 

Percentage  of  Total  Friction. 

VO   " 

e«- 
51 

•31 

u 

.y" 
11 

bi 
•1 

4;    > 

t, 

cfl  o 

P 

VO   y 

II 

7"  x  ID"  Trac 
comotive  Va 

& 
*1 

^  C 

-  OQ 

21"  x  20"  Con 
Balanced  V» 

47.0 

35-4 

35-o 

4i.6 

46.0 

32.9 

25.0 

21.  0 

49.1 

21.8 

6.8 

5-4 

2.5 

5-3 

5-1 
4.1 

13-0 

Valve  and  rod  

26.4 
4.0 

22.  0 

9-3 

21.0 

9-0 

12.0 

Total  

IOO.O 

IOO.O 

IOO.O 

IOO.O 

IOO.O 

The  friction-waste  of  a  very  small  engine,  tested  by  Pro- 
fessor Jacobus,  as  computed  on  the  assumption  of  a  constant 
coefficient  of  8.5  per  cent,  is  as  below.  The  engine  developed 
0.944  D.  H.  P.  at  100  revolutions  per  minute,  with  a  mean 
pressure  of  53  pounds;  its  size  being  3^  inches  diameter  and 
5  inches  stroke,  with  link-motion  and  unbalanced  slide-valve. 

FRICTION   OF   ENGINE. 


D.  H.  P. 

Valve 0.0240 

Piston 0.0030 

Packing 0.0020 

Eccentrics 0.0097 


D.  H.  P. 
Pins  at  cross-head. .  0.0068 

Guides 0.0079 

Crank-pin 0.0985 

Shaft  and  wheel.  . .  0.0230 


Total o.  1 749 

Actual  by  experiment 0.175  H.  P. 

Or  18.5  per  cent.     Efficiency  of  engine 0.815 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


569 


Shafta 

H. 
6x  12 

230  rev. 

12  H.  P. 

P. 

7X  10 
200  rev. 
15  H.  P. 

Crank-pin.  . 
Wrist-pin  .  . 
Guides.  
Valve 

.    0.30 
.    O.O6 
•    0.13 
O  I7d 

0.38 
0.08 
0.12 

0.68 

Eccentrics. 
Piston 

J'1  / 
.    0.08 

o  16 

048 
on 

Packings.  .  . 

.  o.ooe 

j'  *  o 

0.2O 

The  assumption  of  a  coefficient  of  friction  constant,  at  10 
per  cent,  gives  the  following,  for  30  Ibs.  mean  effective  pres- 
sure :* 


Remarks. 

"Including  thrust  of 
piston  rod. 

bWeight  =    500  Ibs. 

c      «        =1500    " 

dValve  balanced. 

eNo  packing  or  rod; 
using  Sweet's  me- 
tallic sleeve. 


Total 1.83          2.64 

Actual 1.64          2.86 

Studying  the  data,  it  is  seen  that,  in  the  engines  here  rep- 
resented, the  friction  of  the  shaft  and  eccentrics  is  the  princi- 
pal item  ;  that  the  friction  of  the  valve  and  its  stem  is  the 
next  most  serious  item  in  the  case  in  which  it  is  tested  under 
pressure  unbalanced,  but  becomes  only  a  fraction  as  great  when 
well  balanced,  and  is  then  comparatively  unimportant  ;  that 
the  friction  of  the  piston  may  be  a  heavy  item,  and  that  of 
the  crank-pin  is  a  very  small  proportion  of  the  total.  Since 
the  sliding  friction  of  the  cross-head  is  known  to  be  consider' 
able,  it  is  at  once  evident,  on  comparing  that  item  with  the 
last,  that  the  friction  of  the  cross-head-pin  must  be  a  very 
small,  and  probably  an  insignificant,  part  of  the  total.  This 
is  also  to  be  inferred  when  the  fact  is  considered  that,  although 
it  is  subject  to  the  same  pressure  as  the  crank-pin,  the  extent 
of  rubbing  motion  during  a  revolution  of  the  engine  is  there 
very  much  less  than  on  the  latter. 


•  Stevens  Indicator;  Oct.  1890;  p.  351. 


57°  A    MANUAL    OF    THE    STEAM-ENGINE. 

The  conclusions  relative  to  the  opportunity  for,  and  the 
methods  of,  reducing  this  waste  of  energy  are,  evidently,  (i) 
that  it  is  advisable  to  secure  a  minimum  shaft-friction,  by  care- 
ful selection  of  material  and  proportioning  and  finishing  of 
journals  ;  (2)  to  make  piston-friction  a  minimum  by  securing 
the  least  possible  pressure  of  rings  and  piston  on  the  internal 
surface  of  the  cylinder ;  (3)  to  adopt  a  good  balanced  valve — 
an  essential  desideratum,  also,  of  all  automatic  regulation — 
and  (4)  especially  to  secure  the  most  efficient  possible  lubri- 
cation. 

In  condensing  engines,  the  wasted  energy,  in  addition  to 
the  above,  consists  of  that  expended  in  taking  the  water  from 
the  condenser  and  expelling  it  from  the  system  ;  the  power 
required  to  move  the  air-pump  valves  and  the  bucket  in  the 
pump-barrel,  the  resistances  of  the  circulating  pump,  when 
a  surface  condenser  is  employed,  and  the  frictions  of  the 
pump  mechanism.  Of  these  quantities,  the  first,  as  a  minimum, 
is  approximately  proportional  to  the  quantity  of  steam  to  be 
condensed ;  the  other  quantities  are  nearly  constant.  The 
expedients  to  be  adopted  to  reduce  these  wastes  are  the  same 
as  in  the  non-condensing  engine,  and  also,  by  careful  design 
and  proportions  of  the  pump-system,  the  reduction  to  the 
least  possible  amount  of  the  friction  of  flow  of  the  water  used 
through  its  various  channels. 

135.  The  Conditions  of  Maximum  Efficiency  of  Ma- 
chine, from  what  has  preceded,  are  seen  to  be  simply  the 
conditions  of  minimum  lost  work  by  friction.  Journals  and 
all  other  rubbing  parts  must  be  of  carefully  adjusted  size,  well 
made,  of  proper  material,  and,  above  all,  well  lubricated.  Pis- 
ton-rings, if  expanded  by  springs,  should  bear  against  the 
cylinder  as  lightly  as  possible,  should  be  made  of  material 
giving  minimum  friction  at  the  temperature  of  their  operation, 
and  under  all  the  other  peculiar  physical  conditions  to  which 
they  are  subjected.  Stuffing-boxes,  if  used,  should  be  deep, 
well  filled,  and  lightly  packed ;  and  the  whole  system,  includ- 
ing valve-gear  and  all  connections,  should  be  arranged  to  offer 
the  least  possible  resistance.  The  machine,  as  a  whole,  should 


THERMODYNAMICS  OF   THE   STEAM-EXGIXE.  5/1 

be  loaded  to  the  maximum,  consistent  with  economy  of  fuel 
and  steam,  and  operated  in  such  manner  and  at  such  speed  as 
will  give  highest  total  efficiency. 

The  lubricating  apparatus  should,  if  possible,  be  so  designed 
as  to  flood  the  journals  constantly,  and  to  utilize  the  lubricant 
fully,  by  a  constant  circulation.  This  system  not  only  reduces 
the  sliding  friction  of  the  machinery  to  a  minimum,  but  also 
usually  gives  rise  to  minimum  risk  from  failure  of  lubrication. 

136.  The  Conditions  of  Maximum  Total  Efficiency,  in 
the  engine,  are  easily  stated  generally,  but  are  not  so  easy  of 
exact  determination  for  a  specified  instance,  or  of  complete 
realization  in  any  case.  In  some  directions,  one  element  of 
efficiency  is  only  promoted  at  the  expense  of  another;  and 
maximum  total  efficiency  is  always  the  resultant  of  compro- 
mises effected  among  conflicting  conditions.  Thus:  increas- 
ing speed  of  engine  usually  diminishes  exhaust-wastes,  while 
increasing  friction-losses;  and,  at  the  best  velocity,  any 
change  of  speed  will  increase  aggregate  loss,  while  diminishing 
some  one  or  more  of  its  elements.  Increase  of  velocity  giv- 
ing rise  to  greater  loss  by  friction  than  is  compensated  by 
decreased  cylinder-condensation ;  a  decrease  in  speed  ex- 
aggerates total  loss  by  producing  waste  at  the  exhaust  in 
excess  of  the  gain  by  decreased  engine-friction.  Similarly :  a 
high  ratio  of  expansion  gives  high  thermodynamic  efficiency: 
but  it  exaggerates  condensation,  and  with  considerable 
rapidity;  the  best  ratio,  from  this  point  of  view,  is  that  at 
which  this  resultant  efficiency  is  a  maximum.  It  is  this  which 
limits  the  ratio  of  expansion  practically  allowable,  often,  in  the 
condensing  engine,  a  small  fraction  of  that  which  the  thermo- 
dynaraic  theory  of  the  case  would  dictate. 

The  final  test  of  total  engine-efficiency,  and  of  satisfactory 
design,  construction,  and  operation,  is  the  measure  of  the  ex- 
penditure of  steam  or  of  fuel  in  the  production  of  the  required 
net,  useful,  work,  the  dynamometric  power  of  the  engine, 
as  shown  by  a  Prony  brake  or  other  apparatus.  The  test  of 
ultimate  value,  to  the  purchaser  and  user,  is  a  still  different 
one :  it  is  the  money-cost  of  the  power  supplied,  and  of  useful 


572  A  MANUAL    OF    THE    STEAM-ENGINE. 

work  done,  as  measured  by  the  total  expense-account  on  the 
treasurer's  books. 

137.  Actual  Efficiencies  and  Economy  of  proposed 
steam-engines  may  be  approximately  computed,  when  operated 
under  conditions  similar  to  those  of  the  experiments  from 
which  the  available  data  are  derived.  As  has  been  seen,  all 
the  expenditures  of  heat  in  the  engine  are  now  recognized ; 
their  magnitudes  have  been  measured ;  the  laws  governing 
their  variation  with  all  the  usual  conditions  have  been,  in  some 
cases  closely,  in  other  instances  roughly,  determined ;  and  it  is 
practicable  to  make  estimates  that  shall  be,  in  many  cases  and 
for  standard  conditions  and  usual  construction  and  methods  of 
operation,  fairly  approximate,  and  which  may  also  serve  to 
guide  the  designer,  the  builder,  and  the  user,  in  making  esti- 
mates for  proposed  constructions. 

The  total  expenditure  of  steam  has  been  seen  to  be  com- 
posed of:  (i)  that  demanded  for  the  thermodynamic  cycle 
proposed  for  the  engine ;  which  can  be  computed  with  perfect 
accuracy ;  (2)  that  required  to  furnish  the  heat  wasted  by  the 
engine  otherwise  than  thermodynamically.  This  latter  quan- 
tity is  divided  into  two  parts :  (a)  that  needed  to  supply  the 
heat  wasted  externally ;  (ft)  that  wasted  by  internal  transfer, 
by  cylinder-condensation,  without  useful  transformation.  All 
these  quantities  are  now  easily  computed,  in  most  cases,  with 
some  degree  of  approximation ;  and  the  total  probable  heat 
and  steam-supply  may  thus  be  obtained  in  the  usual  measures 
of  heat  and  steam  demanded  per  horse-power  and  per  hour, 
and,  when  the  efficiency  of  the  boiler  is  known,  in  fuel,  both 
per  horse-power  per  hour,  and  as  a  total. 

Examples  of  such  computations  have  already  been  given 
for  the  ideal  case. 

It  is  obvious  that  the  computed  expenditures  for  the  ideal 
case  must  be  increased  in  the  proportion  to  which  wastes 
occur,  and  that  all  the  figures  which  have  been  thus  tabulated 
must  be  increased  from  ten  per  cent  upward  to  obtain  probable 
values  of  weight  demanded  of  steam  and  fuel  in  the  actual 
case. 


THERMODYNAMICS  OF   THE   STEA3/-EXGIXE.  S73 

The  following  are  selected  illustrations  of  the  ideal  case  for 
otherwise  common  practice,  at  the  several  pressures  and  ratio 
of  expansion  given ;  i.e.,  for  the  ideal  _ase  in  which  the  steam 

IDEAL  EFFICIENCIES  OF  ENGINE. 


rl.  H.  P.  per 

-  -     :    _  -    - 


20 

2 

•          40 

2   e 

.    .  . 

3.  .  .  . 

!          6° 

3  3 

O   125 

4  •  •• 

So 

4  ° 

o  {•%> 

2    iS 

s.  .  .  . 

....             IOO 

5.0 

o  1=0 

.  . 

-    ;- 

g 

60 

-  -   -; 

So 

3-33 

0.091 

27  78 

-    -- 

s 

MIOO 

c   o 

-  -    ,  - 

•    -  . 

I2O 

10 

1  60 

5  ° 

O    l"*~ 

iS  90 

is  either  worked  in  a  non-conducting  cylinder  or  in  an  other- 
wise perfect  engine,  the  steam  being  kept  in  the  dry  and  satu- 
rated state  by  adding  heat  during  expansion  in  just  the  quan- 
tity needed  to  prevent  its  partial  condensation  in  consequence 
of  the  conversion  of  its  heat  into  work.  Adding  to  the  above 
computed  quantities  of  steam  and  of  fuel  those  demanded  to 
supply  the  wastes  invariably  met  with  in  greater  or  less  amount 
in  all  actual  engines,  we  may  obtain  figures  of  approximate, 
perhaps  closely  approximate,  values,  for  every-day  practice. 

To  determine  the  probable  real  efficiency  of  fluid,  allowing 
for  transfer  without  transformation,  by  internal  wastes  other 
than  thermodynamic.  assume  the  engines  to  be  of  moderate 
size  and  operated  under  familiar  conditions,  such  as  those 
which  were  met  with  in  experiments  conducted  by  the  Author, 
in  which  the  wastes  were  very  exactly  measured  by  the  expres- 
sion c  =  j^^r  =  °-2  */*'  f°r  the  non-condensing  unjacketed  en- 
gine, and  take  the  losses  of  the  jacketed  engine  at  a  common 


574 


A   MANUAL   OF    THE   STEAM-ENGINE. 


proportion,  three  fourths  that  amount,  c  =  o.i5  V  '  r  for  engines 
which  we  will  take  as  of  usual  proportions,  and  will  assume 
D  =  20  inches  diameter  of  cylinder.  The  speed  of  engine  may 
be  taken  as  about  500  feet  per  minute,  that  at  which  our  data 
were  secured,  in  these  cases,  a  =  4,  nearly  (§  130).  Adding  this 
proportion  to  the  previously  computed  amounts  for  the  ideal 
case,  we  obtain  for  the  actual  engine  figures,  assuming  other 
losses  too  small  to  be  here  considered,  which  agree  fairly  with 
common  experience. 

Further,  assume  that  it  is  practicable,  in  each  case,  to  make 
the  mechanical  efficiency  of  the  non-condensing  machine  0.90 
and  the  condensing  engine  0.85,  usual  figures  for  the  two 
classes.  Then  we  obtain  the  following  for  indicated  and  for 
dynamometric  power : 


ACTUAL  EFFICIENCIES  OF  ENGINE. 


Ste 

am. 

Fi 

el. 

I.  H.  P. 

D.  H.  P. 

I.  H.  P. 

D.H.P. 

I  

20 

2 

0.069 

36.2 

42.6 

4.0 

4  •  7 

2  

40 

2-5 

0.085 

29.2 

34-4 

3-2 

3-8 

3  

60 

3-3 

0.098 

25-5 

30.0 

2.8 

3-3 

4  

80 

4.0 

O.IOO 

25.0 

29.2 

2.8 

3-2 

5  

IOO 

5-0 

0.109 

22.9 

26.9 

2.5 

3-0 

6  

60 

2-5 

0.050 

44-9 

50.0 

4.5 

5-o 

7  

80 

3-3 

o  067 

37  -° 

40.  1 

3  7 

8  

IOO 

5.0 

0.073 

34-2 

38.0 

3  4 

Q     8 

9  

120 

5-0 

0.080 

31-3 

34-8 

3-i 

3-5 

160 

5  ° 

o  087 

28  7 

32  o 

Drier  or  superheated  steam,  higher  piston-speed,  larger 
powers  of  engine,  efficient  jacketing,  will  increase  these  effi- 
ciencies by  reducing  wastes ;  the  opposite  conditions  will  de- 
crease them.  Condensing  engines  are  here  found  to  promise 
about  twenty  per  cent  better  performance  than  non-condensing, 
a  promised  fulfilled  in  good  practice. 

The  differences  between  the  steam-consumption  figures  of 


THERMODYNAMICS  OF   THE  STEAM-ENGINE. 


575 


the  ideal  and  the  real  case  represent  those  internal  wastes 
\\  hich  may  be  largely  reduced  by  compounding  ;  they  amount 
to  a  nearly  constant  quantity,  six  pounds  of  steam  for  the  con- 
densing and  ten  pounds  for  the  non-condensing  engines.* 

Similar  computations,  assuming,  as  before,  that  clearances 
may  be  neglected,  and  that  the  ideal  case  is  first  taken,  then 
the  corrections  introduced  for  wastes,  give  the  following  results 
for  an  engine  working  steam  at  500  pounds  total  absolute  ini- 
tial pressure,  subject  to  16  pounds  back-pressure  for  the  non- 
condensing  and  5  pounds  for  the  condensing  machine,  and 
taking  the  evaporation  at  10  pounds  for  the  former  and  9  for 
the  latter;  the  ratios  of  expansion  ranging  from  2  to  160. 
The  condensation-waste  is  taken  for  the  simple  engine  as  the 
same  as  obtained  in  the  Sandy  Hook  experiments,  c  =  o.2  V*r; 
i.e.,  corresponding  to  the  simple  engine  of  good  construction 
and  moderate  speed,  having  about  20  inches  diameter  of  cylin- 
der. The  feed-water  is  taken  at  the  same  temperature  in  all 
cases,  200°  F.  ;  since,  at  such  pressures,  a  high  temperature  is 
advisable  and  is  obtained  by  the  use  of  heaters,  in  the  one  case 
taking  heat  from  the  exhaust-steam,  in  the  other  through  jacket 
and  receiver  wastes.  Buel's  tables  are  here  used  ;  but  Porter's 
or  Peabody's  will  give  similar  results. 

The  data  and  results  are  as  tabulated  below  : 


HIGH  (CONSTANT)  PRESSURE,  r,  VARIABLE. 
v  =  0.942;  /,  =  46y°.42  F.;  H  '=  1224.54  B.T.  U.;  ffi=  815,650  ft.-lbs. 
IDEAL  CASE, 


8 

10 

13 

16 

2O 

25 

30 

.  .   178 

.0 

151.5 

124.0 

105.5 

88.5 

74.O 

63.5 

.   162 

.0 

135.5 

108.0 

89-5 

72.5 

58.0 

47-5 

u  

•   i?5 

,792 

182,805 

191,452 

194,241 

196,692 

196,692 

193,301 

Efficiency.  .  . 
Steam 

o 
n 

.216 

.32 

0.223 
10.80 

0.235 
10.34 

0.238 

IO.2O 

O.242 
10.06 

O.242 

10.06 

0.237 
10.24 

Fuel  

i 

•13 

i.oS 

1.03 

1.02 

1.  01 

i.  or 

i.  02 

*  The  constancy  of  this  waste,  as  thus  computed,  as  already  noted,  accords 
singularly  with  the  results  of  experiment. 


576  A    MANUAL    OF    THE   STEAM-ENGINE. 


Condensing. 
20              30              40              50              60              80 

88.5          63.5          50.0         41.5          35-5          28.0 

23  o 

u 

83.5          58.5          45-0          36.5          30-5          23.0 
226  535     238,066     344,170    247,561     248,240     249,596 

18.0 

Efficiency.  .  .  . 
Steam  

0.278        0.292        0.299        0.304        0.304        0.306 
8  75          8.32          8.  i  i          7.99          7.98          7.93 

0.299 
8  ii 

Fuel  

0.97          0.92          0.90          0.89          0.89          o788 
REAL  CASE,  Non-condensing  ;  Simple  Engine. 

0.90 
16 

I+.2f9... 
Efficiency  .  .  . 
Steam  
Fuel  .... 

1.4242         1.4899         1.5658         1.6325         1.7211 
0.1287         0.1356         0.1376         0.1365         0.1364 
18.95           17-87           17-73           17-54           17-81 
i.  89            i-79            i-77            *  •  75            1.78 

1.800 
0.132 
18.36 
1.84 

Condensing,  Simple  Engine. 
5                     8                 10                 15                25 

30 

i+24/;.... 
Efficiency  ... 
Steam  
Fuel  .  . 

1.447               1-5658            1.6325            1.7746            2.000 

0.1400        0.1486        0.1523        0.1481        0.1434 
17.40           16.54           15-9°           l6-47          16.94 
i.  qi             1.84             1.77             1.83             1.88 

2-095 
0.0139 

17-43 
I.Q3 

Studying  the  above  figures,  it  is  seen  at  a  glance  that,  in 
such  a  case  as  is  taken,  the  best  work  is  done  by  the  ideal  en- 
gine, non-condensing,  at  about  r  =  20  and  condensing  at  r  = 
about  80;  while  there  is  no  great  advantage,  even  in  the  ideal 
engine,  in  going  beyond  r  =  10  expansions  in  the  one  or  20  in 
the  other.  Even  these  figures  are  reduced,  in  the  case  taken  as 
actual,  to  r  =  6  and  r  =  10. 

By  the  adoption  of  the  expedient  of  dividing  the  wastes  by 
compounding  the  engine,  these  best  ratios  can  be  increased 
and  the  expenditure  of  steam  and  of  fuel  decreased  very 
greatly,  as  seen  elsewhere  (Chapter  VI,  §  149),  and  it  is  evident 
from  this  study  of  the  case  and  on  comparison  with  cases  of 
engines  worked  at  lower  pressures,  that  such  high  steam  should 
not  be  used  except  in  multiple-cylinder  engines  of  three  or  four 
in  series. 

We  neglect  the  effects  of  clearance  and  compression,  in  all 
these  cases,  assuming  that,  in  all  cases,  they  are  made  minima, 
the  clearance  being  not  only  reduced  to  the  least  possible  vol- 


THERMODYNAMICS  OF  THE   STEAM-ENGINE.          S77 

ume,  but  that  the  cushion-steam  is  expanded  and  compressed 
substantially  in  equal  proportions,  and  that,  for  this  reason,  its 
action  may  be  neglected.  Him  and  Hallauer  have  shown  that, 
in  practice,  the  cushion-steam  has  not  sensible  effect,  either 
theoretically  or  actually,  in  enhancing  waste  by  cylinder-con- 
densation ;  and  many  experiments  conducted  under  the  super- 
vision of  the  Author  have  similarly  shown  the  cushion-steam  to 
be  so  absolutely  dry,  in  even  small  engines,  as  to  fully  justify 
Hirn's  conclusions.* 

The  Influence  of  Size  of  Engine  may  be  very  important  as 
affecting  wastes  and  the  efficiencies  of  the  engine.  In  all  of  the 
examples  taken,  it  has  been  assumed  that  the  engines  were  of 
fair  size  for  factory  engines,  and  of  moderate  speed  of  piston  ; 
at  least,  such  that  the  rate  of  condensation  found  by  experi- 
ment might  be  fairly  assumed  to  apply  to  them.  It  will  be  in- 
teresting to  endeavor  to  obtain  some  idea  of  the  effect  of  vari- 
ation of  size  of  engine  upon  performance.  That  this  is  not 
necessarily  serious,  with  even  quite  small  engines,  when  proper 
precautions  are  taken  to  make  the  waste  a  minimum,  is  seen  in 
the  results  of  the  trials  of  agricultural  engines,  where  engines 
of  ten  and  twenty  horse  power  are  reported  giving  as  high  ef- 
ficiency as  the  average  of  fairly  good  engines  of  the  same  work- 
ing pressures  at  sea,  both  simple  and  compound  being  com- 
pared. It  is  evident  that  the  greater  extent  of  surface  exposed, 
per  unit  weight  of  working  fluid  subject  to  condensation,  must, 
other  circumstances  being  equal,  give  the  larger  engine  the  ad- 
vantage. 

But  the  heat-storing  power  of  the  unit  of  surface  is  less  as 
the  size  of  engine  is  less ;  since,  if  we  follow  Fourier,  the  rate 
of  absorption  varies,  for  a  given  temperature-head,  nearly  as  the 
square-root  of  the  total  quantity  of  heat  presented,  and  since, 
also,  the  water-flooded  surface  of  the  small  engine  is  less  effec- 
tive, because  of  its  reduced  absorptive  power,  than  the  com- 
paratively dry  surface  of  the  larger  cylinder.  Experience  also 

*  In  making  such  computations,  for  real  cases,  as  are  here  illustrated,  pre- 
liminary to  designing  engines,  good  average  conditions  are  to  be  usually  as- 
sumed; and  when  in  doubt,  less  rather  than  more  favorable  conditions. 


578  A   MANUAL   OF   THE   STEAM-ENGINE. 

seems  to  indicate  a  less  rapid  rate  of  variation  of  internal  waste 
than  is  indicated  by  the  factor  — . 

To  make  this  comparison,  it  is  necessary  to  ascertain  the 
waste  per  unit  area  of  surface  exposed,  per  unit  of  time  of  ex- 
posure, and  per  unit  range  of  temperature  within  the  cylinder. 
The  computations  of  Professor  Marks*  give  for  this  quantity, 
assuming  it  for  present  purposes  a  constant,  a  value  never  far 
from  c  =  0.02047,  which  is  here  taken  as  the  value  affecting  the 
cases  assumed.  Let  the  process  of  computation  already  illus- 
trated be  adopted,  and  let  the  data  be  as  follows : 

Data  : 

Engine,  single-acting  compound. 

Clearance,  20  per  cent. 

Boiler  pressure,  165  Ibs.  per  sq.  in.,  23,660  per  sq.  ft. 

Back  pressure,  18  Ibs.  per  in.,  2592  per  sq.  ft. 

Ratio  of  expansion  in  H.  P.  cylinder,  2.5. 

Ratio  of  low-  to  high-pressure  cylinder,  2.78  to  I. 

Piston-speed,  600  feet  per  minute. 

Initial  volume,  vlt  2.8  feet ;  final,  v,,  7  feet ;  /,  =  8690. 

Results  : 

Weight  of  steam  in  low-pressure  clearance,  0.554  Ib. 

Compression  begins  at  0.047 !  M-  E-  p->  m  H.  P.  cylinder, 
6400  Ibs. 

Ditto  in  L.  P.  cylinder,  1940  Ibs.  per  ft. 

Weight  of  steam  in  L.  P.  cylinder,  1054  Ibs. 

Energy  of  steam  per  Ib.,  138,860  ft.-lbs. 

Efficiency  of  the  steam,  E  =  0.1413. 

Water  per  H.  P.  per  hour,  Ibs.,  17.56. 

Fuel  at  10  Ibs.  per  Ib.,  1.76. 

Heat,  at  usual  equivalent,  per  I.  H.  P.  per  hour,  19,766 
B.  T.  U. 

The  above  figures  show  what  the  ideal  engine  would  do 
under  the  given  conditions,  and  what  would  be  the  performance 

*  Proportions  of  Steam-engine;  3d  ed.,  p.  257. 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


579 


of  the  real  engine,  irrespective  of  size,  were  there  no  wastes. 
With  varying  sizes,  the  volumes,  v,  worked  at  any  given  ratio 
of  expansion,  the  stroke  of  piston  being  made  variable  with 
the  diameter  of  the  cylinder,  will  vary  as  the  cubes  of  the 
diameters;  while  the  surfaces,  s,  exposed  will  vary  as  the 
squares.  The  wastes  occurring  internally  will  thus  vary  as  the 
quantity  s  -t-  z;  or  inversely  as  the  diameter  with  cylinders  of 
similar  proportions.  If  the  stroke  be  kept  unchanged,  the 
diameters  varying,  the  wastes  will  vary  as  above,  with  the 
variations  of  surfaces  and  volumes,  but  less  rapidly  than  hi  the 
first  case  with  a  given  variation  of  power. 

In  illustration,  take  three  engines  of  the  assumed  type, 
having  dimensions  as  below : 

(1)  1 8"  and  30"  X  16"  stroke; 

(2)  9"  and  15"  X    9"; 

(3)  3"  and    5"  X    3" 

Taking  the  internal  wastes,  as  already  proposed,  using  the 
coefficient  c  =  0.02047,  and  computing  the  loss  on  the  areas  of 
the  piston,  the  clearance,  and  port  passages  and  interior  of 
cylinder  up  to  point  of  cut-off,  we  obtain  the  following  results : 

VARIATION*   OF   EFFICIENCY   WITH    SIZE  OF   ENGINE. 


Fuel  and  Wa 

tor  per  H.  P. 

^•^  — 

_ 

\rea  i 

LHP 

Friction. 

LH.  P. 

D.  H.  P. 

perLH.P. 

Ideal.     1 

1.76     17.6 

o.o 

No.  i     1 

10.  16 

220.7 

1-3      23 

2-4:  34 

5-4 

5p.c. 

"     2      i 

2.66 

30.37 

2.8      27.9 

3-1;  30-7 

10.30 

10  p.  c. 

'      3 

0.294 

I.I32 

4.8      48-25 

5-4:  45-2 

30-7 

15  p.  c. 

The  enormous  effect  of  this  method  of  waste  in  small 
engines,  and  the  very  considerable  influence  of  size  upon  its 
magnitude  in  the  smaller  classes  of  engines,  are  thus  well  ex- 
hibited. In  the  above  instance,  the  interior  wastes  increase 
from  5.4  pounds  to  10  and  to  30  pounds  per  I.  H.  P.,  as  size 
decreases,  and  the  consumption  of  steam  thus  rises  from  17.6 


58O  A  MANUAL    OF   THE   STEAM-ENGINE. 

in  the  ideal  case,  to  28  and  48  pounds  for  the  smaller  engines. 
The  modifying  effects  of  the  various  expedients  for  reducing 
wastes  and  approximating  more  closely  in  real  engines  to  the 
ideal  case  of  pure  thermodynamics  will  be  illustrated  in  the 
chapter  on  compound  engines ;  superheating  and  steam-jacket- 
ing ;  in  which  computations  will  be  presented  exemplifying 
those  effects. 

Computing  the  thermodynamic  problem  for  the  compound 
engines  of  the  steamer  City  of  Fall  River  from  the  data 
reported  to  the  Author  by  Messrs.  Adger  and  Sague,  the 
observers,  we  may  profitably  compare  the  results  with  the 
actual  performance.*  This  computation  gives  figures  as 
below.  The  difference,  22  per  cent,  between  the  ideal  and  the 
real  engine,  being,  in  fact,  probably,  mainly  the  waste  in  one 
cylinder,  as  explained  elsewhere,  gives  a  measure  of  the  extent 
to  which  cylinder-condensation  affects  the  most  wasteful  of  the 
two  cylinders. 

The  steam  was,  in  this  case,  dry ;  the  engines  large  (44"  and 
68"  diameters  of  cylinder;  8'  and  12'  stroke  of  piston)  and  the 
efficiency  of  boiler  high.  The  engine  had  an  efficiency  of 
mechanism  of  83  per  cent,  the  paddles  80  per  cent,  66  combined, 
and  the  whole  machine  was  of  excellent  design.  The  lengths 
of  trials  ranged  between  eleven  and  twelve  hours. 

The  following  are  the  data  and  results : 

/,  =  absolute  pressure  of  admission  =  11,808  Ibs.  per  sq.  ft. 
pi  =  absolute  pressure  of  release        =  1363.68     "  " 

/s  =  mean  absolute  back-pressure      =  704.16       "  " 

t<  =  absolute  temperature  of  feed-water  =  558°. 36  Fahr. 

The  corresponding  temperatures,  densities,  and  latent  heats 
are  designated  by  the  same  subscripts: 

A  =  774°-5o  Fahr. ;  /,  =  652°. 32  ; 

Z,,  =  131841.14;  Za  =  19000.39; 

Z>,  =  .1909  ;  D^  —  .02606. 


'Engine  and  Boiler  Trials;  R.  H.  Thurston;   pp.  388-393. 


THERMODYNAMICS  OF  THE   STEAM-EXCIXE.  $8l 

From  these  data  the  following  results  were  arrived  at  by 
considering  the  cylinders  as  non-conducting  and  the  engine 
perfect :  * 

The  ratio  of  expansion  r  =  6.7167. 

Energy  per  cubic  foot  of  steam  admitted,  UDt  =  27183.43 
foot-lbs. 

Heat  expended  per  cubic  foot  of  steam  admitted,  //,/?, 
=  163716.507  foot-lbs. 

Mean  effective  pressure,  or  energy  per  cubic  foot  swept 
through  by  piston. 

UD 

l-  =  4047.5  Ibs.  per  sq.  ft. 


Heat  expended  per  cubic  foot  swept  through  by  the  piston, 

TT  rt 

—  =  24,377  Ibs.  on  square  foot  =  pressure   equivalent  to 

heat  expended. 

UD        U 
Efficiency  of  steam  =  „  n  =  -77  =  .166. 

-T7,//,  -T7, 

Net  feed-water  per  cubic  foot  swept  through  by  piston 

D 
=  —  =  .0284. 


Cubic  feet  to  be  swept  through  by  piston  for  each  indicated 

1980000 
horse-power  per  hour  =  M  E  p    _  4Q.  ,  c  =  489-2  cubic  feet. 


Feed-water  per  I.  H.  P.  per  hour  =  489.2  X  .0284  =  13.89  Ibs. 
Actual  feed-water  =  17.00  Ibs^  nearly. 

13.89 

Difference,  3.11  Ibs.  =  22  per  cent 

*  Steam-engine  Trials;  pp.  388,  389. 


582  A    MANUAL   OF   THE   STEAM-ENGINE. 

due  to  cylinder-condensation  and  leakage-waste  and  other 
wastes. 

The  average  locomotive  of  the  old,  simple,  type  demands 
about  6  pounds  of  good  coal  and  40  pounds  of  steam  per 
horse-power  per  hour. 

Mr.  Clark  found  the  water-consumption  of  the  "Great 
Britain  "  locomotive  to  be,  approximately, 

w  =  i6-j-o.i«-j-o.ooi4«a; 

where  w  was  the  weight  in  pounds  per  indicated  horse-power 
per  hour,  and  a  the  fraction  of  the  stroke  at  which  cut-off  took 
place. 

The  following  are  common  figures  for  usual  performance 
of  stationary  engines  in  1890  : 


GENERAL   COMMERCIAL   ECONOMY   OF   ENGINES   IN   ELEC- 
TRICAL  WORK. 

High-speed,  single  cylinder 35  to  40  Ibs.  water. 

"        "       compound,  non-condensing 25  "27  "  " 

"         "                "          condensing 19  "  21  "  " 

"         "      triple,                     "          16  "  17  "  " 

Corliss  single,  non-condensing : 27  "29  "  " 

"       compound,  condensing 15  "  16  "  " 

"      triple,  "  


If  the  available  energy  of  combustion  in  the  pound  of  coal 
be  taken  as  Uc,  the  coal  consumed  will  be,  per  horse-power  per 
hour, 

U7- 


UCE 

if  the  efficiency,  E,  be  that  of  the  engine  as  computed  on  the 
basis  of  the  given  power.  Thus,  if  E  =  o.  1  5  and  Uc  =  10,000,000 
foot-pounds, 

1,980,000 

W  —  -  —  =1.6;  Ibs. 

10,000,000  X  0.12 


THERMODYNAMICS  OF   THE  STEAM-ENGINE.  383 

Assuming  the  heat  obtainable  for  conversion  into  work  to 
be  10,000,000  foot-pounds  for  each  pound  of  fuel  burned  in  the 
boiler-furnace,  we  have  the  quantities  of  fuel  needed,  at  various 
total  efficiencies,  per  indicated  horse-power  per  hour,  as  below: 

WORK  AND   FUEL  AT  VARIOUS   EFFICIENCIES. 

Ft--lbs.  of  Los.  per  I.  H.  P. 

Efficiency.  Work  per  Ib.  per  boor. 

i  10,000.000  a  198 

0.80  8,000,000  0.25 

0.60  6,000,000  0.33 

0140  4,000,000  0^95 

0.30  3,000,000  0.66 

0.25  2,500,000  0.79 

0.20  2,000,000  0.99 

o.i  8  1.500.000  1. 10 

ai6  1,600,000  1.24 

0.15  1,500,000  1.32 

0.14  1,400,000  1.414 

0.13  1,300,000  1.523 

0.12  1,200,000  1.650 

an  1,100,000  1.800 

aio  1,000,000  1.980 


CHAPTER   VI. 

THE  COMPOUND  OR  MULTIPLE-CYLINDER  ENGINE; 
STEAM-JACKETING   AND   SUPERHEATING. 

138.  The  General  Theory  and  the  Construction  of  the 

multiple-cylinder  engine  are  equally  simple  ;  and  their  correct 
forms  may  be  readily  and  very  exactly  deduced  from  the  prin- 
ciples and  the  facts  already  revealed  by  current  practice  and 
experience  with  the  simple  engine.  As  has  been  seen,  the 
great  source  of  avoidable  wastes  in  the  single  cylinder  is  that 
alternate  heating  and  cooling,  and  that  consequent  wasteful 
condensation  and  re-evaporation  of  steam,  which  is  due  to  the 
exposure  of  the  internal  surfaces  of  the  cylinder  to  the  alter- 
nate heating  action  of  entering  steam  and  cooling  effect  of  ex- 
pansion and  condensation.  Any  expedient  which  will  reduce 
this  waste  by  preventing  that  transfer  of  heat  from  the  steam 
to  the  exhaust  side  of  the  engine  without  transformation  in 
proper  proportion,  into  work,  will  reduce  this  loss  and  increase 
the  economical  value  of  the  machine.  In  "  compound  "  en- 
gines, this  is  done  by  effecting  a  limited  expansion  and  partial 
transformation  of  heat  into  work,  submitting,  so  far  as  may  be 
necessary  to  cylinder-condensation  and  re-evaporation,  but 
then  transferring  the  working  steam,  both  the  uncondensed 
and  the  re-evaporated,  to  a  second  cylinder  in  which  the  latter 
portion  is  enabled  either  to  do  some  work  or  to  balance  its 
waste  more  or  less  fully.  Any  number  of  successive  expan- 
sions may  be  thus  practised  ;  but  experience  indicates  that  not 
more  than  two  is  desirable  at  ordinary  moderate  pressures, 
three  at  from  eight  to  ten  atmospheres,  or  four  with  twelve  to 
fifteen  atmospheres  pressure. 

Experience,  as  well  as   the  study  of   the  distribution  of 

584 


THE   COMPOUND  OR  MULTIPLE-CYLINDER  EXGIXE.     $83 

wasted  work  in  the  machine,  also  indicates  that  a  well-designed 
multiple-cylinder  engine  may  exhibit  higher  efficiency  of 
machine,  Le.,  less  loss  by  friction,  than  ordinary  simple  engines 
arranged  in  pairs ;  thus  giving  still  greater  advantage  when 
employed  for  marine  work  or  wherever  coupled  engines  are 
needed. 

The  multiple-cylinder  engine  is,  therefore,  any  engine  in 
which  steam  is  used  as  the  means  of  transformation  of  heat- 
energy  into  work,  through  a  succession  of  expansions  in  cylin- 
ders placed  **  in  series."  In  construction,  this  succession  of 
steam-cylinders  may  be  obtained,  either  by  using  structurally 
independent  engines,  or  by  making  them  parts  of  a  single 
structure.  The  former  system  is  sometimes  seen,  in  stationary 
engine  practice ;  the  latter  is  usual  in  marine  engines. 

The  question  of  adoption  of  the  compound  engine,  or 
either  form  of  multiple-cylinder  engine,  for  the  usual  work  of 
the  locomotive  or  in  any  case  in  which  the  speed,  pressure,  or 
load,  either  or  all,  is  expected  to  be  variable,  is  complicated  by 
the  fact  that,  under  such  variable  conditions,  it  is  impracti- 
cable to  find  proportions  of  cylinders  suitable,  and  permanently 
so.  Whenever  the  load  and  speed  maybe  expected  to  be 
reasonably  constant,  a  suitable  design  may  be  produced. 
Hence  the  success  of  the  marine  engine  in  these  forms  and  the 
less  completely  satisfactory  results  with  other  cases  in  which 
less  uniform  conditions  are  maintained,  as  in  the  locomotive. 
All  the  conditions  affecting  the  choice  and  use  of  engines  of 
differing  type  are  those  of  practice,  and  quite  apart  from  the 
thermodynamic  problem. 

In  practice,  the  multiple-cylinder  engine  exhibits  several 
advantages,  and  we  may  make  a  fairly-complete  summary 
thus: 

(1)  Reduction  of  expansion  in  a  single  cylinder. 

(2)  Great  restriction  of  internal  waste. 

(3)  Ability  to  adopt  large  ratios  of  expansion,  with  light 
loads,  without  "  wire-drawing." 

(4)  Reduced  leakage  in  engine. 

(5)  Reduction  of  depreciation  of  boiler. 


586  A  MANUAL    OF    THE   STEAM-ENGINE. 

(6)  Lighter  blast ;  smoother  draught ;  less  waste,  annoy- 
ance,  and  danger  from  sparks  and  cinder  ejected  from  locomo- 
tives. 

(7)  Elevated  limit  of  speed  and  power. 

(8)  Reduced  loss  by  tender  and  fuel  haulage. 

(9)  Greater  uniformity  of  crank-moments. 
(10)  Larger  efficiency  of  the  machine. 

139.  The  Wastes  of  the  Engine  are  similar  in  kind,  in 
all  cases,  to  those  of  the  simple  engine.*  Were  it  possible  to 
construct  a  steam-engine  of  which  the  theory  should  be  purely 
thermodynamic,  an  engine  in  which  the  only  waste  of  energy 
should  be  that  known  as  the  necessary  thermodynamic  loss,  its 
theory,  as  has  been  seen,  would  be  most  simple  and  most  satis- 
factory. The  efficiency  of  the  engine  and  the  quantities  of 
heat,  steam,  and  fuel  demanded  for  its  operation  at  a  given 
power  would  be  simple  functions  of  the  physical  properties  of 
the  steam  and  of  its  ratio  of  expansion.  The  engineer,  in  con- 
structing its  theory,  would  only  concern  himself  with  the  quan- 
tity of  heat  imported  into  the  machine,  the  temperatures  of 
the  initial  and  terminal  portions  of  the  expansion-line,  and  the 
relation  of  initial  to  back  pressures.  The  essential  facts  are 
the  magnitudes  of  the  pressures  and  volumes  of  the  steam  and 
the  extent  of  adiabatic  expansion,  and  it  matters  not  whether 
the  engine  be  one  of  a  single  cylinder  or  a  multi-cylinder  en- 
gine of  indefinitely  extended  complexity.  For  this,  the  ideal 
case,  the  indicator-diagram  represents  precisely  the  amount  of 
transformation  of  heat-energy  into  mechanical  work,  and  the 
ratio  of  its  measure  in  units  of  work  to  the  mechanical  equiva- 
lent of  the  total  quantity  of  heat-energy  supplied  to  the  en- 
gine, while  doing  that  work,  is  the  measure  of  the  efficiency  of 
the  engine ;  as  it  is  of  the  thermodynamic  efficiency  of  the 
working  fluid.  The  thermodynamic  efficiency,  the  dynamic 
efficiency  of  the  machine,  and  the  total  efficiency  of  the  engine 
are  here  identical. 


*  This   portion    of   this  chapter  was  presented,  in  part,  at   the    Twentieth 
Meeting  of  the  American  Society  of  Mechanical  Engineers.     See  Trans.  1889. 


THE   COMPOUND  OR  MULTIPLE-CYLINDER  EXCIXE.     587 

To  ascertain  how  much  heat,  steam,  and  fuel  are  demanded 
by  such  an  engine  for  the  performance  of  work,  it  is  only  neces- 
sary to  measure  the  quantity  of  work  done  by  the  steam  upon 
the  piston,  as  shown  by  the  indicator,  and  to  divide  this  quan- 
tity by  the  energy  received  by  the  engine  from  the  boiler ;  the 
quotient  is  the  efficiency  of  the  engine.  As  the  operation  of 
the  engine  approaches  more  nearly  the  conditions  of  best 
effect,  the  magnitude  of  this  measure  of  efficiency  approaches 
a  limit  which  is  expressed  by  the  quotient  of  the  range  of  tem- 
perature worked  through  to  the  absolute  temperature  of  the 
working  fluid  at  entrance  into  the  engine.  The  excess  of  the 
actual  consumption  of  fuel,  in  the  best  engines,  above  the  for- 
mer figure  measures  the  sum  of  all  wastes  in  real  engines  due 
to  imperfections  other  than  of  thermodynamic  cycle.  Thus, 
the  best  work  of  the  Corliss  compound  mill-engine  being  taken 
as  about  sixteen  pounds  of  steam  per  horse-power  and  per 
hour,  where  the  thermodynamic  efficiency  is  about  twenty-five 
per  cent,  the  ideal  case  demands  about  ten  pounds,  under 
similar  conditions  otherwise,  and  the  wastes  amount,  in  this 
case,  therefore,  to  about  six  pounds  per  horse-power  and  per 
hour,  or  sixty  per  cent  of  the  ideal  consumption.  This  com- 
parison is  easily  made  by  the  method  already  presented,  which 
enables  the  thermodynamic  efficiency  to  be  easily  computed 
for  any  given  case. 

The  wastes  of  the  steam-engine  have  been  shown  to  com- 
prehend two  principal  classes :  the  external  and  the  internal 
wastes ;  and  these  latter  are  of  two  distinct  kinds.  We  may 
classify  such  losses  thus : 

(1)  External  wastes ;  consisting  of  those  losses  of  untrans- 
formed  heat  which  are  produced  by  the  conductivity  and  the 
radiating  power  of  the  materials  of  which  the  heated  parts  of 
the  engine  are  composed.     Five  per  cent  should  probably  rep- 
resent as  large  a  percentage  as  is  to  be  reasonably  expected  in 
good  practice  with  engines  of  moderate  or  large  size. 

(2)  Internal  wastes ;  consisting  of  two  parts : 

(a)  Thermodynamic,  unavoidable,  losses  of  heat  rejected  at 
the  lower  limit  of  temperature  of  the  working  fluid  ; 


588  A  MANUAL   OF   THE   STEAM-ENGINE. 

(b}  Wastes  by  internal  conduction  and  storage  of  heat,  fol- 
lowed by  later  rejection  with  the  exhaust-steam. 

To  these  are  to  be  added : 

(3)  Wastes  of  mechanical  energy. 

Of  the  internal  losses,  the  first,  (a),  is,  for  any  given  set  of 
initial  and  final  temperatures  of  working  fluid,  a  fixed  quan- 
tity, and  one  which  measures  the  defect  of  efficiency  of  the 
perfect  engine  working  between  the  given  temperatures.  The 
second,  (ft),  is  a  quantity  of  variable  amount,  capable  of  ameli- 
oration by  one  or  all  of  several  known  expedients,  and  reduci- 
ble from  the  enormous  proportion  observed  in  small  and  ill- 
designed  or  badly  constructed  engines  to  a  very  moderate 
amount  in  large  engines  of  good  type.  The  last  item,  (3),  is 
one  which  is  seldom  large  in  good  constructions,  and  may  in 
some  cases,  by  careful  design,  good  construction,  and  skilful 
management,  be  brought  down  to  less  than  five  per  cent  in 
non-condensing  and  to  perhaps  ten  per  cent  of  the  total  energy 
in  condensing  engines  of  simple  forms  and  high  mean  working 
pressures.  The  unavoidable  thermodynamic  waste  is  rarely 
less  than  seventy-five  or  eighty  per  cent  of  the  total  thermo- 
dynamic demand,  and  the  internal  wastes  by  conduction  and 
storage  with  subsequent  rejection,  by  cylinder  or  internal  con- 
densation, as  it  is  customarily  called,  and  by  leakage,  range 
from  ten  per  cent,  as  a  minimum,  perhaps,  to  twenty-five  or 
thirty  per  cent  of  the  heat  received  from  the  boiler,  in  good 
engines,  to  fifty  per  cent,  in  many  cases,  and  even  to  much 
more  than  the  latter  proportion  in  exceptional  cases.  It  is  this 
which  has  now  been  found  to  constitute,  ordinarily,  the  great 
source  of  loss  and  inefficiency  of  the  real,  as  distinguished  from 
the  ideal,  engine.  Leakage,  in  well-built  engines,  may  be  neg- 
lected as  unimportant ;  but  internal  condensation  is  usually 
both  serious  in  amount  and  extremely  difficult  to  check  ef- 
fectively. 

Since  it  is  easy  to  prevent  serious  losses  by  external  trans- 
fers of  heat,  by  leakage,  or  by  friction  of  engine,  and  since,  as 
is  well  understood,  the  thermodynamic  waste  is  unavoidable, 
and  for  any  given  case  unalterable  by  the  engineer,  it  is  ob- 


THE   COMPOUND  OR  MULTIPLE-CYLINDER  ENGINE.     589 

vious  that  the  direction  in  which  he  must  look  in  his  endeavor 
to  further  improve  the  economical  performance  of  the  engine, 
is  that  which  leads  towards  the  reduction  of  internal  wastes  by 
cylinder-condensation.  This  is  the  direction  which  coming 
inventions  must  take. 

In  comparing  the  simple  with  the  compounded  engine,  in 
average  practice,  it  will  be  found  that  the  former  excels,  in 
the  best  types,  in  the  small  clearance  practicable  in  a  single 
cylinder ;  in  the  adaptability  to  that  type  of  an  effective  ex- 
pansion-gear, as  illustrated  in  the  Corliss  type;  in  its  giving 
a  dynamic  cycle  which  is  represented  by  an  indicator-diagram, 
of  which  the  area  is  very  nearly  that  of  the  ideal  case :  and, 
finally,  in  its  lesser  total  area  of  exposed,  radiating,  and  heat- 
wasting  surfaces,  exterior  and  interior. 

On  the  other  hand,  the  compounded  type  excels  in  the  fact 
of  its  utilizing  the  wastes  occurring  in  the  full  cycle,  step  by 
step,  as  they  take  place,  more  and  more  perfectly  as  the 
number  of  cylinders  and  of  successive  stages  of  expansion 
are  increased,  thus  permitting  an  increase  of  the  practically 
economical  ratio  of  expansion.  It  also  excels,  in  the  marine 
type,  in  which  two  or  three  engines  are  found  to  be  desirable 
in  order  to  secure  a  good  distribution  of  turning  stresses  and 
moments,  by  giving  a  more  uniform  pressure  on  the  crank- 
pin  and  smoother  and  more  nearly  frictionless  rotation  of  the 
shaft. 

The  advantage  may  lie  on  the  one  side  or  the  other,  in 
special  cases  :  and  it  has  usually  been  found  practicable  to 
attain  substantially  the  same  efficiency  of  working  fluid  in  the 
one  type  as  in  the  other  by  exercising  sufficient  care  in  provi- 
sion against  wastes.  The  simple  engine  must  probably  be 
largely  dependent  upon  either  jacketing  or  superheating  for 
high  efficiency ;  while  the  compounded  types  are  more  nearly 
independent  of  these  expedients. 

Comparing  the  ideal  with  the  real  engine,  we  may  take  in 
illustration  the  following  from  available  data  of  engine-opera- 
tion, computing  the  ideal  case  and  comparing  the  results  with 
those  actually  obtained  : 


590  A   MANUAL    OF   THE    STEAM-ENGINE. 

DATA  AND  RESULTS. 

Engines Compound.  Standard. 

Cases I.  II. 

/i  (Ibs.  persq.  in.) 155  13° 

r 4  2 

A 20  20 

Temperature  of  feed-water 60°  F.  60°  F. 

Efficiency  of  steam 0.1445  0.1197 

"  "  furnace  (Rankine's  Eq.) 0.664  0.60 

The  fuel  used  on  trial  was  reported  as  4.1  and  4.7  pounds 
per  D.  H.  P.  per  hour,  respectively. 

Coal  per  D.  H.  P.  per  hour 4.iolbs.  4.7    Ibs. 

"      "     I.  H.  P.     "       "  at  20  p.  c.  friction  3.28  "  3.6      " 

"      "  "          "      "  ideal 2.01   "  2.35    " 

Wastes,  extra-thermpdynamic,  per  cent 30 . 9  37.6 

Value  of  a  (c  =  a  ^r  ) 0.22*  0.26 

A  gain  of  7  per  cent  is  made  by  reduction  of  waste,  by 
compounding,  in  this  instance,  which  represents  an  actual  case 
in  locomotive  practice. 

140.  The  Amelioration  of  Wastes  thus  becomes  an 
important  matter.  The  efficiency  and  economy  of  operation 
of  the  single  cylinder,  the  "  simple  "  engine,  is  at  all  times 
limited  by  internal  waste,  and  the  question  which  all  engineers 
endeavor  to  solve  is :  In  what  manner  may  we  best  proceed  to 
eliminate  or  ameliorate  this  loss?  The  three  methods  which 
have  been  found  advantageous,  and,  in  special  cases,  effective, 
have  been  seen  to  be : 

(1)  Superheating; 

(2)  Steam-jacketing; 

(3)  "  Compounding." 

Superheating  is  a  well-known  but  not  a  common  method. 
It  is  evident  that,  if  the  steam  can  be  introduced  into  the 
engine  at  such  a  temperature  that  the  cooling  action  of  the 
metal  of  the  cylinder  will  not  cause  its  condensation  initially, 
and  the  stroke  may  be  performed  without  condensation  in 

*  Closely  corresponding  with  the  Author's  deduction  for  engines  of  quite 
nearly  equal  volume,  and  earlier  reported. 


THE   COMPOUND   OR  MULTIPLE-CYLINDER  ENGINE.     §9 1 

consequence  of  doing  work,  no  loss  of  heat  from  the  cylinder 
can  take  place  by  re-evaporation  ;  and  if  no  such  loss  occurs, 
the  waste  of  heat  at  entrance,  in  turn,  by  initial  cooling,  will 
be  reduced.  Superheated  steam,  also,  is  a  good  non-conductor 
and  a  non-absorbent  of  heat,  like  the  permanent  gases.  It  is 
thus,  also,  less  liable  to  this  waste.  But  it  is  found  in  practice 
that  superheating  beyond  a  very  moderate  degree,  perhaps 
100°  F.,  is  inadvisable  on  account  of  risks  of  injury  to  engines 
and  cost  of  repairs  to  superheater,  which  more  than  com- 
pensate its  advantages.  It  has  come  to  be  regarded  as  an 
auxiliary  in  economizing,  not  as  a  complete  remedy  for  in- 
terior wastes.  This  method  of  augmenting  efficiency  will  be 
more  fully  discussed  later. 

Steam-jacketing  is  a  common  partial  remedy  for  this  waste. 
By  surrounding  the  steam-cylinder  with  the  steam-jacket,  it 
is  possible  to  produce,  in  part,  the  effect  of  superheating ;  that 
is,  to  secure  drier  steam  in  the  engine  throughout  the  stroke. 
The  amount  of  re-evaporation,  during  the  period  succeeding  cut- 
off and  up  to  the  closure  of  the  exhaust-valve,  and  the  quantity 
of  heat  of  which  the  cylinder  is  thus  robbed,  measures  closely 
the  amount  of  initial  condensation  and  waste  and  the  weight 
of  steam  which  must  be  supplied  in  excess  of  the  thermo- 
dynamic  demand  to  compensate  that  loss.  The  effect  of  the 
addition  of  a  steam-jacket  depends  upon  the  conditions  of 
operation  of  the  engines,  largely,  and  may  be  productive  of 
marked  advantage  or,  under  unfavorable  conditions,  of  no 
important  useful  effect.  With  steam  initially  dry,  the  jacket 
is  probably  usually  helpful ;  but,  with  wet  steam,  or  with  super- 
heated steam,  it  is  of  comparatively  little  value,  even  if  not 
sometimes  a  positively  wasteful  adjunct.  Steam-jacketing  will 
be  made  the  subject  of  a  later  article. 

Of  the  several  available  methods  of  checking  cylinder- 
wastes  of  heat,  it  is  evident  that  only  the  plan  of  securing  a  non- 
conducting interior  surface  is  purely  economical  in  method.  To 
superheat  the  entering  steam  is  to  reduce  a  great  loss  by  sub- 
mitting to  a  small  one ;  and  even  permanent  superheat,  as  in 
the  conversion  of  the  fluid  into  a  gas,  still  leaves  this  loss  only 


592  A   MANUAL    OF   THE   STEAM-ENGINE. 

ameliorated,  not  completely  destroyed.  In  a  single  unjacketed 
cylinder,  heat  carried  out  by  the  exhaust  is  a  pure  waste  ;  in 
the  jacketed  engine,  this  remains  true,  though  in  less  degree, 
not  only  of  the  heat  lost  by  initial  condensation  and  later  re- 
evaporation,  but  also  of  that  heat  which  may  have  been  em- 
ployed in  reducing  its  amount,  either  by  drying  the  prime 
steam,  or  by  the  normal  action  of  the  jacket.  In  multi-cyl- 
inder engines,  the  heat  employed  in  raising  the  temperature 
and  reducing  the  initial  condensation  of  the  steam  in  the  first 
cylinder  is  utilized  in  the  second  by  there  securing  a  better 
quality  of  steam,  as  well  as  by  directly  checking  this  waste. 
All  the  heat  swept  out  of  the  last  cylinder  into  the  condenser 
is  wasted.  Utilization  of  the  added  heat,  in  either  system,  is 
obviously,  at  best,  incomplete.  With  wet  steam,  the  jacket 
may  even  exaggerate,  rather  than  reduce,  the  loss ;  as  it  may, 
with  considerable  expansion,  increase  exhaust-wastes  in  greater 
amount  than  it  decreases  cylinder-condensation.  The  same 
remarks,  to  a  less  extent,  apply  to  the  systems  of  compounding 
where  excessive  expansion  is  adopted.  Superheated,  or  at 
least  dry,  steam  must  be  provided  by  the  boiler  to  insure 
economy,  either  with  or  without  these  special  constructions, 
and  to  enable  the  ratio  of  expansion  to  be  economically  in- 
creased. 

"  Compounding"  or  the  use  of  the  multiple-cylinder  engine, 
in  which  the  steam  exhausted  from  one  cylinder  is  again  worked 
in  a  succeeding  one,  is  now  the  most  familiar  of  devices  for  ex- 
tending the  economical  range  of  expansion  and  increasing  the 
efficiency  of  the  engine.  The  limit  to  useful  increase  of  the 
ratio  of  expansion  of  steam  in  a  single  cylinder  is  found  to  be 
determined  by  the  magnitude  of  the  wastes  incurred  in  the 
operation  of  an  engine  of  which  the  working  cylinder  is  a  good 
conducting  material.  Any  method  of  reducing  this  waste 
of  heat  internally  will  enable  the  efficiency  of  the  engine  to 
be  increased  by  further  profitable  extension  of  the  ratio  of 
expansion. 

141.  The  Problems  in  Compounding  are  now  readily 
stated.  Assuming  it  to  be  possible  to  divide  the  waste  by 


THE   COMPOUND   OR  MULTIPLE-CYLINDER  ENGINE.     593 

cylinder-condensation  and  leakage  by  two  or  more,  it  is  evident 
that  the  limit  to  economical  expansion  and  transformation  of 
heat  into  work  will  be  set  correspondingly  farther  away.  This 
is  done  by  the  multiple-cyclinder  engine :  the  internal  wastes 
are  reduced  approximately  to  those  of  one  of  its  cylinders,  and 
the  gross  percentage  of  waste  is  made  less  in  the  proportion  of 
this  division.  The  heat  and  steam  rejected  as  waste  by  inter- 
nal transfer  without  transformation  from  the  first  cylinder  is 
utilized  in  the  second  nearly  as  effectively  as  if  it  were  received 
directly  from  a  boiler  at  the  pressure  of  rejection  from  the  first 
cylinder.  Insomuch,  therefore,  as  the  pressure  can  be  in- 
creased and  the  increase  utilized  by  the  addition  of  another 
cylinder,  gain  is  secured. 

Common  experience  shows  that  the  best  results  are  ordina- 
rily obtained,  in  each  class  of  multiple-cylinder  engine,  when, 
the  engine  being  properly  designed  for  its  work,  the  terminal 
pressure  for  the  system  can  be  economically  made  something 
above  the  sum  of  back-pressure  in  the  low-pressure  cylinder, 
plus  friction  of  engine.  This  total  may  be  usually  taken, 
probably,  at  about  eight  or  ten  pounds  above  a  vacuum. 
The  latter  figure  will  be  here  assumed. 

142.    The  Three  Fundamental  Principles  are: 

(1)  Economical  expansion  in  a  single  cylinder  has  a  limit, 
due  to  increasing  internal  wastes  ;  which  limit  is  found  at  a 
comparatively  low  ratio  of  expansion. 

(2)  The  method  of  expansion  may  be,  for  practical  pur- 
poses, and  such  as  are  here  in  view,  taken  to  be  approximately 
hyperbolic ;  the  best  terminal  pressure  being  something  above 
that  which  corresponds  to  the  sum  of  all  useless  resistances, 
and  which   may  be   here    taken  as,  for  example,  about  ten 
pounds  per  square  inch  above  a  vacuum.*     The  division  of 
the  initial  tension  by  this  terminal  pressure  will  thus  give  an 

*  Mr.  H.  A.  B.  Cole  finds  the  value  of  the  index  «,  in  ordinarily  good  engines 
of  the  triple-expansion  type,  to  be  approximately  1.2,  varying  but  little  with  the 
range  of  expansion  adopted.  (Converting  Compound  into  Triple-expansion  En- 
gines; Trans.  Brit.  Inst.  N.  A.;  1886.) 


594  4   MANUAL   OF   THE   STEAM-ENGINE. 

approximate  measure  of  the  desirable  ratio  of  total  expansion 
for  the  best  existing  engines. 

(3)  All  steam  entering  any  one  cylinder  will  be  rejected,  as 
steam,  into  the  succeeding  cylinder,  external  wastes  being  neg- 
lected, and  ultimately  into  the  condenser  ;  and  the  full  amount 
of  steam  liquefied  at  entrance  by  absorption  of  heat  by  the 
interior  surfaces  of  the  cylinder  will  be  re-evaporated  later,  and 
will  pass  into  the  condenser  or  into  the  next  cylinder.  Heat 
transferred  in  the  one  direction,  in  the  one  process,  will  be 
transferred  in  precisely  equal  amount  in  the  opposite  direction, 
in  the  other. 

This  last  point  is  important,  and  is  easily  established : 
The  cylinder,  when  in  steady  operation,  is  neither  permanently 
heated  nor  permanently  cooled  ;  no  progressive  heating  can  go 
on,  as  it  would,  in  that  case,  become  heated  above  the  tem- 
perature of  the  steam  and  become  a  super-heater ;  no  progres- 
sive cooling  can  occur,  since,  in  that  case,  the  cylinder  would 
become  a  condenser  of  indefinite  capacity.  It  must,  therefore, 
transfer  to  the  next  element  of  the  system  all  the  heat  which 
it  thus  receives  ;  assuming  that  external  radiation  and  conduc- 
tion may  be  neglected,  and  that  the  Rankine  and  Clausius 
phenomenon  of  liquefaction  of  steam  by  transformation  of 
heat  into  work  is  ignored.*  It  also  further  follows  that  the 
introduction  of  one  or  of  many  cylinders  between  the  terminal 
element  and  the  oiler  does  not,  through  cylinder-condensa- 
tion, affect  the  operation  of  the  final  cylinder,  however  great 
that  condensation  may  be ;  provided  the  introduction  of  the 
added  elements  is  effected  by  raising  the  steam-pressures 
commensurately,  leaving  to  the  final  element  of  the  series  the 
same  initial  pressure  as  at  first.  The  Rankine  and  Clausius  phe- 
nomenon, it  should  however  be  noted,  insignificant  in  amount 
and  effect,  in  any  one  cylinder,  with  its  customarily  low  ratio 
of  expansion,  produces  a  cumulative  condensation  in  the  series, 

*This  the  Author  would  denominate  Hirn's  principle.  See  a  paper  by  M. 
Dwelshauvers-Dery  in  the  Bulletin  de  la  Societ6  Industrielle  de  Mulhouse, 
October  1888,  on  the  theory  of  simple  engines.  A  mathematical  proof  may  be 
found  in  De  Freminville's  Cour  de  Machines  a  Vapeur;  1862;  p.  121. 


THE   COMPOUND  OR  MULTIPLE-CYLINDER  ENGINE.     595 

which,  at  high  total  ratios,  has  already  been  seen  to  be  impor- 
tant, amounting  to  something  between  1 5  and  20  per  cent  of  the 
steam  thermodynamically  demanded.  This  condensation  is 
not  at  all  affected  by  the  principle  of  "  compounding,"  as  the 
heat  thus  surrendered  by  the  steam  is  transformed  into  work 
and  thus  taken  out  of  the  system  instead  of  being  temporarily 
stored. 

The  total  waste  by  this  form  of  loss  is  thus  evidently  meas- 
ured, in  the  case  of  the  multiple-cylinder  engine,  by  the  maxi- 
mum waste  in  one  cylinder.  If  all  are  equally  subject  to  this  loss, 
the  rejected  steam  of  re-evaporation  from  any  one  cylinder,  as 
the  high-pressure  cylinder,  supplies  precisely  what  is  needed  to 
meet  the  waste  by  initial  condensation  in  the  next ;  and  so  on 
through  the  series.  Thus  the  use  of  a  series  of  cylinders,  in 
this  manner,  divides  the  total  waste  for  a  single  cylinder,  ap- 
proximately, at  least,  by  the  number  of  cylinders ;  and  it  is  in 
this  manner,  largely,  that  the  "  compound  "  system  gives  its  re- 
markable increase  of  efficiency. 

The  three  principles  which  have  been  enunciated  give  a 
means  of  constructing  a  philosophy  of  the  multiple-cylinder 
engine,  which  will  meet  all  essential  needs  of  the  engineer.  The 
first  principle  shows  that,  a  limit  existing  to  economical  expan- 
sion in  a  single  cylinder,  the  advisable  number  of  cylinders  in 
series  may  probably  be  determined,  when  that  limit  is  ascer- 
tained for  any  case,  either  by  experiment,  by  general  experience, 
or  by  rational  theory  and  computation.  The  second  principle 
shows  that  we  may  find  an  approximate  measure,  at  least,  of  the 
desirable  total  ratio  of  expansion  for  maximum  efficiency, 
when  the  best  terminal  pressure  for  the  chosen  type  of  engine 
is  settled  upon.  This  total  range  of  expansion  is  divided  by 
the  maximum  admissible  range  for  a  single  cylinder  to  deter- 
mine the  minimum  desirable  number  of  cylinders.  Otherwise 
stated :  The  total  ratio  is  a  quantity  which  should  approxi- 
mately equal  the  admissible  ratio  for  a  single  cylinder  raised 
to  a  power  denoted  by  the  number  of  cylinders.  Combining 
thus  the  two  considerations  referred  to,  we  may  obtain  a  de- 
termination, probably  fairly  approximate,  of  the  proper  mini- 


5<X>  A    MANUAL   OF   THE   STEAM-ENGINE. 

mum  number  of  cylinders  in  series.  The  third  principle  enables 
an  estimate  to  be  made  of  the  total  internal  wastes  of  the 
series,  and  the  probable  expenditure  of  heat  and  of  steam,  and 
permits  a  solution  of  all  problems  of  efficiency  for  the  com- 
pound engine,  of  whatever  type. 

143.  The  First  Step  in  designing  the  "Compound"  En- 
gine is  the  determination  of  the  best  ratio  of  expansion,  under 
the  assumed  conditions  of  operation  and  for  the  given  type  of 
engine,  for  a  single  cylinder ;  then  the  best  ratio  of  expansion  for 
the  series ;  this  study  being  made  largely  from  the  financial  stand- 
point. It  is  not  the  thermodynamic,  nor  the  fluid,  nor  even 
the  engine,  efficiency,  which  must  be  finally  allowed  to  fix  the 
best  ratio  of  expansion ;  but  this  must  be  the  ratio  of  ex- 
pansion at  maximum  commercial  efficiency ;  that  which  will 
make  the  cost  of  operation  at  the  desired  power  a  minimum 
for  the  probable  life  of  the  system.  The  total  ratio  being 
settled  upon,  and  that  allowable,  as  a  maximum,  for  the  single 
cylinder,  it  becomes  easy  to  determine  the  best  number  of  cyl- 
inders in  series.  The  first-mentioned  ratio  is  that  of  maxi- 
mum commercial  efficiency,  as  just  stated  ;  but  the  second 
must  be  taken  as  that  which  gives  highest  efficiency  of  engine, 
the  back-pressure  in  that  cylinder  and  its  friction,  taken  singly, 
being  considered,  together  with  its  proper  proportion  of  the 
friction  of  the  engine  as  a  whole. 

Studying  the  method  of  distribution  of  wastes  among  the 
several  cylinders  of  the  multiple-cylinder  engine,  it  will  be  ob- 
served that,  since  the  pressures  increase  more  rapidly  than  the 
temperatures,  the  range  of  temperature  in  the  high-pressure 
cylinder  is  greatest ;  while,  the  same  weight  of  steam  passing 
through  the  whole  series,  the  low-pressure  cylinder  presents 
the  largest  area  of  condensing  surface  in  proportion  to  quantity 
of  steam  used.* 


*  In  Professor  Schroter's  tests  of  the  Augsburg  triple-expansion  engine,  in 
1889,  the  condensation  in  the  cylinders  ranged  from  an  average  of  14.4  per 
cent,  in  the  small  cylinder,  to  33.7  and  51.9  per  cent,  in  the  intermediate  and 
low-pressure  cylinders,  respectively;  the  total  amounting  to  from  16  to  20 
percent  of  the  whole  steam-supply.  Otherwise  stated,  these  interior  wastes 


THE    COMPOUND   OR  MULTIPLE-CYLINDER  ENGINE.     S97 

144.  The  Extent  of  Economical  Expansion  in  a  single 
cylinder  will  vary  with  the  working  range  of  temperature  and 
pressure,  and  with  the  physical  condition  of  the  working  fluid  : 
but  it  may  be  taken,  as  determined  by  experience,  as  perhaps 
not  above  two  and  a  half  expansions  for  unjacketed  engines 
with  wet  steam,  or  not  over  three  or  four  for  good  practice 
with  the  better  classes  of  engines.  The  total  expansion-ratio 
thus  becomes,  for  the  several  types  of  multiple-cylinder  engines, 
as  below : 

MULTIPLE-CYLINDER   ENGINES. 
No.  cyls.          123  4 

r 2.5  to  3         6.25  to  9  16  to  27  40  to  81 

/, 25  tosolbs.  6oto  loolbs.  I2oto3oolbs.  ssotoSoolbs. 

The  result  of  this  sharing  of  the  wastes  in  the  multiple-cyl- 
inder engine  is  that,  in  the  triple-expansion  engine,  as  an  illus- 
tration, the  total  cylinder-condensation  may  be  reduced  from 
about  30  per  cent,  as  in  the  parallel  case  of  simple  engine,  to 
10  or  12  per  cent.  This  assumes  good  design  and  dry  steam — 
i.e.,  steam  containing  less  than  three  per  cent  water.  In  such 
case,  the  area  of  the  combined  indicator-diagram  should  ap- 
proximate 80  per  cent  that  of  the  ideal  case.  The  compound 
engine  should  approximate  70  per  cent.  In  common  practice 
with  1 50  pounds  steam,  the  temperature  being  equalized  in 
the  triple-expansion  engine,  the  ratios  of  cylinder-volumes  are 
about  i  :  2.5  :  7.5,  or,  equalizing  work,  not  far  from  i  :  2.8  :  7.1. 

Thus  a  triple-expansion  engine  should  do  best  work  up  to  a 
pressure  above  200  pounds,  and  the  four-cylinder  engine  should 
be  adopted  from  that  point  up  to  the  highest  pressures  likely 
to  be  employed  in  the  steam-engine  ;  the  common  double- 
expansion  compound  serving  its  purpose  well  below  the  lowest 
figures  assigned  to  the  triple  engine.  Any  type  of  engine  may 

amounted,  each,  to  from  2^  to  10  per  cent  of  the  total  steam  made;  being,  for 
example,  in  one  trial,  2.6,  6.0,  and  9.7  per  cent  in  the  three  cylinders,  respect- 
ively; the  minima  being  2.2,  5.4.  and  7.3;  and  the  maxima  2.9,  6.4,  and  10.7; 
while  the  totals  ranged  from  16. 1  to  20  per  cent. 


59^  A    MANUAL   OF   THE  STEAM-ENGINE.  ' 

be  made  to  overlap  the  range  assigned  it  by  suitably  providing 
against  wastes  occurring  within  the  engine  ;  as  by  increased 
speed;  by  superheating;  by  any  expedients  giving  higher 
effectiveness  to  the  jackets,  or  by  any  other  method  of  im- 
orovement.  Any  system  which  increases  the  efficiency  of  the 
simple  engine  will  improve  the  efficiency  of  the  compound, 
and  will  correspondingly  increase  the  range  of  pressure 
through  which  it  will  give  satisfactory  gain  as  compared  with 
the  former. 

145.  The  Influence  of  Economical  Expedients  recog- 
nized as  useful  in  other  forms  of  engine,  as  superheating,  jack- 
eting, and  increasing  speed  of  engine,  may  readily  be  perceived 
when  the  method  of  operation  of  the  multiple-cylinder  engine 
is  understood  in  its  relations  to  heat-transfer  and  heat-trans- 
formation. We  may  consider  them  in  their  order : 

(i)  Superheating  the  steam  transferred  from  boiler  to  engine 
results  in  the  supply  of  a  fluid  which  may  surrender  to  the 
metal  of  the  working  cylinder  a  certain  portion  of  heat — meas- 
ured by  the  product  of  its  specific  heat  as  a  gas  into  the  range 
of  superheating  and  into  its  weight — without  the  production  of 
initial  liquefaction.  If  this  quantity  of  heat  is  equal  to  or 
greater  than  the  loss  during  expansion  and  exhaust,  there  will 
be  no  initial  condensation  ;  and  the  waste  from  the  high-pres- 
sure cylinder  will  be  nearly  that  due  the  passage  of  a  gas 
through  it  under  similar  conditions  of  temperature  and  expan- 
sion ;  a  comparatively  small  quantity,  since  any  substance  in 
the  gaseous  state  possesses  low  conductivity  and  slight  power 
of  absorption  and  storage  of  heat.  Should  the  superheating 
be  in  excess  of  this  amount,  the  steam  will  not  begin  to  con- 
dense until  a  later  period,  perhaps  not  at  all ;  the  only  require- 
ment to  prevent  liquefaction  being  now  for  heat  to  supply  the 
amount  required  to  keep  the  steam  dry  and  saturated  while 
expanding  and  doing  work.  If  the  superheating  be  less  than 
the  first-mentioned  quantity,  initial  condensation  will  be  re- 
duced but  not  entirely  prevented.  It  is  probably  never  the 
fact  that  it  is  practicable  to  secure,  safely  and  economically,  so 
much  superheating  as  is  needed  to  keep  the  steam  dry  through- 


SUPERHEATING  AND  STEAM-JACKETIXG.  599 

out  the  stroke.*  In  any  case,  the  quantity  represented  by  the 
superheating  will  be  a  gauge  of  the  amelioration  of  wastes  by 
internal  transfer  of  heat  in  every  cylinder  of  the  series.  The 
steam  leaving  the  high-pressure  cylinder  will  be  to  that  extent 
drier;  and  this  will  be  true  of  the  succeeding  cylinder  or 
cylinders. 

Were  there  no  other  disappearance  of  heat  than  that  due 
to  cylinder-condensation,  superheating  at  the  first  element  of 
the  series  would  give  superheating  at  each  of  the  others.  In 
so  far  as  condensation,  such  as  was  pointed  out  by  Rankine 
and  Clausius  as  the  result  of  conversion  of  heat  into  work, 
takes  effect,  and  so  far  as  other  wastes  by  transfer  without 
transformation  occur,  to  that  extent  will  the  gain,  as  observed 
in  successive  passages  from  cylinder  to  cylinder,  be  reduced ; 
though  the  improvement  of  the  working  conditions  above  as- 
serted will  be  none  the  less  reaL  Each  cylinder  will  have  wet- 
ter steam  than  the  preceding,  in  proportion  as  the  condensa- 
tion doing  work  and  the  losses  by  conduction  and  radiation 
increase,  as  a  total,  cylinder  by  cylinder.  Superheating  at  the 
high-pressure  cylinder  will  produce  a  favorable  effect  all  through 
the  series,  including  the  low-pressure  cylinder.  Cylinder-conden- 
sation will,  nevertheless,  cumulatively  increase  throughout  the 
series,  in  consequence  of  the  fact  that  the  wetter  the  steam  enter- 
ing any  one  cylinder  the  more  the  condensation,  and  the  wetter 
that  leaving  it,  both  by  this  initial  increase  of  humidity  and 
heat-storing  power  and  by  the  additional  moisture  coming  from 
the  Rankine  and  Clausius  phenomenon,  and  from  the  loss  by 
transfer  to  surrounding  bodies.  This  last  action  will,  however, 
be  the  less  observable  and  the  less  important  in  its  effect  as 
the  moisture  of  the  entering  steam  and  the  magnitude  of  the 
waste  by  initial  condensation  become  greater.  The  more 
nearly  the  total  proportion  of  water  in  the  mixture  approaches 
one  half,  the  more  nearly  does  this  phenomenon  become  a 


*  In  one  case  reported  to  the  Author  an  initial  superheating  of  500*  F.  was 
required  togire  50'  F.  superheating  at  exhaust;  100*  F.  has  usually  been  con- 
sidered a  practical  maximum  superheat. 


600  A  MANUAL    OF    THE    STEAM-ENGINE. 

vanishing  quantity.  It  may  probably  be  neglected  entirely  in 
the  computation  of  efficiencies  for  a  large  proportion  of  the 
engines  in  use,  without  introducing  sensible  error,  and  very 
probably  may  be  neglected  in  all  cases  without  invalidating 
conclusions  reached  ignoring  it.  On  the  other  hand,  super- 
heating is  not  likely  ever  to  produce  much  effect  upon  this 
action. 

(2)  Steam-jacketing,  the  expedient  devised  by  Watt  for  the 
purpose  of  reducing  internal  wastes,  is  a  method  of  approxi- 
mately "  keeping  the  cylinder  as  hot  as  the  steam  which  enters 
it,"  as  Watt  states  it,  in  order  that  no  such  chilling  of  the  en- 
tering steam  may  occur.  Authorities  disagree  as  to  what  ex- 
tent and  in  what  manner  the  jacket  is  advantageous  in  the 
multiple-cylinder  engine.  It  is  sometimes  advised  to  jacket 
only  the  high-pressure  cylinder ;  sometimes  only  the  low-pres- 
sure, and  sometimes  the  whole  series,  whether  one,  two  or 
three  cylinders,  or  more.  The  philosophy  of  the  engine  would 
indicate  that,  to  secure  maximum  good  effect,  assuming  the 
jacket  on  the  whole  desirable  at  all,  the  best  system  is  the  lat- 
ter ;  and  that,  since  the  waste  of  the  engine  is  most  nearly 
measured  by  the  losses  of  its  most  inefficient  member,  to  omit 
the  jacket  from  any  one  cylinder  insures  that  the  aggregate 
loss  of  heat  in  the  whole  engine  will  be  increased  by  just  the 
amount  by  which  waste  is  increased  in  that  one  cylinder  by 
such  omission. 

The  question  which  actually  arises  in  practice,  for  the  de- 
signing engineer,  is  whether  it  will  pay  to  jacket  at  all,  or  not. 
It  can  be  readily  seen  that  it  is  not  as  important,  in  a  financial 
sense,  that  the  multiple-cylinder  engine  be  jacketed  as  it  is  to 
jacket  a  simple  engine  of  similar  total  range  of  expansion. 
The  value  of  the  waste  due  to  omission  of  the  jacket  is  less, 
ordinarily,  as  the  number  of  cylinders,  in  series,  is  the  greater. 
It  is  also  seen  that  those  conditions  which  may  make  it  un- 
necessary to  jacket  the  simple  cylinder  make  it  still  less  im- 
portant in  the  multiple-cylinder  engine.  As  piston-speeds  are 
increased,  for  example,  the  necessity  of  the  jacket  decreases, 
and  the  limit  at  which  it  will  pay  here  to  dispense  with  it  is 


SUPERHEATING  AND   STEAM-JACKETING.  6oi 

sooner  reached  than  in  the  single-cylinder  engine.  It  is  this 
principle  which  justifies  the  not  uncommon  practice  of  omit- 
ting jackets  from  engines  which  are  driven  up  to  200  or  300 
revolutions  or  to  1000  feet  a  minute,  or  more,  of  piston-speed ; 
while  pumping-engines,  for  example,  in  which  the  speed  is  low, 
must  usually  be  jacketed,  if  high  duty  is  demanded. 

(3)  High  engine-speed,  a  device  for  reducing  internal  wastes, 
as  well  as  decreasing  cost  of  construction  and  weight,  is  evi- 
dently a  matter  of  less  serious  importance  as  the  number  of 
cylinders  is  increased ;  yet  it  is  equally  evident  that,  to  secure 
maximum  efficiency,  it  is  essential  that  the  time  of  exposure  to 
the  action  of  the  wasteful  influences  in  each  cylinder  be  made 
a  minimum.  At  modern  and  customary  speeds  of  piston  and 
of  rotation,  the  value  of  these  several  expedients  for  improving 
performance  is  much  less  than  formerly ;  but  all  are  to  be 
adopted  where  it  is  hoped  to  secure  such  high  efficiency  as  is 
coming  to  be  demanded  of  the  designing  and  the  constructing 
engineer.  So  long  as  the  advantages  of  further  gain  in  this 
direction  are  safely  attainable  for  the  simple  engine,  they  are 
still  desirable,  and  may  prove  attainable,  in  the  multiple-cylin- 
der machine. 

Non-conducting  cylinders,  such  as  were  partly  secured  by 
Smeaton  by  the  use  of  his  wood-lined  pistons  and  heads,  and 
such  as  have  since  been  sought  by  Emery  and  others ;  such  as 
were  shown  to  be  needed  by  Watt,  and  later  more  conclusively 
by  Rankine  and  his  successors,  would  do  away  with  the  neces- 
sity of  compounding  on  the  ground  of  thermodynamic  gain ; 
but  would  leave  the  advantages  of  the  multiple-cylinder  en- 
gine, on  the  score  of  better  division  of  stresses  and  work,  un- 
affected. 

Clearances  are  usually  greater  in  the  multiple-cylinder  than 
in  the  simple  engine  ;  but  it  is  also  seen  that  the  loss  by  clear- 
ance, and  the  rejected  steam  thus  unutilized,  in  any  one  cylin- 
der, goes  to  fill  the  clearances  of  the  next ;  and  thus  the  loss 
by  this  method  of  waste  is  divided  approximately,  also,  by  the 
number  of  cylinders,  as  in  the  case  of  other  losses.  It  remains 
advisable  to  reduce  the  "  dead-spaces"  as  much  as  is  practi- 


602  A   MANUAL   OF  THE  STEAM-ENGINE. 

cable;  but  the  importance  of  this  matter  is  less  than  in  the 
case  of  the  simple  engine. 

Thus  the  adoption  of  the  multiple-cylinder  engine  reduces 
wastes  of  every  kind,  except  those  coming  of  increased  radia- 
tion from  the  exterior,  where  the  total  area  is,  commonly,  in- 
creased, and  the  loss  due  to  the  friction  of  the  engine  when 
the  number  of  cylinders  is  in  excess.  These  are,  however, 
minor  wastes. 

146.  The  Number  of  Cylinders  to  be  introduced  in  series 
is  finally  settled  by  financial  considerations.  The  fact  that  the 
loss  by  internal  wastes  is  measured  by  that  of  one  of  the  cylin- 
ders only  indicates  that,  as  a  matter  of  economy  of  heat, 
simply,  there  is  no  natural  limit  to  the  number ;  except  that 
the  losses  by  external  conduction  and  radiation  may  finally 
more  than  compensate  the  gain  by  further  complication.  This 
principle  is  easily  shown,  thus: 

The  work  performed  is  proportional  to  the  quantity 
I  -j-  log  r,  and  the  cost  of  that  work  is  proportional  to  the 

quantity  I  -j-  ar>*»,  since  the  expansion  in  one  cylinder  is  the 
nth  root  of  the  total  ratio  of  expansion  for  the  series  ;  ;;/  being 
taken  as  the  index  determined  by  the  rate  and  method  of 
variation  of  the  cylinder-condensation  with  variation  of  the 
ratio  of  expansion,  and  which  is  not  far  from  m  —  2  ;  and  a  is 
a  constant  coefficient,  not  far  from  0.2.  The  cost  of  power, 
measured  in  terms  of  steam  expended  thermodynamically  and 
by  internal  wastes,  is  a  minimum  when  the  quotient  of  the  two 
expressions, 

i  +  log  r 
i  -f-  armn 

above  is  a  maximum ;  this  is  a  maximum  when  the  denomi- 
nator is  a  minimum  ;  and  this  is  a  minimum  when  the  value  of 
n  increases,  without  limit. 

Assuming,  in  illustration,  as  the  result  of  general  experience 
in  good  practice,  that,  under  the  best  customary  conditions  of 
operation,  a  good  simple  engine,  working  at  high  pressure, 


SUPERHEATING  AND  STEAM-JACKETING.  603 

condensing,  and  at  the  best  ratio  of  expansion  for  maximum 
engine-efficiency,  may  be  fairly  expected  to  give  as  good  a 
result  as  two  pounds  of  fuel  of  satisfactory  quality  per  horse- 
power and  per  hour.  Under  similarly  favorable  conditions,  we 
may  also,  with  equal  likelihood,  anticipate  a  probability  that  we 
may  obtain  better  work  with  multiple-cylinder  engines  in  some- 
where about  the  following  proportion : 

Con-          Gain,  Gain, 

Engine.  sumption.     TotaL  Difference. 

Simple,  one  cylinder 2  Ibs.  

Compound  (double-expansion). . .    1.6  20  p.  c,  20  p.  c. 

Triple-expansion 1.4  30  10 

Quadruple-expansion 1.25  40  10 

Quintuple-expansion «  i.i  50  10 

The  figures  in  the  first  three  cases  are  based  upon  what  is 
probably  ample  experience ;  the  others  are  obtained  by  infer- 
ence from  the  rate  of  progression  thus  established,  and  upon 
the  principle,  above  enunciated,  that  the  waste  is  reduced  in 
proportion,  approximately,  to  the  number  of  cylinders  in  series. 
The  probable  first  cost  and  running  expense  of  adding  one  and 
another  cylinder  to  any  given  type  is  easily  ascertained  by  the 
engineer;  and  he  can  then,  in  such  cases,  readily  determine 
whether  the  gain  fairly  to  be  anticipated  is  sufficient  to  com- 
pensate the  cost  of  its  acquirement,  and  to  give  a  fair  margin 
of  profit. 

Another  important  inference  from  what  has  preceded  is 
that  the  question  of  use  of  one  or  another  type  of  multiple- 
cylinder  engine  is  not  primarily  settled  by  the  magnitude  of 
the  steam-pressure  to  be  adopted ;  although  it  may  be  taken 
as  settled  by  experience  and  by  the  financial  aspect  of  the 
question,  as  just  indicated,  that  it  will  not  usually  pay  to  com- 
pound a  machine  working  at  very  low  pressures ;  nor  to  adopt 
a  third  cylinder  until  the  pressure  approaches  some  four  or 
five  atmospheres;  the  advisability  of  adding  cylinder  after 
cylinder  being,  in  part,  determined  by  the  rise  in  pressure,  at 
the  rate  of  perhaps  not  more  than  one  cylinder  for  each  four 


O04  A    MANUAL   OF   THE   STEAM-ENGINE. 

or  five  atmospheres  of  pressure.  Whatever  the  pressure,  how- 
ever, compounding  will  divide  the  total  internal  thermal  loss, 
approximately,  by  the  number  of  cylinders  in  series ;  but  it 
does  not  at  all  follow  that  the  efficiency  of  engine,  or  the  com- 
mercial efficiency,  will  be  reduced  in  similar  ratio.  On  the 
contrary,  as  will  be  seen  later,  it  will  never  pay  to  carry  the 
complication  as  far  as  the  study  of  the  case  from  this  point  of 
view  would  dictate.  The  discrepancy  will  be  found  to  be  the 
greater  as  the  real  engine  more  closely  approaches  ideal  perfec- 
tion ;  the  simple  engine  becoming  the  more  desirable  type  as 
the  efficiency  of  it,  and  of  each  of  the  several  elements  of  the 
compound  engine,  becomes  greater. 

147.  As  respects  Size  of  Engine,  it  is  now  easily  seen 
that  the  gain  by  compounding  is,  so  far  as  the  considerations 
here  studied  are  concerned,  at  least,  likely  to  prove  even  more 
marked  with   small  than  with  large   engines.     As   the  wastes 
are  invariably,  under  similar  working  conditions,  greater  as  size 
decreases,  the  desirability  of  reducing  those  losses  would  seem 
likely,  ordinarily,  to  be  also  greater.     In  the  case  of  the  adapta- 
tion of  this  system  to  small  engines,  the  effect  of  cylinder- 
condensation    remains,    in    each   cylinder,   well    marked,   ordi- 
narily, as  is  seen  in  the  hitherto  unnoticed  effect  observable 
where  such  small  engines  are  constructed  of  the  Wolff  type, 
and  the  first  effect  of  the  cooling  action  of  the  metal  upon  the 
entering  steam  is  shown  by  the  sudden  drop  of  pressure  be- 
tween the  two  cylinders,  at  the  moment  of  opening  communi- 
cation ;  the  fall  being  like  that  seen  when  exhaust  occurs  into 
the  atmosphere  from  a  high  terminal  expansion,  and  amount- 
ing, often,  to  several  pounds.* 

148.  Problems  relating  to  the    relative  efficiency  of   the 
various  classes  of  multiple-cylinder  engine  may  now  be  readily 
solved,  the  needed  data  being  obtainable,  by  assuming  the  above 
enunciated  principles  to  be  applicable,  and  first  computing  the 
efficiency  of  the  representative  ideal  engine,  and  then  ascertain- 


*This  has  been  noticed  and  provided  for  by  the  designers  of  a  familiar  type 
of  single-acting  compound  engine. 


SUPERHEATING  AND  STEAM-JACKETING.  605 

ing  the  probable  wastes  of  heat,  of  power  and  of  work,  of  the 
several  cylinders,  and  of  the  engine  as  a  whole.  Obviously, 
the  computation  for  the  ideal  engine  is  the  same,  whether  the 
system  is  simple  or  complex.  The  wastes,  however,  vary  with 
each  type,  and  with  every  size  and  proportion  of  engine.  If, 
as  is  now  often  possible,  we  may  ascertain  the  approximate 
measure  of  waste  for  each  cylinder  and  for  each  engine,  what- 
ever its  type,  it  becomes  perfectly  practicable  to  determine  the 
relative  merits  of  each,  and  the  probable  efficiency  and  con- 
sumption of  heat,  of  steam,  and  of  fuel,  also,  if  the  efficiency  of 
the  boiler  is  given  or  can  be  computed.  The  difference  of 
efficiency  among  the  several  types  or  examples  indicates  the 
relative  standing  of  those  various  examples,  and  furnishes  the 
basis  for  computation  of  all  the  efficiencies. 

The  following  are  illustrations  of  approximate  solutions  of 
such  problems,  as  arising  in  common  practice  or  as  illustrated 
in  the  experiences  of  the  engineer  seeking  to  ascertain  which 
of  all  available  designs  is  the  best  for  the  special  purposes  in 
view: 

The  differences  between  the  steam-consumption  figures  of 
the  two  tables  given  in  the  preceding  chapter  for  the  ideal  and 
the  actual  efficiencies  of  simple  engines  have  been  seen  to  be 
the  measure  of  those  wastes  which  may  be  largely  reduced  by 
compounding ;  a  nearly  constant  quantity,  6  pounds  of  steam 
for  the  condensing  and  10  pounds  for  each  form  for  the  non- 
condensing  engines.  A  two-cylinder  compound  engine  should 
reduce  these  wastes  to  approximately  3  and  5  pounds,  a 
triple-expansion  to  2  and  to  3.3  pounds.  Case  No.  5,  in 
the  last  table,  using  23  pounds  of  steam  per  hour  per  horse- 
power, would,  as  a  compound  engine,  demand  20  pounds,  as  a 
triple-expansion  19  pounds,  and  as  a  quadruple-expansion 
engine  about  18.2. 

A  familiar  type  of  tandem  compound  high-speed  engine  is 
usually  operated  at  a  pressure  of  about  1 10  pounds  by  gauge, 
at  a  ratio  of  expansion  of  9  and  with  cylinders  having  the 
ratio  of  2.3  to  I.  The  following  is  the  result  of  investigation 


606  A    MANUAL   OF   THE   STEAM-ENGINE. 

of  this  case,  thermodynamically.  It  is  first  assumed  that  tl;c 
engine  is  supplied  with  steam  of  variable  pressure,  next  that 
the  pressure  is  constant  at  the  figure  intended  by  its  builders 
and  the  ratio  of  expansion  varied.  The  deductions  from  these 
studies  of  efficiency  are  that  both  the  boiler-pressure  and  the 
ratio  of  expansion  assumed  by  the  builders  are  very  nearly 
ideally  right  for  best  economy  with  that  form  of  engine.  Fur- 
ther gain  could  be  better  secured,  however,  in  this  case,  by  an 
increase  of  the  expansion  than  by  that  of  the  steam-pressure 
at  the  given  ratio  of  expansion. 

It  is  here  assumed  that  the  friction  of  engine  is  10  per 
cent,  the  efficiency  of  machine  being  90  per  cent,  and  that 
jacket-wastes  are  8  per  cent,  and  external  radiation  5  per  cent ; 
the  net  "efficiency  of  engine"  thus  becoming  about  77  per 
cent  the  thermodynamic  "  efficiency  of  steam."  The  pressure 
in  the  valve-chest  is  taken  as  0.97  that  in  the  boiler. 

It  must  be  borne  in  mind,  however,  that  the  investigation 
represents  the  ideal,  not  the  actual,  case,  and  that  the  consump- 
tion of  steam  and  fuel  and  the  real  efficiencies  will  be  some- 
what different ;  possibly  varying  from  the  computed  figures  10 
to  15  per  cent,  and  correspondingly  reducing  the  ratio  of  ex- 
pansion and  the  pressure  for  best  effect. 


HIGH-SPEED  ENGINE. 

Variation  of  Pressure, 
f,  =  4  ;     r  =  Ki  X  K*  -  9. 


Boiler  pressure  

ft 

50 

75 

IOO 

no 

120 

140 

160 

1  80 

Engine        "     

Pi 

48.5 

72.8 

97.0 

107 

116 

125 

155 

175 

Receiver     "     

A 

20.  8 

29.0 

37-2 

40.5 

43-8 

50.3 

50.9 

63-4 

Mean  total"     

Pm 

9.15 

12.8 

16.4 

17.8 

19-3 

22.1 

25-3 

27-9 

Meaneff.     "     

A 

5-15 

8.76 

12.4 

13.8 

15-3 

18.1 

21.0 

23.9 

"  Heat-pressure".  .  . 

A 

50.8 

69.0 

87.2 

94-5 

1  02 

116 

131 

155 

Effic.  of  Steam  

Et 

O.IO 

.127 

.142 

.146 

.150 

.156 

.l6l 

.163 

Effic.  of  Engine  

£. 

0.08 

.099 

.in 

.114 

.117 

.122 

.126 

.127 

"Water-rate"  

w 

17-3 

13-8 

12.5 

12.0 

ii.  8 

II.  2 

IO.g 

10.8 

SUPERHEATING  AtTD  STEAM-JACK  ETIXG.  6o/ 


*  =  106.7. 

Ezpansioa  ratio  ----  r  6  8  10  12  15  iS  21 

Receirer  pressure  .  .  f,  4*  4*  39  39  37  35  34 

Total  mean       4     ..  /.  22.4  17.9  14-  5  "-3  9-°9  6-94  5-34 

MeancffectiTe"     ../«  18.4  13.9  10.5  8.29  6.42  4.94  3.86 

"Heai-preasore'.../^  206  134  92  °7  48  36  27 

Efl&c,  oi  Steam  .....  £,  0.09  .102  .113  .120  .129  .134  .138 

"Engine  ----  £,  0.07  .000  .089  .094  .102  .105  .109 

"  Waier-raie"  ......    W  14.2  12.3  n.i  10.5  9.65  9.35  9.0 

The  actual  efficiencies  will  be  reduced  by  the  wastes  to 
considerably  smaller  figures,  as  hereafter  shown,  and  the  water- 
rate  thermodynamically  computed  will  be  increased,  in  such 
engines,  ordinarily,  by  ten  pounds,  more  or  less,  according  to 
size  and  speed  of  engine,  clearances,  and  other  variable  condi- 
tions affected  by  design,  construction,  and  operation.  With 
compound  engines,  the  added  quantity  may  be  taken,  for  en- 
gines of  considerable  power,  as  about  6  pounds  for  compounds, 
4  for  triple-expansion,  and  3  for  quadruple-expansion. 

The  compound  non-condensing  engine  is  often  employed, 
especially  where  it  is  difficult  to  secure  a  good  and  unfailing 
supply  of  condensing  water.  The  following  are  the  results  of 
the  investigation  of  this  case,  taking  the  total  absolute  press- 
ure, and  the  back-pressure  constant,  as  below,  and  assuming  a 
variable  ratio  of  expansion  within  the  limits  r  =  2  and  r  =  20. 
The  Rankine  exact  method  and  formulas  are  employed  as 
before. 

Let/,  =  180  Ibs.  per  sq.  in.,  absolute  ;  /,  =  16;  r  =  var- 
iable. 

Assume  the  available  heat  of  the  fuel  at  10.000.000  ft.-lbs.. 
and  the  evaporation  to  be  10  pounds  of  steam  per  pound  of 
coal,  as  representing  best  practice,  with  a  good  feed-water 
heater  and  dry  steam  supplied  at  the  steam-chest.  Steam 
used,  unity;  vt  =  2.315. 

Then  we  obtain,  in  the  mariner  already  indicated  : 


608  A   MANUAL   OF   THE   STEAM-ENGINE. 

NON-CONDENSING   ENGINE. 

IDEAL  CASE. 

U  —  404,330;  /i  =  180;    />a  -  16;  ^  =  140°  F.;  7*4=600°  F.;   ^,=2.315; 
/&4  =  83,459. 


4.6-? 

"•  J 

5-79 

j'jjj 
7.72 

3 
11.58 

23.15 

•a 

30.87 

46  1O 

/„ 

Q*VJ[ 

94.07 

74.12 

54.57 

35.70 

17.00 

14.50 

H*-'1  j*-> 
8.12 

77, 

357,280 

342,595 

323,977 

298,282 

255,838 

2A7    T  AA 

21  c  2S& 

Ht 

911,263 

907,385 

902,646 

896,456 

886,867 

*<\  19  x*t*f 

885,006 

•^1  D>^0° 
878,462 

U'  

47,407 

62,071 

80,6^0 

106,176 

148,515 

157,140 

188,707 

h  

.  .  . 

874,849 

885,661 

899,540 

918.945 

952,830 

958,733 

984,075 

M.  E.  P... 

71.1 

74-5 

72.6 

63-7 

44-5 

34-8 

28.3 

h  (rej.)-  •  •  - 

827,442 

823,590 

818,890 

812,861 

804,315 

801,593 

795,308 

Effic.  St.  p. 

c.. 

5-42 

7.01 

8.96 

"•5 

15-4 

16.4 

19.2 

Fuel  per  H. 

P. 

per  hour 

3.65 

2.81 

2.21 

1.72 

1.28 

1.  20 

IO.2 

Steam   per 

H. 

P.  per  hour. 

36.5 

28.1 

22.1 

17.2 

12.8 

12.0 

1.02 

REAL  CASE. 


Assume  steam-wastes  approximately  constant  at  6  Ibs. ; 
engine-friction  to  demand  3  Ibs.  steam  in  excess  of  that  com- 
puted. 


Indicated  Power. 


Steam    .  .  . 

42.5 

J.*t*                                                            —  •fc7  — 
34.1                      28.1                          23.2 

18.8 

18.0 

16.2 

Dynamometric  Power. 

Fuel 

4.52 

3.71           3-H             2.62 

2.18 

2.10 

1.92 

.      45.2 

37.1           31.  1             26.2 

21.8 

21.  0 

IQ.2 

As  another  interesting  case,  assume  a  boiler-pressure, 
/>!  =  250,  absolute,  and  back-pressures  of  16  and  5  pounds, 
respectively,  for  the  non-condensing  and  the  condensing  en- 
gine, feed-water  temperatures  203°  and  104°  F.,  jacketed 
engines  of  such  size  and  speed  as  to  give  internal  wastes 
approximating  0.075  \/r,  due  to  the  action  of  the  exhaust- 


SUPERHEATING  AND   STEAM-JACKETING.  609 

period.  Take  Rankine's  system  of  computation  for  the  jack- 
eted engine  as  the  probably  best  approximation.  Take  the 
evaporation  at  10  and  9  pounds  for  the  two  cases,  respectively. 
Determine  the  variation  of  efficiency  with  varying  expansion. 

In  this  case,  it  will  be  seen  that  the  variation  of  coal-con- 
sumption will  differ  from  that  of  steam,  in  consequence  of  the 
fact  that  a  part  of  the  heat  supplied  the  engine  enters  by  way 
of  the  jacket,  and,  when  condensed,  this  portion  of  the  steam 
simply  flows  back  to  the  boiler  —  if  the  drain-pipes  are  properly 
arranged  —  and  does  not  enter  into  the  measure  of  feed-water 
supply  ;  though  the  heat  which  it  conveys  comes  from  the  fuel, 
as  really  as  does  that  transferred  by  the  steam  entering  the  cyl- 
inder. The  fuel  may  thus  be  divided  into  two  parts  :  that  sup- 
plying heat  to  the  entering  steam  ;  and  that  giving  heat  to  the 
jacket.  The  measure  of  the  heat  supplied  by  the  jacket  may  be 
obtained  by  deducting  from  the  total  computed  heat-supply 
that  required  to  furnish  the  steam  entering  the  cylinder  with 
its  initial  store.  This  gives  us 


The  weight  of  water  and  of  steam  worked  in  the  cylinder 
is.  per  H.  P.  per  hour, 

W=  1,980,000-=-  If  ', 

where  V  is  the  work  performed  by  one  pound  of  steam.  The 
division  of  this  quantity  by  the  rate  of  evaporation  gives  the 
weight  of  fuel.  It  will  be  observed,  on  examining  the  tabu- 
lated results  of  such  computations,  that  the  minimum  water- 
rate  does  not  correspond,  precisely,  to  the  maximum  efficiency; 
a  consequence  of  the  steady  circulation  of  the  jacket-steam 
and  water.  The  minimum  coal-consumption,  on  the  other 
hand,  does  correspond  exactly  with  the  best  efficiency;  as 
it  should.  The  following  are  the  data  and  results  of  com- 
putation : 


6lO  A   MANUAL   OF   THE   STEAM-ENGINE. 


STEAM-ENGINE  EFFICIENCY:   IDEAL  AND  ACTUAL. 
NON-CONDENSING  ENGINE. 


/i  =250;     vi 
...         5 

=  1.84;    / 
8 

3  =  16;     Ui 

Ideal  Case. 
10 

=  420,280; 
15 

*«  =  132, 
20 

g.2 

14.7 

18.4 

27.6 

36.8 

ff 

.  .    875   141 

897,647 

908,357 

927,296 

940,694 

Ay.. 

Ef 

77,890 

o  1671 

100,396 
.1794 

111,106 
.1821 

130,045 
.1793 

143,443 

.1-20 

W.. 

13-54 
1.35 

12.29 
1.23 

11.96 
i.  20 

11.91 
1.19 

12.24 
1.22 

Ft 

o.  14 

0.16 

0.17 

0.19 

0.22 

p 

1.39 

1.37 

1.38 

1.44 

5 

8 

Real  Case. 

10 

15 

20 

i+< 

Ee 

t  fr..     1.17 
.   ...    0.143 

1.  21 

.148 

1.24 

.147 

1.29 
.139 

1-34 
.129 

W 

it  82 

14  90 

14  80 

15.37 

16.34 

F... 

1.74 

1.68 

1.69 

1.78 

1-93 

CONDENSING  ENGINE. 

/  =  250;    v,  =  1.84;    /a  =  5;     U\  =  420,280;    A4  =  55,612. 
Ideal  Case. 


r.  .  • 

v*.  .  , 

5 
9.20 
.  .  951  889 

IO 

18.40 

985  105 

20 

36.8 
1,017,442 

30 

55-2 
1,036,  144 

40 
73-6 
1,049  °J8 

50 
92.0 
i  059  080 

hi 

143  443 

162  145 

185  081 

Ef  . 
W 

0.169 

12  32 

.198 

.216 

.221 

8  66 

.220 

8  =H 

.216 

8  fa 

F,  . 
Ff 

1-37 
12 

I.OO 
17 

.96 

•_95 

.96 

F  , 

1.27 

I  17 

I  13 

5 

Real  Case. 
20 

Ee.. 

W  .. 
F... 

tV~r..  I-  17 
145 
H.38 
.   1.74 

1.24 
.160 
12.58 
1.57 

1-34 
.162 

12.01 

1.41 
.156 
12.36 
i.  60 

1.47 
.149 
12.66 
i.  60 

1-52 
.141 

13.24 

1.70 

The  above  corresponds  to  the  case  of  an  engine  of  perhaps 
one  thousand  horse-power,  working  under  favorable  conditions  ; 


SUPERHEATING  AND   STEAM-JACKETING.  6l  I 

a  simple  engine,  well  jacketed,  and  supplied  with  dry  or  slightl} 
superheated  steam.  With  effective  superheating  and  at  the 
best  expansion  ratios,  the  wastes  have  been  actually  brought 
down,  as  reported  on  trials  made  by  engineers  of  reputation,  to 
an  additional  four  pounds  of  steam  and  half  pound  of  fuel,  and 
with  considerably  lower  pressures  ;  or,  for  the  best  cases  to- 
date,  the  performance  has  been  made  to  approximate  within 
thirty  or  forty  per  cent  of  the  ideal  minimum. 

All  these  cases,  however,  fail  to  represent  modern  practice  ; 
since  they  do  not  assume  a  sufficient  expansion  to  give  best 
results  when  compounded.  The  benefits  of  the  multiple-cyl- 
inder type  are  best  seen  with  extreme  ratios  of  expansion, 
where  internal  wastes  would  prove  excessive  in  the  simple 
engine. 

149.  As  Examples  of  coming  problems,  and  as  better  illus- 
trations of  advanced  practice,  take  a  quadruple,  compared  with 
a  triple-expansion,  engine  at  a  pressure  of  200  pounds  per  square 
inch,  absolute,  with  a  back-pressure  of  8  pounds  and  a  total 
ratio  of  expansion  of  16,  or  of  2.5*  in  the  one  case  and  of  2*  in 
the  other.  The  condenser  is  worked  at  a  temperature  of  1 50° 
F.,  in  both  cases,  the  feed  being  at  145°  F.  The  friction  of 
engine  is  taken  in  both  at  15  per  cent,  the  efficiency  of  machine 
being  0.85.  The  boiler  evaporates  nine  pounds  of  water  per 
pound  of  coal.  The  engines  are  jacketed  efficiently,  and  of 
such  proportions  that  the  waste  may  be  fairly  taken  to  be 

probably  measured  approximately  by  the   factor   c  =  -~  V~r 

=  0.15  V~r  =  0.15  l7^  for  the  one  case  and  c  =  0.15  ^~2  in 
the  other,  or  24  and  21  per  cent,  for  the  three-  and  the  four- 
cylinder  engines,  respectively.  For  a  single  engine,  of  similar 
character,  in  this  respect,  it  would  be  £  =  0.15  VT6  =  0.60, 
nearly. 

Adopting  the  method  and  formulas  already  employed,  we 
obtain  the  following  results : 

For  the  ideal  case,  which  would  give  the  same  figures  for 
both  engines,  we  find  the  following,  the  slight  discrepancies 


6l2 


A    MANUAL   OF   THE   STEAM-ENGINE. 


being  due  to  the  corresponding  difference  in  total  expansion, 
taking  the  one  to  work  at  a  ratio  of  2.5  for  each  cylinder,  and 
the  other  at  2  : 

IDEAL  MULTIPLE-CYLINDER  ENGINE  EFFICIENCIES. 


Engine. 

No. 
Cylinder. 

E. 

B.  T.  H. 
per  I.  H.  P. 

Water  per 
I.  H.  P. 

Coal  per 
I.  H.  P. 

1 

Triple  

Total 

I 
2 

3 

.0811 
.0730 
.0779 
.231 

11761 

10.85 

I.-JC 

Quadruple. 
Total 

i 

2 

3 
4 

.0637 
.0598 
.0580 
.0598 
2414 

11577 

10.68 

The  consumption  of  water  and  of  fuel  is  thus  seen  to  be  ex- 
extremely  low,  as  compared  with  the  actual  performance  of  the 
preceding  cases  of  simple  engines  at  lower  pressures.  Adding 
the  prescribed  allowances  for  internal  wastes,  we  have : 

EFFICIENCIES  OF  REAL  ENGINES. 


Engine. 

Water  per 
I.  H.  P. 

Coal  per 
I.  H.  P. 

Ideal 

Simple 

Triple 

I*   4 

r3  ! 

I  4 

Had  these  engines  been  unjacketed,  assuming  waste  greater 
by  one  third  in  the  actual  and  unchanged  in  the  ideal  case,  we 
might  probably  have  obtained  the  following  : 

UNJACKETED  REAL  ENGINES. 


Engine. 

Water  per 
I.  H.  P. 

Coal  per 
I.  H.  P. 

Ideal                .... 

I    2 

Simple  

2    2 

1.6 

13  8 

1.5 

SUPERHEATING  AND   STEAM-JACKETING.  613 

The  gain  by  increasing  complication  thus  decreases  as  the 
number  of  cylinders  increases,  whatever  the  rate  of  internal 
waste. 

Going  into  higher  and  unaccustomed  pressures,  it  may  be 
interesting  to  endeavor  to  compute  the  probable  performance 
of  a  well-designed  quintuple-expansion  engine,  working  at  a 
pressure  of  500  pounds  per  square  inch.  The  ratio  of  expan- 
sion is  taken  at  r  =  2.3*  =  64.4,  the  back-pressure  at  five 
pounds.  These  results  may  be  compared  profitably  with  the 
case  of  the  simple  engine  discussed  in  Chapter  V,  §  137,  in 
which  somewhat  similar  data  are  taken.  Assume  data  thus: 

QUINTUPLE-EXPANSION   ENGINE. 

Data: 

pi  —  500  X  144  =  7!>ooo  Ibs.  per  sq.  ft. 
A  =  5  X  144  =  720. 
r  =  2.3s  =  64.4. 

Results : 

/,  =  862.2  Ibs.  per  sq.  ft.,  6  Ibs.  per  sq.  in. 

Heat  expended  per  lb.,  H  —  27,324  ft.  Ibs.  =  1898  B.  T.  U. 

77- 

pt  =  -jf  =  4464  Ibs.  per  sq.  ft.,  31  Ibs.  per  sq.  in. 

'* 
ph  =  17,330  Ibs.  per  sq.  ft,  120.3  Ibs.  per  sq.  in. 

Efficiency  of  fluid,  E  =%=  0.2576. 
Pk 

B.  T.  U.  per  I.  H.  P.  per  hr.  =  10,189. 

Steam  per  I.  H.  P.  per  hr.,  at  1 100  units  per  lb.,  =  9.32  Ibs. 

Coal  per  I.  H.  P.  per  hr.,  at  9  Ibs.  evap.,  =  1.03 ;  say  i  lb. 

For  this  case,  therefore,  the  weights  of  steam  and  of  fuel, 
for  unity  efficiency,  would  be  approximately  2.4  pounds,  and 
about  0.3  pound  per  horse-power  per  hour.  Were  the  internal 
wastes  to  be  taken  as  in  the  first  part  of  this  discussion,  as  indi- 
cated by  experiments  the  rereferred  to,  we  should  have  the  fol- 
lowing, assuming  the  losses  to  be  reduced  in  proportion  to  the 
number  of  cylinders  employed,  and  the  efficiency  of  mechan- 


6i4 


A   MANUAL    OF   THE   STEAM-ENGINE. 


ism  to  be  0.95  for  the  simple  engine ;  0.90,  0.90,  0.85,  and  o.8s 
for  the  compounded  engine  in  the  five  cases  given,  respectively : 

EFFICIENCIES  OF  MULTIPLE-CYLINDER  ENGINE. 


Engine. 

Water  per 
I.  H.  P  . 

Fuel  per 
I.  H.  P. 

E.  E. 

Water  per 
D.P.H. 

Fuel  per 
D.  H.  P. 

Pounds. 
9.32 

Pounds. 
I 

I 

Pounds. 
9.32 

Po  nds. 

Simple  jacketed  
Double-expansion  

20.5 
14.9 
13.0 

2.2 
1.6 

95 
90 

GO 

21.4 
16.5 
15.0 

-4 

.8 
.7 

euadruple-expansion  .  . 
uintuple-expansion  .  . 

12.  1 
II.  6 

1-34 
1.24 

ss 

85 

14.4 

13-6 

.6 

•  5 

The  above  is  sufficient  to  give  a  fair  idea,  assuming  the 
figures  satisfactorily  approximate  for  the  conditions  assumed, 
of  the  advances  to  be  anticipated  through  the  use  of  higher 
pressures  and  ratios  of  expansion,  and  with  saturated  steam. 
These  figures  may  be  further  decreased  by  increasing  boiler- 
efHciency,  by  superheating  the  steam,  and  by  other  methods 
of  improvement. 

150.  The  General  Results  of  Experience  and  of  experi- 
ment accord,  very  satisfactorily,  in  cases  of  good  design  and 
construction  and  of  good  management,  with  the  deductions 
and  computations  which  have  now  been  presented. 

Differences  of  type  produce  differences  of  performance, 
however,  that  sometimes  modify  the  general  conclusions  which 
have  been  stated,  to  an  observable  extent.  Thus  the  conclu- 
sions of  Hallauer,  after  comparing  the  performance  of  the 
simple  Corliss  engine,  with  its  efficient  valve-gear  and  small 
clearance-spaces,  with  the  ordinary  Woolf  compound,  both 
working  at  about  5  atmospheres  pressure,  were  that  the  one 
was  substantially  equal  to  the  other ;  although  the  ratio  of  ex- 
pansion of  the  latter  was  comparatively  large,  and  both  at  their 
best  working  ratios.*  This  fact  is  probably  quite  as  much  due 
to  the  comparatively  small  port-spaces  and  clearances,  and  the 
separated  steam  and  exhaust  ports  of  the  Corliss  engine,  as  to 
any  other  cause. 


Trans.  Soc.  Indust.  de  Mulhouse;  1878. 


SUPERHEATING  AND  STEAM-JACKETING.  615 

A  notable  difference  between  the  conditions  dictating  the 
design  and  construction  of  the  locomotive  and  the  marine  en- 
gine  is  observed  in  these  facts :  the  former  must  be  proper, 
tioned  and  built  to  meet  a  great  range  of  resistance  and  speed ; 
as  it  must,  on  a  level,  haul  at  high  velocity  against  low  resist- 
ance ;  on  a  steep  gradient,  it  must  pull  heavily  at  low  speed. 
It  may  at  one  time  haul  light  passenger  trains,  at  another 
handle  a  heavy  and  slow  merchandise  traffic.  The  latter,  on 
the  other  hand,  has  a  steady  load  and  practically  constant 
speed,  under  ordinary  conditions  of  operation.  The  locomotive 
is  given  large  cylinders  to  meet  the  exigencies  of  heavy  loads, 
and  a  link  valve-gear  to  give  high  expansion  and  compression 
ratios  under  the  opposite  conditions.  This  is  not  as  essential 
with  the  marine  engine;  with  which, since  the  power  demanded 
varies  as  the  cube  of  the  speed,  the  variation  of  velocity  is  usu- 
ally moderate.  These  differences  favor  the  use  of  the  multiple- 
cylinder  engine  at  sea  more  than  on  land,  notwithstanding  the 
fact  that  it  is  less  affected  than  the  older  type  by  variations 
from  the  normal  load.  The  necessity  of  proportioning  the 
locomotive  for  its  maximum  pull  and  the  comparatively  con- 
stant liability  to  enormous  variations  of  load  and  speed,  its 
short  periods  of  working  and  frequent  stops,  and  its  exposed 
cylinders  and  exaggerated  wastes,  are  all  conditions  telling 
against  this  engine. 

Experience  at  sea  indicates  that  a  good  double-cylinder, 
compound,  engine,  with  steam  at  100  pounds  by  gauge  (7  at- 
mos.,  nearly)  should  not  demand  more  than  2.2  pounds  (l  kg.) 
of  fuel  of  good  quality  per  horse-power  per  hour;  a  triple- 
expansion  engine  1.8  pounds  (0.8  kg.)  ;  and  a  quadruple-expan- 
sion engine  1.5  pounds  (0.7  kg.);  the  steam-pressures  and  ratios 
of  expansion  adopted  being  appropriate  to  each. 

The  very  considerable  economy  to  be  noted  in  such  com- 
parisons is  not  usually  wholly  attributable  to  differences  in  de- 
sign and  construction  of  engine.  The  greater  steam-pressure 
and  resultant  higher  ratio  of  expansion  adopted  with  the  later 
engines  is  generally,  in  part,  the  cause  of  the  observed  gain. 
But  the  simple  engine  could  not  be  economically  worked  with 


610  A   MANUAL   OF   THE  STEAM-ENGINE. 

as  high  a  ratio  of  expansion  at  such  pressures  as  the  compound 
engine,  and  the  latter  thus  possesses  a  decided  advantage ; 
which  advantage  is,  as  is  now  known,  due  to  its  better  ar- 
rangement for  checking  exhaust-wastes. 

Trials  of  agricultural  engines,  made  by  Sir  Frederick  Bram- 
well  and  Mr.  Anderson,*  indicate  that  the  efficiency  of  machine 
may  be  as  high  in  compound  as  in  simple  engines,  and  give  for 
the  value  of  this  factor  from  0.75  to  0.94,  the  common  values 
approximating  0.85,  the  steam  consumed  being  about  33 
pounds  per  dynamometric  horse-power  and  per  hour  in  the 
best  simple  engines,  and  22  in  the  better  class  of  small  com- 
pound engines;  the  corresponding  coal-consumption  being 
nearly  3  and  2  pounds,  respectively.  The  total  friction  of  en- 
gine was  thus  about  15  per  cent  of  the  total  power,  or  3  Ho  P. 
on  a  2O-H.  P.  engine. 

On  the  steamer  Suez,  the  replacement  of  two-cylinder  com- 
pound by  quadruple-expansion  engines  was  reported,  "with 
the  same  kind  of  coal,  the  same  revolutions,  the  same  speed  of 
ship,  and  the  same  propeller,"  to  have  reduced  the  fuel-con- 
sumption 34  per  cent.  The  steam-pressure  was  raised,  how- 
ever, to  above  150  pounds.f 

An  experience  extending  over  three  years,  according  to 
Mr.  R.  Wylie,  with  steamers  having  compound  and  triple- 
expansion  engines  gave  a  marked  difference  in  favor  of  the 
latter,  the  former  using  nearly  14  tons  a  day,  the  latter  loj; 
the  former  averaging  2.16  pounds  of  fuel  per  horse-power  and 
per  hour,  the  latter  1.414 

The  quadruple-expansion  engines  of  the  steamship  Singa- 
pore were  reported,  in  1890,  to  have  demanded  but  1.122 
pounds  of  best  navigation  coals  per  hour,  per  I.  H.  P. 

The  compound  pumping-engine  designed  by  Mr.  Corliss,  in 
1879,  f°r  tne  Pawtucket  (R.  I.)  water-works,  a  small  engine  of 
but  15  and  30  inches  diameter  of  cylinders  and  30  inches  stroke 


*  Jour.  Royal  Agricult.  Soc.  of  England;  vol.  xnu    1887. 
f  London  Engineer;  Feb.  24,  1888;  p.  162, 
t  Trans.  Brit.  Inst.  M.  E.;  1886. 


SUPERHEATING  AXD   STEAM-JACKETING.  6l/ 

of  piston,  was  reported,  in  the  year  1889, to  nave  given,  for  the 
year,  an  average  duty  of  124,500,000  foot-pounds  for  100  pounds 
of  fuel  consumed,  on  an  evaporation  of  approximately  9  pounds 
of  water  per  pound  of  fuel,  or  13.7  pounds  of  steam  and  of 
feed-water,  and  1.5  pounds  of  coal,  per  horse-power  per  hour 
for  the  whole  year.*  This  extraordinary,  probably  unexampled, 
result  is  presumably  due  to  the  high  steam-pressure  (125  pounds 
by  gauge) :  the  choice  of  the  most  economical  ratio  of  expan- 
sion (18)  for  that  case ;  continuous  steady  work  against  a  high 
head ;  unusually  high  speed  for  a  pumping-engine  (50  revolu- 
tions per  minute),  and  remarkably  good  proportions  and  con- 
struction. In  this  engine,  heads  as  well  as  sides  of  both  engines 
are  jacketed ;  but  with  apparently  small  practical  advantage, 
either  because  of  its  speed,  its  employment  of  superheated 
steam  or  of  an  actual  defect  in  jacketing. 

An  examination  of  records  of  trials  of  60  engines  in  various 
parts  of  the  world,  and  under  a  great  variety  of  conditions, 
and  for  periods  averaging  about  five  months,  gives  an  average 
gain  of  1 8£  per  cent,  in  comparing  the  compound  locomotive 
with  the  simple  engine.f  Trials  in  the  United  States,  on  the 
E.  Tennessee,  Va.,  and  Ga.  Railway,  resulted  in  the  reporting 
of  a  gain  of  1.6  pounds  fuel  per  train-mile,  or  of  19  per  cent, 
for  standard  engines,  and  of  4  pounds  per  mile,  or  31  per  cent, 
for  lo-wheel  engines  by  compounding.*  Mr.  Urquhart  reports 
a  gain  of  i8±  per  cent  in  liquid  fuel  during  the  year  1890  and 
on  a  million  of  miles  run. 

The  economy  of  the  multiple-cylinder  engine  is  thus  seen 
to  be  mainly  due  to  the  cascade-like  action  of  the  machine,  in 
its  disposition  of  the  heat-wastes  in  such  manner  that,  with  a 
given  total  range  of  expansion,  the  total  internal  waste  is  re- 
duced approximately  in  proportion  to  the  number  in  series : 
but  it  also  is,  in  part,  a  consequence  of  the  fact  that  the  total 
condensing  power  is,  or  may  be,  less  than  that  of  the  single 

*  Annual  Report. 

\  Compound  Locomotives;  A.  T.  Woods;  Jour.  Assoc.  Eng.  Societies;  Maj 
1890. 

\  Railway  Review;  1890. 


6l8  A    MANUAL    OF   THE   STEAM-ENGINE. 

cylinder  that  might  displace  it.  Comparing  the  condensing 
power  of  a  triple-expansion  and  of  a  compound  engine,  for 
example,  with  that  of  the  corresponding  simple  engine,  as 
measured  by  the  product  of  range  of  temperature  in  each 
cylinder  by  its  cooling  surface,  it  will  be  found,  as  shown  by 
M.  Demoulin,*  that  the  ratios  of  the  sums  of  these  products 
for  each  engine  is  not  far  from  65,  75,  and  100,  respectively, 
for  usual  practice;  the  reciprocals  of  which  ratios,  1.3,  1.33, 
and  i,  nearly,  measure  rather  closely  the  commonly  stated 
ratios  of  relative  economy. 

Assuming  a  steam-pressure  of  approximately  127  pounds 
per  square  inch  by  gauge,  a  ratio  of  expansion  of  10  and  a 
back-pressure  of  4  pounds,  M.  Demoulin*  compares,  in  this  re- 
spect, the  simple,  the  two-cylinder  compound,  and  the  "  triple- 
expansion"  engines.  These  have  diameters,  respectively,  of  I 
metre,  of  om.75  and  im.5,  and  of  om.6i,  om.g6,  and  im.5  ;  and 
lengths  of  stroke,  of  im.5  for  the  first  and  I  metre  for  the 
others. 

Multiplying  the  ranges  of  temperature  in  each  cylinder  by 
the  total  areas  of  cylinder  exposed  to  steam,  their  products  are 
compared  and  the  triple-expansion  engine  shown  thus  to  pos- 
sess an  advantage  of  15  per  cent  over  the  double  and  34  per 
cent  over  the  simple  engine.f 

The  work  of  the  compound  engine  illustrates  a  feature  of 
the  more  economical  types  of  that  engine  which  is  especially 
valuable  when  the  load  is  not  fixed  and  appropriate  to  the 
machine.  Thus,  in  the  figure,  we  have  the  method  of  variation 
of  economy  with  varying  ratios  of  expansion  with  three  types 
of  single-acting  engine.  It  is  seen  that  the  efficiency  of  the 
compound  is  comparatively  unaffected  within  any  usual  range 
of  variation  of  load. 

In  the  figure  the  upper  curve  represents  the  efficiency  of  the 
non-compound  engine  under  variable  loads.  Many  tests  have 


*  Machines  a  Vapeur;  Paris,  1890;  p.  6. 

f  Etude  sur  les  Machines  Compound  a  Triple  Expansion;  Paris,  Baudry  & 
Cie.;  1885. 


SUPERHEATING  AND   STEAM-JACKETING. 


619 


determined  the  two  corresponding  curves  for  the  compound 
engine,  both  with  and  without  vacuum. 

This  peculiarity  of  the  more  economical  type  of  engine 
makes  it  the  more  desirable  where  varying  resistance  is  to  be 
encountered. 

As  a  general  result  of  experience,  it  may  be  concluded  that, 
for  the  average  case,  with  good  engines  of  the  several  classes : 

(i)  The  volume  of  steam  shown  by  the  indicator,  when 
superheated,  or  thoroughly  dry,  steam  is  used  in  well-jacketed 
compound  engines,  of  moderate  size,  is  nearly  the  same  as 


FIG.  155. — ECOK 


computed  for  a  similar  ideal  engine,  both  at  cut-off  and  at  the 
end  of  stroke.  The  actual  excess  may  be  taken  as  not  above 
fifteen  per  cent  by  weight  at  the  first  and  ten  per  cent  at  the 
second  point,  if  we  follow  Hirn,  in  such  cases  as  were  studied 
by  him. 

(2)  Ordinary,  nearly  dry,  steam — i.e.,   not  containing  five 
per  cent  moisture — worked  in    jacketed  simple  engines,  may 
usually  be  expected  to  exhibit  an   excess  at  least   one  half 
greater  than  in  the  preceding  cases,  for  good  average  practice. 

(3)  Moderately  wet  steam  in  any  jacketed  engine,  or  dry 


02O  A   MANUAL   OF   THE   STEAM-ENGINE. 

steam  in  an  unjacketed  engine  of  any  considerable  size,  may  be 
expected  to  exhibit  a  waste  of  the  kind  here  considered  increas- 
ing rapidly  with  the  ratio  of  expansion,  and  often  double  in 
amount  that  observed  in  the  first  case,  above,  in  even  good 
practice. 

(4)  Wet  steam,  in  small  and  unjacketed  engines,  especially 
if  worked  at  low  speeds,  may  be  expected  to  be  condensed  to 
such  an  extent  as  to  give  rise  to  expenditures  of  heat,  steam, 
and  fuel  enormously  in  excess  of,  often  several  times  greater 
than,  those  computed  for  the  similar  ideal  case. 

(5)  The  advantages  of  thus  placing  cylinders  in  series  is 
less  as  wastes  are  less  in  the  simple  engines,  as  costs  are  less, 
and,   in    more   detail,  as  the   steam  is   drier,  expansion   less, 
speeds  of  engine  higher,  and  as  power  demanded  is  greater ; 
and  the  number  in  series  is  less  for  best  effect,  in  all  cases,  as 
the  performance  of  the  actual  engine  approaches  more  nearly 
that  computed  for  the  ideal. 

151.  The  Balance  of  Forces  at  the  main  shaft,  in  the 
multiple-cylinder  engine,  may  often  prove  a  matter  >>f  real  con- 
sequence. Mr.  John  Elder,  in  1866,  stated  that  it  was  perfectly 
possible  that  a  saving  of  10  per  cent  and  more  of  the  indicated 
power  might  be  wasted  in  an  engine  by  avoidable  friction  at  the 
shaft.*  He  ascribed  much  of  the  advantage  of  "compounding" 
to  the  division  of  the  work  of  the  engine  and  to  the  better  con- 
sequent  adjustment  of  pressures  on  the  shaft  and  pins.  A 
three-cylinder  engine,  with  its  cranks  at  angles  of  120°,  may  be 
made  to  work  with  almost  a  balance  of  thrusts  and  pulls  at  the 
shaft.  A  double-cylinder  compound  engine,  with  cranks  set 
opposite,  is  also  thus  advantageous;  and,  in  both,  the  maximum 
pressures  become  a  fraction  of  those  in  the  simple  engine. 

The  comparison  of  three  similar  British  naval  vessels,  the 
Arethusa,  the  Octavia,  and  the  Constance,  fitted,  respectively, 
with  a  pair  of  simple,  trunk,  engines,  with  cranks  at  45°,  a  set 
of  three  single  cylinders  with  cranks  at  120°,  and  a  three-cylin- 
der "compound  "  engine,  in  1865,  running  from  Plymouth  to 


Rankine's  Life  of  Elder;  1871. 


SUPERHEATING  AND   STEAM-JACKETING.  021 

Funchal,  resulted  in  giving,  as  the  fuel-consumption,  3.64,  3.17, 
and  2.51  pounds  per  horse-power  per  hour;  while  the  last  two 
ships  are  reported  to  have  shown  a  relative  efficiency  of  mech- 
anism of  100  to  127;  or  of  79  to  100.*  This  difference  was 
slightly  lessened  as  speeds  and  power  increased.  The  last- 
described  disposition  of  the  engine  also  conduces  to  smooth- 
ness of  motion  and  to  regularity  in  crank-pin  pressures  and 
turning  moments. 

Variations  of  pressure  on  the  running  parts  of  the  engine, 
due  to  extreme  ranges  of  expansion,  in  the  simple  engine,  may 
sometimes,  and  especially  in  marine  engines,  prove  objection- 
able, and  thus  to  constitute  another  argument  in  favor  of  the 
use  of  the  multiple-cylinder  engine.  The  steamers  Polynesia 
and  Circassian,  of  the  Allan  Line,  were  originally  fitted  out,  the 
one  with  compound,  the  other  with  simple,  engines.  In  all 
other  respects  they  were  alike.  They  were  so  designed  that 
the  same  expansion  could  be  adopted  in  both.  The  result  was 
that  the  simple  engine  was  badly  shaken  and  injured,  the  ma- 
chinery was  removed,  and  engines  similar  to  those  of  the  Poly- 
nesia were  put  in,  with  thoroughly  satisfactory  results.f 

The  extent  to  which  the  stresses  and  strains  due  to  high- 
pressure  steam  are  relieved  by  "  compounding  "  the  engine  may 
be  readily  seen  by  computing  these  quantities  for  parallel 
cases.  It  will  be  found  that  the  simple  engine  is  subject  to 
double  stress  when  expanding  10  to  12  times,  as  when  working 
at  a  ratio  of  expansion  of  3!  to  4,  and  must  be  correspondingly 
heavier  and  stronger.  In  multiple-cylinder  engines,  the  total 
stresses  may  be  made  substantially  equal  in  each,  and  the  range 
of  pressure  reduced,  and  the  strains  as  well,  in  similar  propor- 
tion. A  condensing  triple-expansion  engine,  at  ten  atmospheres 
pressure  (150  Ibs.)  by  gauge,  would  be  subject  to  about  one 
fifth  the  stresses,  on  each  piston  and  its  connections,  that 
would  come  upon  the  piston  of  its  large  cylinder,  if  all  the 
work  were  done  within  it,  or  in  a  simple  engine  of  the  same 
size. 

*  Rankine's  Life  of  Elder;  p.  44- 

f  King:  Report  on  European  Ships  of  War;  1877. 


622  A    MANUAL   OF   THE  STEAM-ENGINE. 

This  reduction  of  loads  is  so  considerable  that  it  is  actually 
possible,  at  high  pressures,  to  save  weight  of  engine  by  com- 
pounding. At  very  low  pressure  the  simple  engine  has  the  ad- 
vantage, both  in  weight  and  efficiency. 

From  the  constructors'  point  of  view,  "compounding"  the 
steam-engine  often  becomes,  with  the  now  usual  boiler-press- 
ures, a  matter  of  vital  importance ;  since  it  would  be  imprac- 
ticable to  successfully  work  the  simple  engine  under  those 
pressures,  and  with  the  enormous  variations  of  pressure  due  to 
a  high  ratio  of  expansion.  To  do  so  would  compel  the  adop- 
tion of  such  size  and  weight  of  parts,  and  such  special  propor- 
tions of  journals,  as  would  make  the  engine  excessively  heavy 
and  costly,  while  at  the  same  time  causing  great  loss  of  engine- 
power  through  the  friction  of  its  own  parts. 

152.  Steam-jackets  on  Engines,  whether  simple  or  other, 
have  one  and  the  same  main  purpose,  in  every  case  and  on 
every  type — the  reduction  of  internal  wastes  due  to  initial  con- 
densation. In  the  older  Worthington  direct-acting  type,  and 
perhaps  in  other  pumping-engines,  the  use  of  the  jacket  may 
bring  an  incidental  advantage  of  some  practical  value,  enabling, 
as  it  does  in  this  case,  the  stroke  to  be  completed  at  a  higher 
ratio  of  expansion  than  it  could  otherwise  be,  a  result  of  the 
higher  terminal  pressures  produced  by  it,  and  of  prevention  of 
water  in  the  cylinders. 

A  special  reason  for  the  use  of  the  jacket  on  engines  liable, 
as  is  the  Cornish  pumping-engine,  or  to  a  certain  extent  in 
marine  engines,  for  example,  to  be  stopped  occasionally  for  in- 
tervals of  greater  or  less  length  and  to  be  started  up  again  at 
a  moment's  notice,  is  that  the  cylinder  can  be  kept  heated,  the 
engine  "warmed  up,"  however  long  the  stop,  and  thus  kept  in 
condition  for  immediate  starting,  without  danger  or  delay. 
The  jacket  also,  incidentally,  is  useful  in  keeping  the  bore  of 
the  cylinder  unstrained,  if  properly  constructed.  This  is  con- 
sidered so  important  that,  in  some  cases,  the  "liner"  is  inserted 
only  after  the  engine  is  set  up  in  place. 

As  is  well  known,  the  use  of  the  steam-jacket  was  original 
with  Watt,  who  remarks,  in  a  letter  to  Professor  Jardine,  that. 


SUPERHEATING  AND  STEAM-JACKETING.  623 

after  his  experiments  on  the  Newcomen  model,  his  next,  and 
an  easy,  step  was  "  to  inquire  what  was  the  cause  of  the  great 
consumption  of  fuel.  This,  too,  was  readily-  suggested:  viz.,  the 
waste  of  fuel  which  was  necessary  to  bring  the  whole  cylinder, 
piston,  and  adjacent  parts,  from  the  coldness  of  water  to  the 
heat  of  the  steam  no  fewer  than  15  or  20  times  a  minute."  * 

He  invented,  first  the  separate  condenser,  then  the  st^.-jn- 
jacket,  in  order  "  to  keep  the  steam-cylinder  as  hot  as  the 
steam  which  entered  it."  The  cause  of  the  great  internal 
waste  detected  by  Watt  is  now  well  known  and  has  been  de- 
scribed as  cylinder,  or  internal,  or  initial  condensation. 

Combes,  in  papers  presented  to  and  published  by  the  Aca- 
demic des  Sciences,  was  probably  the  first  to  introduce  into  the 
theory  of  the  steam-engine  the  consideration  of  that  phenome- 
non, discovered  by  Watt,  to  check  the  wasteful  effects  of  which 
the  latter  invented  the  steam-jacket.f  That  author  gradually 
gave  shape  to  his  ideas,  as  time  went  on,  publishing  them  in 
1845.*  and,  later,  in  i863~67.§  He  says  in  his  first  paper,  just 
mentioned :  "  The  utility  of  the  jacket,  or  rather  that  of  heat- 
ing the  cylinders  of  steam-engines  from  the  outside,  ...  is 
rendered  unquestionable,  both  by  direct  experiment  and  by 
detailed  observation  of  the  phenomena  characterizing  the  action 
of  steam  in  the  cylinder,  and  the  logical  discussion  of  these  ob- 
servations." "  Jackets  have  not  for  their  main  result  the  main- 
tenance of  the  temperature  of  the  steam  during  expansion  ; 
their  use  consists  in  the  prevention  of  refrigeration  of  the  walls 
of  the  cylinder  while  in  communication  with  the  condenser :" 
probably  the  first  exact  statement  of  this  effect  ever  printed.  [ 

Mr.  Gill,  as  early  as  1844,  says :  "  If  the  cylinder  be  supplied 
with  dry  steam,  and  no  heat  is  dissipated  by  radiation,  there 
will  still  be  a  loss  of  heat  in  the  cylinder  occasioned  by  the 
sudden  expansion  of  the  steam  when  the  communication  with 

*  History  of  the  Steam-engine;  Thorston;  p.  S3. 

t  Comptes  Rendos;  1843. 

£  Traitfe  d'exploration  des  Mines. 

§  Priocipes  de  .'a  Tbeorie  Mecankme  de  la  Cbalenr. 

|  Memoirs  of  1*43;  P-  *45- 


624  A    MANUAL   OF   THE   STEAM-ENGINE. 

the  condenser  is  opened.  ...  As  the  heat  for  evaporation  is 
furnished  by  the  hot  metal  of  the  cylinder,  piston,  etc.,  such 
heat  must  be  returned  to  them  by  the  condensation  of  steam 
during  the  succeeding  stroke,  such  condensation  and  evapora- 
tion going  on  until  an  equilibrium  is  established."  He  sug- 
gests superheating  as  the  best  remedy.* 

Hirn  published  his  Mtf moire  sur  /'  Utility  des  Enveloppes  it 
Vapeur  in  1855.!  This  memorable  paper  gives  us  the  first 
analysis  of  experiments  showing  the  quantitative  measures  of 
the  thermal  action  of  the  walls  of  the  steam-cylinder.  He 
concludes : 

"  (i)  There  is  a  capital  difference  between  the  thermal  phe- 
nomena characterizing  two  types  of  engine  :  In  the  simple  en- 
gine, the  cylinder-walls  always  yield  heat  to  the  steam  during 
expansion  ;  though  the  amount  is  less  when  the  jacket  is  work- 
ing than  when  shut  off.  In  the  Wolff  engine,  the  surfaces  of 
the  cylinder  take  heat  from  the  steam,  even  during  the  expan- 
sion, and  lose  it  again  during  the  exhaust." 

"  (2)  With  the  simple  engine  the  walls  of  the  cylinder  give 
to  the  steam  the  same  amount  of  heat  with  as  without  the 
jacket ;  but,  in  the  former  case,  the  heat  is  given  up  during  the 
expansion,  and  thus,  without  cost,  adds  considerably  to  the 
amount  of  work  done ;  while,  without  the  jacket,  this  heat  is 
all  lost  by  being  thrown  into  the  condenser  without  doing  any 
work,  uselessly  evaporating  the  condensed  water,  mainly  after 
the  exhaust-valve  has  opened." 

As  explained  by  many  recent  writers,  the  benefit  of  the 
jacket  comes  of  the  facts  that  it  not  only  reduces  initial  con- 
densation but  insures  that  a  part,  at  least,  of  such  heat-waste 
as  does  take  place  shall  occur  through  condensation  within  the 
jacket,  where  it  does  no  additional  harm,  instead  of  in  the  cyl- 
inder, where  it  would  produce,  indirectly,  wastes  out  of  all  pro- 
portion to  its  own  amount.  It  is  by  allowing  the  surfaces  of  the 
cylinder  exposed  to  the  entering  steam  to  become  as  hot,  ap- 
proximately, as  the  steam  itself,  and  nearly  or  quite  dry,  so  as 

*  Improvements  of  the  steam-engine;  Weale's  paper;  Jan.  1844. 

f  Bulletin  de  la  Societe  Industrielle  de  Mulhouse;  t.  xxvn.  pp.  105-206. 


SUPERHEATING  AND  STEAM-JACKETIXG.  625 

to  largely  check,  if  not  to  prevent,  initial  condensation,  that  the 
steam-jacket  gives  its  economic  advantage. 

As  has  been  well  stated  by  Holmes :  •*  A  jacket  operates  in 
two  ways,  in  keeping  the  temperature  of  the  cylinder-walls 
constant :  first,  by  keeping  the  working  steam  comparatively 
dry,  it  reduces  the  power  of  the  sides  of  receiving  heat  from, 
and  of  giving  it  out  to,  the  former,  and  thus  deprives  the  sides 
of  the  power  of  taking  up  the  extremes  of  temperature  which 
would  otherwise  be  possible ;  and,  second,  whatever  differences 
of  temperature  would  actually  occur  are  further  greatly  re- 
duced by  the  flow  of  the  heat  from  the  jacket-steam  to  the 
inner  walls  of  the  cylinder.  It  is  only  the  heat  supplied  in  the 
latter  process  which  costs  the  jacket-steam  anything.  The 
great  gain  due  to  the  rendering  of  the  working  steam  non-con- 
ducting  and  non-radiating  costs  nothing  whatever ;  seeing  that 
it  is  an  indirect  effect  of  keeping  the  sides  hot.  Thus,  the 
steam-jacket,  though  for  half  the  time  warming  the  exhaust, 
has  proven  in  the  majority  of  cases  to  be  an  undoubted  source 
of  economy."  * 

The  operation  of  the  jacket  may  thus  be  defined  to  be  that 
of  improving  the  working  fluid,  converting  a  defective  into  an 
efficient,  changing  a  heat-absorbing  into  a  non-absorbing  ma- 
terial, a  wet  into  a  dry  vapor,  or  into  a  gas,  more  or  less  com- 
pletely. 

Thus  the  quantity  of  heat  and  steam  lost  in  the  jacket  is 
not,  as  often  assumed  and  stated,  precisely  the  equivalent  of 
the  amount  which  would,  without  it,  be  wasted  inside  the  cylin- 
der. The  real  effect  of  the  jacket  is  to  present  a  compara- 
tively hot  and  dry  internal  surface  to  the  entering  working 
steam,  and  thus  to  prevent  any  condensation  of  that  steam  at 
its  admission,  and  corresponding  re-evaporation  during  exhaust. 
The  transfer  of  heat  by  internal  conduction  is  thus  made  to 
take  effect  between  dry  surfaces  and  through  a  comparatively 
dry  medium  with  the  result  of  greatly  reducing  the  quantity 
so  transferred  and,  to  the  extent  of  that  reduction,  adding  to 

*  The  Steam-engine;  1887;  p.  451. 


626  A   MANUAL   OF   THE  STEAM-ENGINE. 

the  efficiency  of  the  engine.  The  jacket  wastes,  if  it  is  one  of 
high  efficiency,  only  the  quantity  of  heat  needed  to  preserve 
the  working  steam  in  the  "  dry  and  saturated  "  condition. 

The  jacket  thus  acts  usefully  in  two  distinct  ways  :  (i)  by 
preventing  exchange  of  heat  between  the  steam  and  the  cylin- 
der-walls, by  keeping  the  steam  more  nearly  gaseous ;  (2)  by 
reduction  of  the  range  of  temperature  occurring  within  those 
metallic  masses,  and  of  their  tendency  to  initiate  and  continue 
the  waste. 

Throughout  the  whole  cycle  of  the  engine,  however,  the 
jacket  is  either  transferring  heat  through  the  sides  of  the 
cylinder  to  the  steam,  or  is  compensating  a  previous  loss  by 
storing  heat  in  the  metal  composing  the  inner  layers  of  cylin- 
der, piston,  and  heads ;  constantly  draining  heat  into  the 
engine  from  the  boiler,  and  all  the  time  wasting  it ;  either  by 
transfer  without  transformation,  or  by  transformation  within 
a  smaller  range  of  temperature  than  the  maximum.  It  is  a 
wasteful  device  for  preventing  or  ameliorating  a  greater  waste. 

When  this  latter  is  a  larger  loss  than  that  due  to  the  jacket 
itself,  a  gain  occurs;  when  the  internal  wastes  are  otherwise 
reduced  to  the  magnitude  of  minimum  jacket-waste,  that 
accessory  has  no  value;  whenever,  as  by  superheating,  or 
other  device  or  combination  of  expedients,  the  interior  wastes 
are  made  less  than  the  normal  waste  due  the  jacket  itself,  the 
latter  can  have  no  useful  effect ;  and  finally,  an  inefficient,  or  an 
exceptionally  wasteful,  jacket  may  possibly  prove  absolutely 
hurtful.  This  has  been  observed,  for  example,  in  some  re 
ported  cases  of  locomotive  performance,  and  in  cases  which, 
perhaps,  the  heat  wasted  from  it  during  the  terminal  portion 
of  the  expansion-period  and  during  the  exhaust-stage  is  more 
than  the  equivalent  of  the  earlier  gain  by  reduced  initial  con- 
densation and  during  expansion.  This  last  effect  may  be  a 
consequence  of  excessive  wetness  of  steam,  causing  the  pres- 
ence of  water  in  its  mass  up  to  and  beyond  the  termination  of 
the  expansion-line. 

The  action  of  an  effective  jacket,  notwithstanding  its  pro- 
duction of  a  drain  of  heat  into  the  cylinder,  results  in  greatly 


SUPERHEATING  AND   STEAM-JACKETING.  62J 

accelerating  the  re-evaporation,  and  in  its  completion  at  so 
early  a  period  in  the  stroke  as  to  accomplish  two  results :  (i) 
the  conversion  of  the  water  from  this  condensation  into  effec- 
tive working  fluid  ;  (2)  the  drying  and  warming  of  the  walls  of 
the  cylinder  so  completely,  before  the  succeeding  admission, 
as  to  make  the  heat-absorption  and  the  consequent  initial  con- 
densation minima.  The  net  result  is  usually  a  gain  by  reduc- 
tion of  interior  wastes ;  and  the  exterior  losses,  although 
exaggerated  by  the  increased  areas  of  surface  exposed,  remain 
insignificant  when  the  cylinder  is  properly  clothed. 

153.  The  Action  of  the  Jacket,  in  Detail,  is  probably 
not  complicated ;  but  it  is  obscure  because  of  the  facts  that  it 
is  so  far  out  of  reach  of  the  investigator  that  the  variations 
of  temperature  and  in  heat-storage  and  transfer  affect  variable 
quantities  of  metal  and  fluid  which  the  engineer  cannot  easily 
measure,  and  are  subject  to  intricate  and  uncertain  physical 
changes  of  condition  and  quality  of  the  mixture  of  steam  and 
water,  or  possibly,  at  times,  of  dry  and  superheated  steam, 
similarly  difficult  of  determination. 

We  will  examine  several  typical  cases  (see  §  122,  Fig.  140, 

P-473): 

(i)  Jacket  and  cylinder  receive  gaseous  steam;  i.e.,  the  fluid  is 
highly  superheated  and  behaves  like  a  gas. 

In  this  case  the  action  of  the  jacket  tends  to  keep  the  inner 
walls  of  the  cylinder  up  to  its  own  temperature.  Assume  this 
possible.  The  gaseous  steam  enters  the  cylinder  at  maximum 
temperature,  expands,  doing  work,  constantly  losing  both  heat 
and  temperature,  down  to  a  minimum,  at  exhaust,  and  is 
finally  discharged,  it  may  be  assumed,  dry  but  saturated. 
Each  entering  charge  finds  the  inner  surface  of  the  cylinder 
slightly  cooler  than  itself,  before  expansion  begins,  but  absorbs 
its  heat  continually,  once  expansion  has  begun,  up  to  the  close 
of  the  exhaust-period.  This  heat  is  partly  utilized  by  conver- 
sion into  work,  but  within  a  reduced  range  of  temperature 
and  with  reduced  efficiency,  and  is  in  part  discharged  as  pure 
waste.  But  the  total  quantity  so  absorbed  will  be  small,  since 
the  fluid  has  small  specific  heat,  large  specific  volume,  and 
insensible  conductivity. 


628  A    MANUAL   OF  THE  STEAM-ENGINE. 

Precisely  what  the  internal  waste  would  be  under  such  con- 
ditions  is  not  precisely  known;  but  experience  with  gas-engines 
and  with  superheated  steam  would  indicate  that  it  would  not 
usually  be  ten  per  cent  in  large  engines,  and  probably  not  be 
less  than  five  for  what  might  be  taken  as  fair  examples. 

We  may  perhaps  call  eight  per  cent  the  normal  waste  due 
to  the  action  of  the  jacket,  and  the  minimum  to  be  anticipated 
with  the  best  possible  jacketing.  The  gain  by  the  use  of 
a  jacket  is  approximately  the  difference  between  this  and  the 
waste  of  the  same  cylinder  without  the  jacket.  Experience 
indicates  this  to  be,  usually,  in  such  cases,  a  very  small  quantity, 
and  often  inappreciable. 

(2)  Jackets  and  cylinders  receive  dry  steam.  In  this  case,  the 
jacket  readily  keeps  the  external  surface  of  the  cylinder-walls 
at  maximum  temperature,  that  of  the  steam  itself,  and  due  its 
pressure.  The  slightest  reduction  of  temperature  at  once  pro- 
duces condensation  in  the  jacket,  and  the  temperature  of  the 
cylinder-surface  next  the  jacket  is  restored  by  absorption  and 
storage  of  the  latent  heat  of  the  jacket-steam  so  condensed. 
This  process  of  transfer  by  condensation  is  known  to  be  one  of 
such  great  rapidity  that  we  are  justified  in  assuming  that  the 
surface  of  the  cylinder  which  is  exposed  to  jacket-steam  is  kept 
up  fully  to  the  temperature  of  the  latter  throughout  the  whole 
cycle. 

Consider  the  four  phases  of  the  engine-cycle :  (i)  induction; 
(2)  expansion  ;  (3)  exhaust ;  (4)  compression.  During  the  first, 
the  steam  has  the  same  temperature  and  pressure  on  both  in- 
terior and  exterior  of  the  cylinder-walls ;  during  the  second 
period,  differences  of  temperature  and  pressure  on  the  two  sur- 
faces are  observed,  progressively  increasing  to  the  end  of  the 
expansion  and  the  establishment  of  the  back-pressure  ;  during 
the  exhaust,  this  difference  remains  nearly  constant  and  a 
maximum;  while  the  compression-period  sees  this  difference 
once  more  reduced,  we  will  assume,  to  zero.  Thus  both 
"prime"  steam  and  jacket-steam  at  first  unite  in  restoring  to 
the  metal  heat  lost  during  the  preceding  cycle,  and  none  passes 
from  the  jacket  into  the  interior  of  the  cylinder.  Jacket-heat 


SUPERHEATING  AND   STEAM-JACKETING.  629 

flows  into  the  engine  throughout  the  remainder  of  the  cycle, 
and  is  partly  converted  into  work,  partly  transferred  and  wasted 
as  heat ;  and  the  proportion  of  these  two  quantities,  the  partial 
waste  by  inefficient  transformation  and  the  pure  waste,  is  de- 
termined both  by  the  extent  to  which  expansion  is  carried  and 
by  the  quality  of  the  working  fluid.* 

If  the  steam  be  dry  or  nearly  so,  at  the  close  of  the  first 
period,  and  if  the  second,  the  expansion-period,  is  sufficiently 
prolonged,  the  action  of  the  jacket  and  the  heat-storing  prop- 
erty of  the  metal  of  the  cylinder  promptly  results  in  superheat- 
ing the  expanding  steam  and  so  checking  further  waste  of  heat 
from  jacket,  and  from  cylinder-walls,  during  the  terminal  period 
of  expansion  and  during  the  exhaust,  and  thus  allows  the  jacket 
to  raise  the  temperature  of  the  cylinder  promptly  and  fully  to 
that  of  the  entering  steam.  This  being  accomplished,  initial 
condensation  is,  in  turn,  reduced  to  an  unimportant  quantity ; 
the  total  waste  is  mainly  jacket-waste,  and  is  a  minimum. 

•  On  the  other  hand,  if  the  amount  of  water  produced,  either 
by  initial  condensation  or  by  the  work  of  expansion,  or  both,  is 
so  great  that  it  cannot  be  all  re-evaporated  early  in  the  stroke, 
and  if  the  cooling  of  the  cylinder-walls  is  thus  continued,  the 
jacket-waste  becomes  increased,  the  waste  which  it  is  intended 
to  check  may  remain  serious,  and  the  result  may  be  a  consider- 
able net  loss  and  but  little  or  no  advantage  from  the  jacket. 

This  must  be  the  result,  probably,  to  a  greater  or  less  ex- 
tent, whenever  the  drying  of  the  cylinder  and  steam  is  not 
nearly  or  quite  completed  at  the  opening  of  the  exhaust-valve, 
as  when  the  jacket  is  defective  or  the  steam  too  wet.  It  would 
seem  possible  that  intermediate  conditions  might  prove  to  be 
those  of  best  jacket-action. 

The  process  is  here,  probably,  one  in  which  the  first  effect 
of  the  jacket,  during  expansion,  is  to  dry  the  steam  which  con- 
tains, always,  if  not  superheated,  suspended  within  its  mass, 
more  or  less  of  the  water  of  initial  condensation ;  next  the 

*  The  resistance  to  transfer  of  heat  from  the  metal  into  a  gas  is  30  or  40 

times  as  great  as  to  water. 


630  A    MANUAL    OF   THE    STEAM-ENGINE. 

checking  of  condensation  due  to  the  work  of  expansion,  and 
finally  the  superheating  of  the  steam,  if  the  earlier  stages  are 
completed  early  enough,  and  existing  conditions  permit.  The 
first  portion  of  this  process  gives  a  gain  of  work  by  adding 
steam  to  that  existing,  as  such,  at  the  beginning  of  expansion ; 
the  latter  portion  by  giving  the  steam  larger  work-power.  The 
whole  operation  is  a  waste  of  a  smaller,  to  gain  by  reducing  the 
waste  of  a  larger,  quantity  of  heat-energy. 

During  the  exhaust-period  there  is  a  pure  waste  of  heat 
with  a  compensating  gain  by  drying  and  heating  the  interior 
surfaces  of  the  cylinder  preparatory  to  the  entrance  of  the  next 
charge  of  steam.  Compression  has  a  similar  effect,  as  a  result 
of  the  conversion  of  the  work  of  compression  into  heat. 

During  the  engine-cycle,  the  metal  is  first  drenched  by  the 
water  of  condensation,  which  gives  it  heat  from  the  entering 
steam,  then  cooled  by  evaporation  and  lowering  of  tempera- 
ture during  expansion,  and  then  it  is  dried  off,  and  is  finally 
warmed  up,  more  or  less  nearly  to  the  temperature  of  the 
prime  steam,  by  the  combined  action  of  the  jacket  and  com- 
pression. 

(3)  Wet  steam  is  supplied.  In  this  case,  the  jacket,  on  its 
side,  acts  precisely  as  before.  The  water  in  the  steam  in  the 
jacket  drains  out  or  is  trapped  off,  and  is  returned  to  the  boiler, 
leaving  the  steam  practically  dry,  as  before.  But  the  interior 
of  the  engine  is  placed  under  quite  different  conditions : 

In  addition  to  the  heat  demanded  of  the  jacket  to  keep  the 
working  steam  dry,  and  to  first  dry  off  and  then  warm  up  the 
interior  surfaces  of  the  cylinder,  a  quantity  of  heat,  which, 
within  limits,  will  be  larger  as  the  steam  is  initially  wetter,  and 
which  may  be  often  very  great,  is  drawn  from  the  metal  and 
from  the  jacket,  throughout  substantially  the  whole  cycle,  to 
evaporate  all  or  a  part  of  the  entrained  water,  and  to  then,  if 
possible,  dry  off  the  metal  and  to  heat  it  up  again  to  the  maxi- 
mum temperature.  Not  only  is  this  amount  of  heat  increased 
with  increase  in  quantity  of  water  entering  with  the  steam  ;  but 
the  proportion  of  heat  drained  off  wastefully  in  the  terminal 
portion  of  the  expansion,  and  throughout  the  exhaust-period, 


SUPERHEATING  AND  STEAM-JACKETING.  631 

is  continually  increased  as  the  quantity  of  water  to  be  evapo 
rated  is  greater ;  so  that  it  may  readily  be  believed  that  the 
interior  of  the  cylinder,  drenched  and  flooded  with  water  at 
the  opening  of  the  steam-valve,  may  continue  to  act  as  a 
waste-producing  boiler  quite  through  the  cycle ;  thus  causing 
an  enormous  loss  during  the  exhaust-period,  when,  the  differ- 
ence of  temperature  being  a  maximum,  the  heat  which  the 
jacket  is  capable  of  thus  wasting  becomes  itself  a  maximum 
and  both  absolutely  and  relatively  very  large. 

If  the  water  of  initial  condensation  is  not,  in  any  instance, 
all  re-evaporated  during  the  expansion-period,  it  will  be  re- 
converted into  steam  during  the  exhaust-period. 

It  is  thus  obvious  that  the  quality  of  the  boiler-steam  is  a 
vitally  important  matter ;  and  it  may  be  easily  seen  that  dry 
steam  is  an  essential  element  of  successful  action  of  the  jacket. 
It  may  perhaps  even  be  possible,  under  specially  unfavorable 
conditions  in  this  respect,  that  a  jacket  may  do  more  harm  by 
loss  of  heat  during  this  wasteful  period  than  it  can  save  by  its 
legitimate  action  earlier  in  the  cycle.  It  is  as  unquestionably 
the  fact  that  dry  steam  is  essential  to  the  best  action  of  the 
jacket,  as  that  superheated  steam,  as  shown  later,  may  render 
the  jacket  unnecessary  and  useless. 

It  is  uncertainty  as  to  the  condition  of  the  steam  supplied, 
and  the  probability  that  it  may  have  been  both  wet  and  vari- 
able in  its  humidity,  that  makes  it  difficult  to  secure  safe  and 
jeliable  deductions  from  many  experiments  hitherto  made  on 
jacketed  engines.  It  is  impossible  to  base  on  data  obtained  in 
such  cases  any  useful  computations. 

M.  Him  concludes,  from  observations  made  by  him  on  en- 
gines with  and  without  jackets,  that  the  action  of  the  walls  of 
the  cylinder  can  only  affect  the  working  mixture  of  steam  and 
water  either  in  actual  contact  or  in  close  juxtaposition  with 
them.  This  conclusion  is  confirmed  by  the  computations  and 
experiments  of  Cotterill  and  of  Dixwell,  and  of  many  other 
authorities. 

Under  ordinarily  favorable  circumstances,  and  in  ordinary 
practice,  as  M.  Dwelshauvers-Dery  remarks:  "If  the  jacket  be 


632  A   MANUAL   OF   THE   STEAM-ENGINE. 

applied  to  a  single  cylinder,  it  gives  up  little  heat,  although  the 
effect  produced  is  very  considerable  ;  for  the  larger  part  of  the 
heat  given  up  by  the  walls,  and  employed  in  useful  work  during 
expansion,  is  that  already  imparted  by  the  steam  to  the  metal 
during  admission.  In  a  compound  engine,  on  the  other  hand, 
the  heat  given  up  by  the  steam  in  the  jacket  increases  the  work 
performed  during  expansion."* 

We  find,  thus,  that  the  jacket  may  produce  economy  by 
simply  preventing  external  losses  from  the  working  barrel,  giv- 
ing absolutely  no  heat  to  the  steam,  but  simply  preventing  its 
losing  as  much  as  it  otherwise  would,  at  the  critical  instants,  by 
transfer  to  the  metal  of  the  cylinder.  It  is  easy  to  see  that  the 
use  of  the  jacket  is  ordinarily  advantageous  by  preventing 
transfer  of  heat  to  the  metal  of  the  cylinder  during  admission, 
and  that  the  function  of  the  jacket  is  usually  substantially 
completed  at  the  close  of  this  period,  and,  consequently,  that 
the  engine  of  large  diameter  and  small  stroke,  a  given  volume 
being  assumed,  and  with  jacketed  heads,  has,  ideally  at  least, 
an  advantage.  In  general,  the  greater  the  area  of  wetted  sur- 
faces, and  the  wetter  those  surfaces,  the  greater  is  the  waste 
and  the  more  is  a  jacket  needed  ;  but,  possibly,  also,  the  nearer 
may  be  the  limit  beyond  which  the  jacket  ceases  to  be  advan- 
tageous. 

154.  Jacket-wastes  and  Cylinder-wastes,  in  the  sense 
in  which  the  latter  term  has  come  to  be  understood,  must  evi- 
dently be  carefully  distinguished.  In  an  engine  without  the 
jacket,  it  is  obvious  that  the  latter  form  of  loss  has  no  limit,  up 
to  that  set  by  the  complete  raising  of  the  whole  mass  of  metal 
exposed  to  prime  steam  up  to  the  temperature  of  the  latter, 
with  subsequent  equally  complete  rejection  and  waste  of  this 
store  of  energy,  down  to  the  temperature  of  exhaust  and  back- 
pressure ;  except  as  the  limit  is  determined  by  conductivity  of 
metal  and  fluid  and  by  restriction  of  the  period  of  action.  Ex- 
perience proves,  however,  that  high  speed  of  engine,  by  reduc- 
ing the  time  allowed  for  alternate  absorption  and  rejection  of 

*  Lond.  Eng'g;  Dec.  13,  1889;  p.  692. 


SUPERHEATING  AND   STEAM-JACKETING.  633 

heat  by  the  metal,  and  by  making  the  quantity  of  steam  passed 
through  the  engine  greater  relatively  to  this  waste,  may,  in 
large  engines,  especially,  reduce  it,  as  a  percentage  of  heat  sup- 
plied,  to  a  comparatively  small  amount. 

Jacket-wastes,  on  the  other  hand,  are  determined  by  the 
mean  difference  of  temperature  between  jacket  and  cylinder 
and  by  the  quality  of  the  working  fluid.  In  the  same  engine, 
they  may  be  great  with  large  expansion  and  small  with  late  cut- 
off ;  or  large  with  wet  steam  and  insignificant  with  effective 
superheating.  But  they  can  never  become  zero ;  nor  can  a 
jacketed  engine  ever  be  entirely  free  from  waste  internally  by 
complete  suppression  of  these  two  forms ;  both  will  always 
have  sensible  value,  and  probably  considerable  magnitude. 

The  economy  of  steam-jacketing  is  evidently  the  difference 
between  the  total  intrinsic  cylinder-wastes  without  the  jacket 
and  those  wastes  with  it,  reduced  by  the  amount  of  the  jacket- 
waste  proper.  Since  no  heat  can  pass  from  jacket  to  cylinder- 
steam  during  the  steam-stroke,  up  to  the  point  of  cut-off,  and 
since  all  heat  supplied  later  is  either  partly  or  wholly  wasted,  it 
is  obvious  that  the  net  loss  is  a  minimum,  and  the  gain  by  the 
use  of  the  jacket  is  a  maximum,  when,  later,  it  dries  off  and 
brings  the  temperature  of  the  interior  of  the  cylinder  up  to  that 
of  initial  steam  with  most  promptness,  completeness,  and  cer- 
tainty. 

The  total  jacket-waste  is  easily  determined,  and  is,  for  many 
cases,  well  known,  being  obtained  simply  by  measuring  the 
water  draining  from  the  jacket,  and  deducting  from  the  total 
heat  which  it  represents  that  wasted  externally  by  conduction 
and  radiation,  a  quantity  of  small  amount  and  easy  of  approxi- 
mate computation,  if  not  determinable  by  direct  experiment. 

It  is  obvious  that  a  steam-jacket  will  be  useful  or  injurious, 
more  or  less,  accordingly  as  it  wastes  less  or  more  heat — by  the 
drain  constantly  going  on,  into,  and  through  the  engine,  to  the 
condenser  or  the  atmosphere — than  it  saves  by  reducing  the 
normal  internal  wastes  of  the  unjacketed  engine.  It  may,  at 
one  or  another  period,  in  the  cycle  of  the  engine,  thus  effect  a 
net  saving  or  a  net  loss ;  or  it  may  produce  no  sensible  effect ; 


634  A   MANUAL   OF   THE   STEAM-ENGINE, 

and  the  total  net  result  may  be  either  a  positive,  a  negative,  or 
a  doubtful  gain.  Any  case  in  which,  through  the  use  in  it  of 
exhaust  steam  or  steam  of  too  low  pressure,  or  in  consequence 
of  malconstruction  or  misuse,  the  jacket,  on  the  whole,  acts  as 
a  refrigerator,  will  give  a  negative  and  wasteful  net  result. 

Could  a  perfectly  efficient  jacket  be  made,  in  the  sense  of 
being  capable  of  instantly  and  fully  supplying  any  demand, 
however  sudden  or  great,  for  heat  needed  at  the  beginning  of 
the  stroke,  on  the  interior  of  the  engine,  and  could  the  steam 
be  supplied  perfectly  dry  initially,  the  vapor  would  remain  per- 
fectly dry  throughout  the  stroke  ;  none  would  be  condensed  at 
the  beginning,  to  be  re-evaporated  later,  at  the  expense  of  heat 
from  the  jacket ;  and  the  cost  would  be  only  that  of  the  com- 
paratively small  normal  heat-waste  of  a  dry  gas ;  while  a  saving 
would  be  effected  of  substantially  all  the  initial  condensation 
that  would  otherwise  have  occurred,  and  at  insignificant  ex- 
pense. 

Under  such  conditions,  the  more  readily  the  jacket  surren- 
ders heat,  the  less  the  amount  it  is  called  upon  to  yield,  and  to 
waste.  This  was  first  seen  and  proved  by  Hirn. 

The  weight  of  steam  condensed  in  the  jackets  is  a  very 
variable  quantity.  It  obviously  may  be  taken  as  a  measure  of 
the  efficiency  of  jacket-action  ;  but  it  may  nevertheless  be  the 
fact  that  highest  efficiency  of  jacket-action  may  not  insure 
maximum  efficiency  of  engine,  as  it  may,  especially  with  wet 
steam,  induce  excessive  wastes  during  the  exhaust-period. 
The  amount  of  this  condensation  is  variable  between  very  wide 
limits.  The  Pawtucket  Pumping-engine  gives  but  five  per 
cent.  In  Professor  Unwin's  report  on  the  Worthington  "  High- 
duty"  Engine  he  gives  the  jacket-water  as  15  to  20  per  cent  of 
the  total  ;*  in  the  Lawrence  and  Lynn  engines  of  Mr.  Leavitt's 
design,  it  amounted  to  about  16  per  cent ;  f  in  Donkin  &  Co.'s 
engine  at  the  Eichburg  paper-mill  it  was  10  per  cent,:}:  and 


*  Lond.  Eng'g;  Dec.  7,  1888;  p.  566. 

f  Eng'g  and  Mining  Jour.;  Nov.  25,  1871. 

\  Zeitschrift  des  Vereins  Deutscher  Ing. ;  Apr.  1869. 


SUPERHEATING  AND   STEAM-JACKETING.  635 

about  the  same  on  the  London  Gas  Works,*  on  expenditures  for 
these  several  engines  of  17,  14.4,  16.8,  22.2,  and  25  pounds  of 
water  per  horse-power  per  hour. 

The  minimum  jacket-drainage  reported  by  investigators  is 
below  ten  per  cent  and  its  lowest  value  may  be  perhaps  safely 
assumed  at  about  five  per  cent ;  which  may  be  taken  as  the 
jacket-waste  proper.  With  perfectly  dry  steam,  it  has  been 
known  to  be  less  than  five  per  cent.  By  the  expenditure  of 
five  to  fifteen  per  cent  in  this  direction,  therefore,  a  reduction 
of  cylinder-condensation  from  twenty  to  forty  per  cent  down  to 
perhaps  ten  or  less  may  be  sometimes  effected ;  and  this  net 
gain  of  ten  to  twenty-five  per  cent  then  constitutes  the  advan- 
tage of  jacketing  in  such  cases  as  the  above. 

With  the  introduction  of  other  methods  of  reduction  of  the 
second  form  of  loss,  the  relative  value  of  the  jacket,  and  the 
return  for  its  expenditure  and  waste  become  less,  and,  with 
high  engine-speed  and  compounding,  or  superheating,  the  gain 
may  become  insignificant ;  a  deduction  amply  confirmed  by 
experience. 

In  the  development  of  the  thermodynamic  theory  of  the 
steam-engine  (1859),  Rankine  assumes  "that  the  steam  in  the 
cylinder,  while  expanding,  receives  just  enough  of  heat  from  the 
steam  in  the  jacket  to  prevent  any  appreciable  part  of  it  from  con- 
densing, without  superheating  it."  This  assumption  is  founded 
on  the  fact  that  dry  steam  is  a  bad  conductor  of  heat  as  com- 
pared with  liquid  water,  or  with  cloudy  steam,  and  that  after 
cloudy  steam  has  received  enough  of  heat  to  make  it  dry,  or 
nearly  dry,  it  will  receive  additional  heat  very  slowly.  The 
assumption  is  justified  by  the  fact  that  its  results  are  confirmed 
by  experiment.t  Rankine's  assumption,  as  is  now  well  under- 
stood, involves  the  further  assumption  that  the  jacket  is  pre- 
liminarily effective  in  preventing  initial  condensation.  His 
theory  of  the  jacketed  engine  thus  becomes  the  theory  of  a 
dry,  saturated,  steam  engine. 


*  Lond.  Eng'g;  Feb.  i,  1878. 
f  Steam-engine;  §  287,  p.  396. 


636  A    MANUAL    OF   THE   STEAM-ENGINE. 

155.  Computations  of  Efficiency  of  jacketed  engines  and 
of  jacket-waste  may  be  made  which  are  fairly  approximate  for 
good  examples  of  actual  practice.  From  what  has  preceded,  it 
is  seen  that  the  ideal  engine  with  non-conducting  cylinder,  free> 
as  it  is,  from  internal  wastes,  must  have  higher  efficiency  than 
the  ideal  jacketed  engine  which  is  subject  to  pure  jacket-waste, 
but  not  to  the  second  method  of  internal  loss ;  while  the  real 
engine,  with  its  combined  jacket-  and  cylinder-wastes,  reduced 
by  the  jacket,  as  the  latter  are,  to  a  minimum  amount,  is  more 
wasteful  than  either  of  the  preceding,  but  is  more  efficient  than 
the  same  real  engine  would  be  without  a  jacket.  In  the  ideal 
cases,  jacketing  results  in  loss ;  in  actual  cases,  it  commonly 
produces  gain.  Could  we  approximate  in  real  engines  to  the 
ideal  conditions,  we  might  lose,  rather  than  gain,  by  the  action 
of  the  jacket;  should  the  jacket  actually  waste  during  exhaust 
more  than  it  saves  on  the  steam-stroke,  it  might  also,  in  ineffi- 
cient engines,  even,  produce  loss.  It  gives  maximum  gain  under 
intermediate  conditions  and  when  its  own  waste  is  a  minimum, 
while  its  activity  in  reducing  other  loss  is  a  maximum. 

The  following  results  of  computation  illustrate  these  deduc- 
tions. The  methods  and  formulas  adopted  are  the  same  as 
those  previously  presented.  In  all  cases,  the  real,  not  the  ap- 
parent, ratio  of  expansion,  is  assumed,  and  no  allowance  is 
made  for  compression. 

COMPARISON  OF  THE  EFFICIENCY  OF  IDEAL  JACKETED  AND 
UNJACKETED   CYLINDERS. 

The   approximate  formulas    are    here    used,  having   been 
proved  sufficiently  accurate  for  present  purposes. 
ASSUMPTIONS  :  Ideal  non-condensing  engines. 
DATA: 

/,  =  60,  80,  100,  1 20  Ibs.  per  sq.  in.  (absolute). 
-=0.15  ;  0.2;  0.25  ;  0.3;  0.4;  0.5. 

/3  =  1 8  Ibs.  per  sq.  in.  (absolute). 
T<=  110°  F. 


SUPERHEATING  AND  STEAM-JACKETING.          637 

RESULTS: 

(a)  Pressures — Unjacketed  Non-conducting  Cylinders. 

0.15        0.2          0.25         0.3          0.4          0.5 


pi 


A? 
A 

.407 

.496        .572 

.639 

-748 

.533 

60:  /. 

24.42 

29.76      34.32 

3S.34 

44-83 

49.95 

A 

6.42 

11.76       16.32 

20.34 

26.83 

31.98 

80:  pm 

32.56 

39.68      45-76 

51-12 

59.84 

66.64 

A 

14.56 

21.68        27.76 

33.12 

41.84 

48.64 

100:  pm 

40.70 

49.60        57-20 

63-00 

74-8o 

83  30 

A 

22.70 

31.60        39.20 

45-90 

56.80 

65-30 

120:  pn 

48.84 

59.52        68.64 

76.63 

89.76 

99  96 

A 

30.84 

41.50        50.64 

58.68 

71.76 

81.96 

#,A  =  i3iA  +  4,ooo       A 

=  lbs. 

persq. 

in 

144      144 


60  827.8 

80  1094-4 

100  1361.1 

120  1627.8 


=  rpt        pt  —  Ibs.  per  sq.  in. 


144 

^A 
144 

i 

r 

0.15            0.2 

0.25 

0.3 

0.4 

0.5 

>,=    60 

42.8             58-8 

65.28 

67.8 

67.2 

63.06 

>,=    80 

97            108.4 

111.04 

110.4 

104.6 

97.28 

01  =  IOO 

151.1         158 

156.8 

150.3 

142 

130.6 

»i  =  I2O 

205.6        207.6 

202.56 

195.6 

179.4 

163.9 

638  A    MANUAL    OF   THE   STEAM-ENGINE. 

(b)  Pressures — Jacketed  Cylinders. 


A 

0.15 

o 

.2 

0.25 

o-3 

0.4 

0-5 

r 

PjH_ 

.417 

.505 

.582 

.648 

-756 

.840 

Pi 

25.02 

30. 

•30 

34-92 

38.88 

45-36 

50.40 

pe 

7.02 

12 

.30 

16.92 

20.88 

27-36 

32.40 

pi  =     80:  pm 

33.36 

40 

.40 

46.56 

51.84 

60.48 

67.20 

Pe 

I5-36 

22. 

40 

28.56 

33-84 

42.48 

49.20 

pi  =  ioo:  pm 

41.70 

50.50 

58.20 

64.80 

75.60 

84.00 

Pe 

23.70 

32. 

50 

40.20 

46.80 

57.60 

66.00 

/l  =  1  20:  pm 

50.04 

60. 

60      . 

,69.84 

77.76 

90.72 

100.80 

Pe 

32.04 

42. 

60 

51.84 

59-76 

72.72 

82.80 

I5-5A 

P 

* 

r 

\          o. 

15 

O.2 

0.25 

0.3 

0.4 

o-5 

p    for  pi  = 

60       139 

>5 

186 

232-5 

279 

372 

465 

ph  for/t  = 

80         186 

248 

310 

372 

496 

620 

p    for  pi  = 

ioo        232 

•  5    ' 

310 

387-5 

465 

620 

775 

ph  for  /i  = 

120            279 

372 

465 

558 

744 

930 

UD, 


(c)  Efficiencies-, 
(a)  For  the  unjacketed  cylinders  £,  = 

(V)  For  the  jacketed  cylinders  E,  =  ^. 


A- 


F    t 
*,-- 


0.15 

42.8_  = 


-5—    =    II! 

1361 

232-5  ~' 
205.6 


- 

1361 


=  .116 

=.105 


310 

207.6 

I627T8=-15 


16.92 


1094.4 
28^56 

lj*r- 
1361 

40   2 

387.5  • 

202 . 56 


827.8 


"°t- 
1094.4 

372~    " 

I50_3_  = 
1361 

46,8     __ 
465 

'95.6  . 
1627.8" 


27.36 


T^T 

66 


627.8 
82.8 


SUPERHEATING  AND  STEAM-JACKETING.  639 

(a)  For  Maximum  Efficiency  of  Fluid. 
/,  60  80  100  120 

0.3  0.25  o^  Ot2 

Et  jo82  .101  .116  .128 

/:,  JO75  .092  .105  .114 

£  .914  .911  .905  -899 

It  will  be  observed  that  maximum  efficiency  of  fluid  in- 
creases as/,  increases,  and  the  value  of  r  for  maximum  efficiency 

also  increases  as/,  increases ;  but  the  value  of  -j?  decreases  as 

/,  increases — that  is,  the  loss  due  to  the  jacket  increases,  in  these 
ideal  cases,  with  increase  of  initial  pressure. 

(>)  Fuel-amstimptwn.  Assume  an  effective  evaporative 
power  of  9  to  I ;  then  the  available  heat  per  Ib.  of  coal  = 
6,700,000  ft.  Ibs. 

60  X  33*000       0.295 

r  vx  f-  „      — —  =  — ~-  =  Ibs.  of  coal  per  H.  P.  per  hour. 
E  X  6,700,000        E 

IDEAL  ENGINE.    FUEL-CONSUMPTION. 

/,...    60        8O  IOO  I2O 

Lbs.  coal  per  H.  P.  per  hr. — Unjacketed.  3.6    2.85  2.55  2.3 

«                «.      «     «       Jacketed....   3.9     3^  2.8  2.5 

The  fact  that  the  steam-jacket,  as  employed  on  the  steam- 
engine,  of  whatever  form  and  arrangement,  is  intrinsically  a 
wasteful  element,  and  that  its  use  only  gives,  in  certain  cases, 
an  economical  advantage  by  its  repression  of  wastes  of  larger 
magnitude,  is  also  shown  by  the  following  illustrations,  com- 
puted with  and  without  jacket  for  various  ratios  of  expansion. 
The  results,  as  given  in  the  following  tables  and  as  illustrated 
in  the  curves  plotted  from  them,  show  clearly  that  the 
jacketed  engine  is  always  more  wasteful  than  the  ideal  un- 
jacketed  engine.* 

*  Jomal  Franklin  Institute  ;  April  1891.     "  On  a  Maximum  Efiaeacy«I~ 
Steam-jacket ;"  R.  H.  Tlmisum. 


640 


A   MANUAL    OF   THE   STEAM-ENGINE. 


Making  the  computations  by  the  methods  already  employed 
and  tabulating  the  results,  we  have,  for/,  =  115  Ibs.  absolute, 
*i  =  799°  F-»  and A  =  4: 


EFFICIENCIES  OF  WORKING  FLUID. 
Steam-engine,  Jacketed  and  Unjacketed. 


Cut-off. 
0.05 
.10 

•15 
.25 

•35 
•45 
•55 
•75 

1. 00 


Ratio  Exp. 
2O.OO 
IO.OO 

6.66 
4.00 

2.85 

2.22 
1.82 

i-33 

1. 00 


Eff.  without. 
0.2073 


•1795 
.1566 

.1358 
.1237 
.1119 
.0898 
.0707 


Eff.  with  Jacket. 
0.1930 
.I808 
.1665 
.1442 
.1302 
.1209 
.1087 
.0812 
.0707 


Ratio  of  expansion. 
FIG.  156. — EFFECT  OF  JAGKEI 


SUPERHEATING  AXD   STEAM-JACKETIXG.  641 

An  examination  of  the  tables,  of  the  curves  still  better,  wfll 
show  clearly  the  wasteful  influence  of  the  steam-jacket,  as  an 
element  considered  by  itself.  Within  the  useful  range  of  prac- 
tice, from  about  five  or  six  to  fifteen  or  twenty  expansions, 
under  the  assumed  conditions  of  initial  pressure  and  cut-off,  it 
it  is  seen  that  the  loss  by  its  application  is  fairly  constant  at 
something  over  one  per  cent,  in  these  cases ;  rapidly  falling  to 
zero  as  the  ratio  of  expansion  falls  from  the  lower  figures  to 
unity.  The  consumption  of  steam,  in  pounds  per  horse-power 
per  hour,  may  be  computed  very  approximately  by  dividing  2.3 
by  the  computed  efficiencies.  The  cases  assumed  are  for  con- 
densing engines,  and  the  evaporation  always  taken  at  nine  pound? 
of  steam  per  pound  of  fuel,  the  fuel  expenditure  may  be  gauged 
by  dividing  the  weight  of  steam  computed  by  9.  This  gives, 
for  example,  about  12.06  and  12.95  pounds  for  the  unjacketed 
and  for  the  jacketed  engine,  respectively,  at  a  ratio  of  20, 
in  steam  demanded;  and  of  about  1.33  and  1.44  pounds  of 
fueL  For  a  ratio  of  expansion  of  4,  the  figures  becoine 
about  1 6  and  17.3,  respectively,  for  the  steam  and  1.75  and  1.85 
pounds  of  fueL  At  full  stroke,  the  figures  become  35  pounds 
of  steam  and  of  feed-water,  and  4  pounds  of  fuel  per  horse- 
power and  per  hour,  for  both  engines. 

The  consumption  of  fuel  by  the  ideal  jacketed  engine  is 
thus  found  to  exceed  that  of  the  ideal  unjacketed  engine.  To 
determine  what  such  engines  would  actually  demand,  we  must 
know  their  size,  speed,  and  such  other  data  as  will  enable  us  to 
estimate  the  probable  cylinder-wastes.  Assuming  that  they 
are  of  such  size  and  character  as  to  give  wastes  for  the  unjack- 
eted and  jacketed  engines,  respectively,  of  0.2  ifr  and  of 
o.i  V7,  they  would  consume : 

Actual  Consumption  of  FueL 

p^ 60         80         100         120 

(a)  Unjacketed 4-8       4-O         3-2         2.8 

(0)  Jacketed. 4-2       3-8         3-O         2-7 

The  ratio  of  expansion  would  usually  be  larger  at  these 
higher  pressures  and  the  actual  gain  by  the  jacket  greater. 


642  A  MANUAL    OF   THE   STEAM-ENGINE. 

But  the  assumption  made  in  these  computations — that  the 
steam  is  kept  by  the  steam-jacket  just  dry  and  saturated  during 
expansion — is  probably  never  true  except  with  initially  dry 
and  perhaps  superheated  steam.  The  fact  is,  more  likely,  that 
waste  usually  goes  on  during  the  whole  exhaust-period,  and 
that  the  total  jacket-waste  is  thus  seldom  less  than,  and  may 
often  even  exceed,  ten  per  cent.  A  maximum  efficiency  of 
jacket  is  always  found  in  practice  between  full  stroke,  where 
the  cylinder-waste  is  a  minimum,  and  extreme  expansion, 
where  jacket-waste  is  a  maximum,  extending  through  the 
exhaust-period.  Fortunately,  this  maximum  rises  as  pressure 
increases,  precisely  as  required  for  best  results. 

It  is  obvious  that,  in  the  computation  of  probable  efficiency, 
and  of  steam-consumption,  in  the  case  of  the  engines  efficiently 
jacketed,  in  the  manner  here  assumed,  the  volume  of  steam  at 
the  opening  of  the  exhaust-valve,  measures  the  amount  used  and 
requires  no  correction.  A  table  will  be  found  in  the  Appendix, 
computed  by  Mr.  Buel,  exhibiting,  concisely,  the  nomenclature, 
data,  formulas,  and  results  for  this  case. 

The  following  table*  represents  the  results  of  computations 
of  probable  efficiency  and  performance,  on  the  assumption 
that  the  initial  pressure  is  250  pounds  per  square  inch,  absolute, 
the  internal  wastes  as  found  in  experimental  work  already 
referred  to,  and  measured  by  the  expression  I  -f-  O-O/5  Vr,  the 
engine  being  a  jacketed  tandem-compound  engine,  and  these 
wastes  assumed  to  be  those  due  a  single  jacketed  cylinder  of 
moderate  size  and  under  usual  conditions  of  operation.f  Back- 
pressures are  taken  as  5  pounds  condensing,  and  16  non-con- 
densing, feed-temperatures  as  104°  F.  and  203°  F.,  respectively, 
and  the  evaporations  as  10  to  11  respectively.  Rankine's 
assumption  as  to  effectiveness  of  jacket  is  accepted,  the  wastes 
above  referred  to  being  taken  as  those  of  the  exhaust-period. 


*  Trans.  Am.  Soc.  M.  E.;  ccccli;  vol.  xii;  1891. 

f  Mon.  Haton  de  la  Goupilliere  coincides  with  Sinigaglia;  who  says  that  this 
function  was  first  proposed  by  the  Author,  and  subsequently  confirmed  by  direct 
experiment  at  Sandy  Hook  and  elsewhere. — Cours  des  Machines;  vol.  u. 


SUPERHEATING  AXD  STEAM-JACKETLXG. 

COMPOUND  STEAM-EXGINE—  JACKETED. 

NON-COXDEXSIXG. 


643 


•: 

::.-:  ' 


CONDBXSIK 


3    .»„,      9-» 

K>                 1    I2.AO 

W   "     36-8 
30     •*    ,:  55.1 

,|  ^ 

»      -       9Z.o 

5»-9 

-     i      _:,-,;           -           ^     ^     =££     ^        -            ::„:.. 

XOX^TOXDEXSIXG. 


IHHU   ;  -  - 1 


*  !  Is  - 1 
I  :Bl5 


S-^i  H 


COXDEKSIXC. 


873999       TAP    I  -i«"9 


a: 


W  ,.,«  -M4*  "4-3JJ  «-»t» 
-*?*  »-»»,  ->597  «  ^  «  573 
.JTij  ..335'  .rf«,«  008  1.563 
.ndl  «-4ii3  .isfi*  a-jfc:  »-6oi 


36>oo  OML  per  sq.  ft.  ^  >9>  •»•  Per  sq.  in. 


644  A   MANUAL    OF   THE    STEAM-ENGINE. 

It  will  be  seen  that  the  efficiencies  range  from  16.7  to  18.2 
per  cent  in  the  case  of  the  non-condensing,  and  from  16.9  to 
22  per  cent  for  the  condensing  engine,  the  maximum  being 
found  at  a  ratio  of  expansion,  in  the  first  case,  of  about  10,  and 
in  the  second  of  about  30.  Beyond  these  ratios  the  terminal 
pressure  falls  below  the  back-pressure,  and  a  waste  follows, 
instead  of  gain,  by  further  expansion. 

These  results  are  still  better  exhibited  by  the  curves  (Figs. 
157  and  158)  plotted  from  the  numerical  values  ;  the  ideal  case, 
in  both  sets,  being  represented  by  dotted  lines,  and  the  real 
engine  giving  the  widely  different  curves  in  full  line.  The 
great  difference  between  the  condensing  and  the  non-condens- 
ing engine,  for  the  ideal  case,  is  well  shown,  not  only  as  to 
consumption  of  fuel  at  similar  ratios  of  expansion,  but  also  as 
affected  by  changing  values  of  that  ratio.  The  gain  by  expan- 
sion in  the  former  case  continues  far  beyond  that  at  which  the 
latter  finds  a  limit ;  while  the  point  of  maximum  effect  is  far 
more  sharply  defined  with  the  non-condensing  engine.  Varia- 
tion from  the  best  ratio  for  the  latter  causes  much  more  marked 
loss  than  with  the  condensing  engine.  The  numerical  values 
obtained  are  presumably  those  which  we  should  obtain  if  we 
were  to  find  a  way  of  building  engines  with  working  cylinders 
having  non-conducting  inner  surfaces.  The  points  of  maximum 
efficiency  and  those  for  minimum  consumption  of  steam  and 
of  fuel  are  coincident  in  these  cases,  and  also  that  for  minimum 
supply  of  feed-water.  As  will  be  seen  presently,  this  last  is  not 
the  case  for  jacketed  engines,  in  either  the  ideal  or  the  real 
case,  in  consequence  of  the  fact  that  a  part  of  the  working 
fluid  circulates  continuously  between  jacket  and  boiler  and 
makes  no  demand  upon  the  source  of  supply  for  replenishment. 

The  efficiencies  of  the  real  engine  range  from  13  to  about 
15  per  cent,  and  from  14  to  16  per  cent,  in  the  two  engines, 
respectively  ;  while  the  best  results  are  now  given  at  a  ratio  of 
expansion  of  not  far  from  8  and  20  in  the  two  cases,  respec- 
tively. The  water-consumption  has  increased  from  12  to  14.8 
pounds,  and  from  8  to  12  pounds,  and  the  fuel  account  has 
risen  from  1.36  to  1.68  and  from  1.13  to  1.55  pounds  per  horse- 


SUPERHEATING  AND  STEAM JACKETIXG.  645 


-  -  -  :      ::«:•;•-     : 


COMPOUND  JACKETED  ENGINE. 


"7 


J_ 


\ 


646 


A    MANUAL    OF    THE   STEAM-ENGINE. 


FIG.  158. — FUEL  AND  WATER  CONSUMPTION. 


SUPERHEATING  AND   STEAM-JACKET1XG.  647 

power  and  per  hour  for  non-condensing  and  for  condensing 
engines.  These  changes  are  best  seen  on  the  curves ;  the  lower 
sets  being  those  for  the  real  engine,  and  the  differences  being 
best  exhibited  by  the  shaded  areas  separating  the  pairs  on  the 
second  plate. 

It  will  be  seen  that  the  effect  of  this  introduction  of  wastes 
in  the  ideal,  as  in  the  real,  engine  is  to  greatly  reduce  that 
ratio  of  expansion,  which  gives  maximum  efficiency,  and  to 
make  variation  from  that  ratio  of  maximum  efficiency  more 
seriously'  productive  of  loss :  while  at  the  same  time  making 
the  differences  between  the  several  cases  less  than  in  the  ideal 
engine.  The  following  are  the  values  of  the  ratios  for  maxi- 
mum efficiency  and  for  minimum  steam  and  water  consumption 
for  the  cases  taken : 

COMPOUND  JACKETED  ENGINE, 
/i  =  250;  p%  =  5  and  16;  r  variable. 


CASK. 


r  for  maximum  efficiency n  8.5  ;:  17 

Water-rate j       12  14.75  8.5  12 

Fuel-rate \         1.35  ]       1.68  i.i     ]         1.55 

The  real  measure  of  the  useful  power  of  an  engine  is  the 
dynamometric  power  at  the  point  at  which  the  engine  delivers 
its  energy  to  the  machinery  of  transmission.     A  well-built  non- 
condensing  engine  should  have  an  efficiency  of  machine  as 
high  3592.5  per  cent.     An  equally  well-built  condensing  engine 
should  approximate  90  per  cent  efficiency  of  machine.     Tak- 
ing these  values,  the  last  table  becomes  modified  thus : 
COMPOUND  JACKETED  ENGINE. 
(Data  as  above.) 


Ideal. 

Real. 

IdeaL 

ReaL 

II 

8.5 

:  - 

17 

Water  per  D    H   P  

13 

16 

8-5 

13-5 

Fad  ner  D.  H.  P.  .  . 

1-5 

i.S 

1.2 

1-7 

648  A    MANUAL   OF   THE    STEAM-ENGINE. 

156.  Limitations  of  Jacket-action  have  been  noted,  in 
many  cases  ;  and,  while  the  precise  methods  of  operation  of 
their  various  causes  have  not  always  been  fully  revealed,  we 
are  perfectly  familiar  with  their  general  action  and  effects.  It 
has  been  found  that  the  use  of  superheated  steam,  the  com- 
pounding of  the  steam-engine,  or  the  increase  of  speed  of  pis- 
ton and  of  rotation  —  in  fact,  any  circumstance  independently 
promoting  economy  —  reduces  the  value  of  the  jacket,  and  sets 
a  limit  beyond  which  it  would  presumably  have  no  useful  ef- 
fect. That  this  limit  is  sometimes  reached  is  unquestionable. 
Him  first  detected  such  limitation  in  the  application  of  super- 
heated steam  to  a  compound  engine.  Later  experience  has 
very  often  illustrated  the  fact  that  the  jacket  may  be  of  little 
service,  especially  on  compounded  high-speed  engines  ;  and  it 
is  sufficiently  obvious  that  any  conditions  which  tend  to  make 
the  net  jacket-waste  and  the  net  cylinder-waste  equal,  either 
by  exaggerating  the  former  or  by  reducing  the  latter,  will  tend 
to  bring  about  this  result  ;  as  will  any  defect  in  the  design, 
construction,  or  operation  of  the  jacket  which  renders  it  ineffi- 
cient in  its  working. 

Precisely  where  the  limit  is  reached  in  any  class  of  engines 
is  not  easy  to  determine.  A  clue  to  the  solution  of  such  prob- 
lems is  found  in  the  measurement  of  the  condensation  in  the 
jacket  ;  the  quantity  of  water  trapped  off  being  a  measure  of 
the  total  heat-supply  to  the  cylinder,  dry  steam  being  received 
from  the  boiler. 

Mon.  Dwelshauvers  Dery,  analyzing  the  data  supplied  by 
test  of  the  Whitworth  Laboratory  experimental  engine,  obtains 
the  following  : 

Let  Q  =  heat  supplied  by  the  boiler,  directly  ; 
<2,  =  that  supplied  by  the  jacket  ; 
T  =  total  indicated  work  ; 
E  =  rejected  heat  externally  ; 

C~\-c  =  that  sent  to  the  condenser. 
Then 


__ 

Q+Q, 


SUPERHEATIXG  AXD  STEAAf-JACKETIXG. 


649 


Referring  to  six  tests  in  three  of  which  the  jackets  were  all 
in  use,  and  in  three  of  which  they  were  on  the  reservoirs,  only, 
and  were  shut  off  on  the  cylinders,  the  following  table  is  ob- 
tained :  * 


HEAT-DISTRIBUTION. 


Number  of  trial 


Heat  of  the  direct  steam. 
Hear  of  fh»  iarket 

*r 

0.749 

- 

o.Si6 

0.869 

0.893 

0.904 

Work 

,  -  :. 

T 

0.16^ 

- 

Radiated  waste 

E 

o  127 

o  oqi 

o  060 

Q  +  Qi 

Heat  utilized  by  jacket, 

Q-E 
<?  +  <?. 

0.124 

O.I2O 

0.124 

0.091 

0.054 

j  0.051 

HMI  r*»i«*t^H 

-  —  -• 

r».-fW* 

/~>     1     /I 

o,  720 

0.035 

10.519 

v;  T  vr» 

Thus,  deducting  the  quantities  of  heat  wasted  by  external 
radiation,  the  jackets  supply  an  almost  perfectly  uniform  quan- 
tity of  heat,  the  figures  being  12.4,  12,  and  12.4  per  cent  in  the 
first  three  trials  ;  the  cause  of  the  greater  variation  in  the  last 
three  cases  is  indeterminate  from  the  available  data. 

Mon.  Dwelshauvers  concludes  from  his  somewhat  extended 
observations,  and  experimental  researches,  that,  other  things 
equal,  and  under  usual  working  conditions,  the  jacket  has  little 
value  at  a  low  ratio  of  expansion  ;  and  that,  to  enable  it  to  be 
of  much  service,  that  ratio  must  exceed  at  least  5.  He  has 
observed  an  economy,  in  his  own  trials,  of  1 5  per  cent  at  a 
ratio  of  5,  of  3  to  4  per  cent  at  ratios  approximating  3.3.  In 
compound  engines,  when  the  expansion  in  the  high-pressure 
cylinder  is  small,  he  sees  little  advantage  in  the  use  of  the 
jacket ;  while  he  considers  it  indispensable  on  the  large  cyl- 
inder. Heat  wasted  in  the  smaller  cylinder  may  be  utilized 

*  Correspondence. 


6$O  A  MANUAL   OF   THE   STEAM-ENGINE. 

in  the  larger  ;  but  waste  from  the  latter  cannot  be  compen- 
sated. 

Could  the  conditions  assumed  for  the  ideal  case,  as  illus- 
trated in  the  cases  of  jacketed  engine  and  dry  saturated  steam, 
elsewhere  computed,  be  actually  secured,  the  exhaust  deliver- 
ing dry  steam  to  the  condenser,  it  is  probable  that  the  waste  of 
heat  from  the  cylinder  during  that  period  would  be  slight  and 
the  efficiency  of  the  engine  in  actual  operation  thus  made  to 
approximate  a  maximum.  Were  the  jacket  made  so  effective 
— as,  for  example,  in  the  case  of  Donkin's  gas-heated  jacket — 
as  to  superheat  the  steam  exhausted  ;  or  were  it  so  ineffective, 
as  is  probably  usual,  as  to  permit  the  exhaust-steam  to  be  sent 
to  the  condenser  wet,  it  is  probable  that  the  resultant,  total, 
efficiency  would  be  less.  This  consideration  justifies  an 
apothegm  of  Dwelshauvers-Dery  :  the  waste  by  the  cylinder- 
walls  is  measured  by  the  heat  demanded  to  evaporate  the  water 
in  the  exhaust-steam  at  the  end  of  the  expansion-period. 

In  all  cases  where  the  cylinders  are  provided  with  steam- 
jackets,  if  practicable,  steam  should  be  introduced  into  the 
cylinder-heads ;  and  non-conducting  coverings  should  be  ap- 
plied to  the  heads  as  well  as  to  the  cylinders,  proper.  The 
jacket-steam  should  not  be  allowed  to  become  either  stagnant 
or  charged  with  air  ;  and  it  should  not  pass  into  the  cylinders. 
The  jacket  should  be  neither  too  greatly  nor  too  slightly  ener- 
getic ;  its  action  should  be  sufficient  to  insure  dryness  of  the 
surfaces  of  the  cylinder  at  the  close  of  the  exhaust,  so  as  to 
prevent  initial  condensation  ;  but  it  should  not  superheat  the 
steam  during  expansion  or  exhaust.*  Such  efficiency  of  the 
jacket  must  apparently  be  secured,  first,  by  proper  construction 
of  the  jacket  and  cylinder  and,  secondly,  and  especially,  by  in- 
suring reasonably  dry  or  slightly  superheated  steam. 

It  would  seem,  from  all  that  has  preceded,  that  where  a 
high  ratio  of  expansion  is  proposed  in  any  one  cylinder,  and 
when  the  steam  supplied  it  is  initially  dry,  or  fairly  dry,  the 
steam-jacket  may  be  confidently  expected  to  give  an  unmis- 

*  See  Ledieu:  Machines  a  Feu;   1882;  p.  714. 


SUPERHEATING  AND  STEAM-JACKETING.  6jl 

takable  and  very  desirable  economy,  even  from  the  final  com- 
mercial point  of  view  from  which  all  costs,  direct  and  inci- 
dental, are  noted ;  but  when  the  expansion  is  restricted,  the 
range  of  temperature  in  the  cylinder  slight,  the  steam  super- 
heated, or,  on  the  other  hand,  when  it  is  so  wet  that  the  jacket 
connot  completely  dry  and  thoroughly  reheat  the  metal  of  the 
cylinder  before  it  is  again  exposed  to  the  entering  steam,  the 
value  of  the  steam-jacket  may  become  questionable,  or  null,  or 
even  negative. 

A  good  jacket  covers  all  active  condensing  areas,  permits 
neither  water  nor  air  to  remain  in  it,  returns  all  water  of  con- 
densation immediately  to  the  boiler,  and  is  itself  well  covered 
by  non-conductors. 

In  1886,  a  "  Research  Committee"  was  appointed  by  the 
British  Institution  of  Mechanical  Engineers,  to  investigate  the 
action  of  the  steam-jacket.*  A  very  extensive  collection  of 
data  pertaining  to  the  efficiency  of  the  jacket  was  secured,  and 
from  these  the  following  figures  were  collated  and  results  de- 
duced :f 

The  first  case  is  a  single-cylinder  non-condensing  Corliss 
engine,  21.65X43.31  inches,  the  body  only  jacketed.  The 
jackets  were  supplied  by  a  small  pipe  from  the  main  steam- 
pipe  and  were  automatically  drained. 

The  second  case  is  a  single-cylinder  condensing  engine 
(Corliss),  cylinder  dimensions  as  before,  body  only  jacketed ; 
experiments  carried  on  at  the  same  place,  in  the  same  manner. 

The  third  case  is  a  horizontal  compound  condensing  tandem 
engine,  the  body  of  the  cylinders  only  being  jacketed.  The 
whole  steam-supply  to  the  cylinders  passed  through  the  jackets, 
which  were  drained  by  trap ;  and  when  not  in  use  the  jackets 
were  open  to  the  air. 

The  last  trials  were  carried  on  at  a  constant  boiler-pressure 


*  Proceedings.  1890. 

f  journal  Franklin  Institute;  Apr.  1891.     "  On  a  Maximum  Efficiency  of 
Steam-jacket;"  R.  H.  Thurston. 


652 


A    MANUAL    OF   THE   STEAM-ENGINE. 


of  42  pounds  above  the  atmosphere  and  a  piston-speed  of  196 
feet  per  minute. 

VARYING  JACKET-EFFICIENCIES. 


Ratio  of  Exp. 
2      6.2 

I    6 
<    5 

Eff.  of  Jacket. 
Per  Cent. 

21-33 
20.6  1 

15-79 

Elatio  of  Exp. 

8 

10     7 
1     6 
*    5 
4 

Eff.  of  Jacket, 
Per  Cent. 

7-38 

5-94 
4-67 
3-6 
1.64 

5-5          •§          13 
15            f          12 

i    4                          9 
3             j            9 

.6 

.63 
-38 

10 

i  I 

^  g 

5 

7-45 
6.28 

3-84 
3-o8 
2.03 

a    4 

J     3 

<     2 

7.64 

7 
3-93 

12 

0      " 

H         IO 

<l 

7 

23 
23 
23 
23 

21 

20 

-43 
.82 
.78 
,2 

5-      9 

ii     8 
<    7 

19.23 
20.45 

22.55 

•5 
•32 

9 
7     8 

^    6 

26.34 
26.34 
26.24 
26.5 

IO 

&    9 

i     8 

u 

21 
22 

'9 
16 

12 

•95 

iM 

-23 

.66 
•34 

9 
ii     8 

^    6 

29 
29-35 

30  * 
31.62 

IO 

9 

8.62 

In  the  first  case,  that  of  the  simple  non-condensing  Corliss 
engine,  the  heads  unjacketed,  we  find,  taking  the  first  example, 
and  plotting  the  data,  that  the  use  of  the  jacket  reduced  the 
cylinder-wastes  from  about  25  per  cent  of  the  ideal  consump- 
tion of  steam  and  feed-water  to  about  half  that  proportion, 
for  ratios  of  expansion  approximating  6;  from  one  third  to 
about  one  tenth,  at  a  ratio  of  5  ;  and  apparently  from  20  to 
IO  per  cent  at  4.4.  The  same  general  effect  is  observed 


SUPERHEATING  A.VD   STEAM-JACKETING.  653 

throughout,  with  some  discrepancies  which  may  be  due  either 
to  varying  action  of  the  jacket  or  to  slight  errors  of  observa- 
tion, or  to  both  combined,  the  latter  being  the  probable  fact. 

In  this  first  case?  also,  it  will  be  observed  that  the  jacket 
gives  best  results,  with  1 10  pounds  of  steam,  when  the  ratio  of 
expansion  approximates  6.  When  the  steam-pressure  falls  to 
approximately  80  pounds,  the  best  work  of  the  jacket  occurs 
at  a  ratio  not  far  from  4.75;  while,  at  the  pressure  of  50 
pounds,  the  value  of  the  jacket  increases  through  the  whole 
range  of  the  experiments:  and  not  only  so,  but  the  curve 
assumes  a  rectilinear  form,  indicative  of  probable  improvement 
indefinitely  in  the  direction  of  increasing  expansion.  The 
highest  efficiencies,  however,  either  with  or  without  the  jacket 
are  found,  in  this  case,  at  the  lowest  ratios  adopted,  and  indi- 
cate a  maximum  value  at  about  3.25.  The  ratios  of  expansion 
for  maximum  efficiency  of  fluid,  in  the  other  cases,  are  seen  to 
be,  for  1 10  pounds,  about  5,  and  for  80  pounds,  about  3.5. 

Similarly  studying  the  performance  of  the  condensing 
engine,  we  find  that  the  best  work  done,  whether  jacketed  or 
not,  is  at  a  ratio  of  expansion  of  10  (at  a  steam-pressure  of  1 10 
pounds),  but  that  the  jacketed  engine  reduces  the  internal 
wastes  from  50  per  cent  at  highest  ratios,  and  from  one  fourth 
at  the  lowest  ratios,  in  the  case  of  the  unjacketed  engine,  to  5 
per  cent,  and,  in  some  cases,  probably  to  within  the  magnitude 
of  the  errors  of  observation.  At  a  pressure  of  90  pounds,  the 
best  ratio  seems  to  be,  for  this  engine,  under  the  given  condi- 
tions of  operation,  about  6.5  when  unjacketed,  and  8.5  jack- 
eted; while  the  lower  pressures  still  further  reduce  both  the 
efficiencies  and  the  savings  effected  by  the  jacket.  The  best 
work  of  the  jacket,  as  an  economizer  of  heat,  is  done,  at  high 
pressure,  at  a  ratio  of  expansion  of  12  or  more.  In  all  cases  it 
seems  to  be  the  fact,  with  these  engines,  at  least,  that  the 
jacket  is  useful  beyond  the  ratios  of  maximum  efficiency  of 
fluid. 

The  compound  engine  is  operated  at  altogether  too  low  a 
pressure  to  bring  out  the  best  effect  of  compounding;  but  it 
exhibits  the  same  general  effects  which  have  been  noted  in  the 


654  A    MANUAL   OF   THE   STEAM-ENGINE. 

cases  of  working  of  simple  engines.  The  effect  of  the  jacket 
is  less  pronounced  than  in  the  simple  engine,  and  the  effi- 
ciencies of  fluid  vary  less  with  variation  of  the  ratios  of  expan- 
sion. It  gives  its  best  result  at  ratios  of  expansion  ranging 
from  7.5  to  10.5,  the  variations  of  value  being  very  much  more 
observable  in  the  last  case,  in  which  both  jackets  are  in  use, 
than  in  either  of  the  others,  at  least  in  that  case  in  which  only 
the  high-pressure  jacket  was  employed.  By  far  the  best  work 
was  done  by  the  engine  when  both  jackets  were  in  use. 

The  discovery  of  a  maximum  efficiency  of  jacket  throws 
some  light  upon  the  causes  of  the  conflicting,  and  sometimes 
apparently  irreconcilable,  results  of  trials  of  engines  with  and 
without  jackets,  and  with  jackets  variously  constructed.  The 
discovery  may  prove  of  value  to  the  designer,  as  aiding  him  in 
securing  the  best  proportions  and  arrangement  of  his  engine. 

157-  Jackets  on  Multiple-cylinder  Engines  have  given 
varying  results;  but  the  general  action  of  this  accessory  in 
these  machines  may  be  readily  traced.  It  is  substantially  the 
same  as  in  the  simple  engine ;  but  its  effects  are,  in  some 
respects,  characteristically  different. 

In  each  cylinder,  and  throughout  the  series,  the  jacket  is 
a  source  from  which  heat  continually  drains  into  the  working 
fluid,  adding  constantly  to  its  stock  of  heat-energy.  Where 
the  conversion  of  heat  into  work  is  considerable,  or  where  the 
wastes  of  heat  or  of  steam  are  large,  the  effect  may  be  simply 
to  reduce  the  rapidity  of  condensation  during  the  expansion- 
period,  as  well  as  to  check  initial  condensation  and  to  waste 
heat  during  the  exhaust-period  ;  but  where  the  jacket  is  effec- 
tive and  these  losses  are  less,  the  result  is  not  only  to  raise  the 
temperature  and  pressure  of  the  steam,  during  expansion,  but 
also  to  make  the  steam  entering  each  successive  cylinder  drier 
and  drier,  as  compared  with  the  case  in  which  the  jacket  is  not 
used. 

This  may  even  result,  in  some  cases,  perhaps,  in  not  only 
preventing  initial  condensation  in  the  series,  after  the  first 
cylinder,  but  in  giving  dry,  or  even  appreciably  superheated, 


SVPERH&ATllTG  AKD  STRAit-JACKETlNG.  655 

steam  throughout;  the  jacket  supplying  steam  mainly  to  do 
work,  and  not  to  waste. 

In  computing  probable  expenditures  of  heat,  steam,  and 
fuel,  for  the  compound  engine,  as  affected-  by  the  jacket^  it  is 
seen  that  the  method  of  treatment  is  precisely  the  same  as  in 
the  cases  already  illustrated.  The  ideal  case  is  first  computed : 
next  the  wastes  are  added,  each  cylinder  being  treated  sepa- 
rately, and  the  wastes  of  the  system  taken  as  equal  to  the  loss 
of  the  most  wasteful  cylinder  in  the  series.  These  wastes  are 
computed  for  each  cylinder  as  for  the  jacketed  simple  engine, 
and  are  ordinarily,  perhaps,  one  half  to  two  thirds  as  great  with 
as  without  the  jacket.  The  advantage  of  the  jacket  will  be 
thus  found  to  be  less  as  the  number  of  cylinders  is  increased. 

The  philosophy  of  the  multiple-cylinder  engine,  as  already 
outlined,  would  obviously  indicate  that,  to  secure  maximum 
good  effect,  assuming  the  jacket  on  the  whole  desirable  at  all. 
the  best  system  is  to  jacket  all :  and  that,  since  the  waste  of 
the  engine  is  measured  by  the  waste  of  its  most  wasteful  mem- 
ber, to  omit  the  jacket  from  any  one  cylinder  insures  that  the 
aggregate  loss  of  heat  in  the  whole  engine  will  be  increased  by 
just  the  amount  by  which  waste  is  increased  in  that  one  cylin- 
der by  such  omission. 

The  resulting  effect,  in  detail,  is  evidently  the  following: 
Assume  the  intermediate  cylinder  to  be  unjacketed.  That 
cylinder,  being  exposed  to  a  wider  range  of  heating  and  cooling 
action  as  it  alternately  takes  steam  and  exhausts  it.  is  subject 
to  a  greater  waste  by  internal  condensation  than  either  of  the 
others :  it  thus  discharges  into  the  next  cylinder  a  nearly  equal 
quantity  of  heat  and  steam,  but  it  does  less  work  than  it  would 
have  otherwise  done,  and  to  that  extent  produces  decreased 
efficiency.  Assume  the  high-pressure  cylinder  unjacketed,  it 
demands  more  steam  from  the  boiler,  as  it  condenses  a  larger 
proportion  of  that  entering  by  this  process  of  initial  liquefac- 
tion :  it  is  thus  itself  more  wasteful  and  furthermore  transmits 
to  the  succeeding  cylinders  a  larger  quantity,  and  therefore 
a  more  uneconomical  apportionment,  of  steam  than  it  would 
otherwise  have  released.  In  proportion  as  its  own  efficiency 


656  A    MANUAL    OF   THE   STEAM-ENGINE. 

is  thus  reduced,  it  reduces  the  economical  working  of  the 
whole  ;  and,  in  proportion  as  the  steam  rejected  from  it  is 
a  less  economical  storehouse  of  heat  for  use  in  the  other  cylin- 
ders, they  are  in  turn  rendered  less  efficient.  The  low-pressure 
cylinder  being  left  unjacketed,  it  becomes  more  wasteful  in  pro- 
portion to  the  increased  initial  condensation  thus  permitted, 
and  the  whole  system  is  again,  to  that  extent,  given  impaired 
efficiency. 

With  high  speeds  of  engine,  however,  and  especially  if  com- 
pounded, or  when  using  superheated  steam,  these  wastes  be- 
come too  small  to  be  sensibly  affected  by  the  jacket ;  and  on 
"high-speed  engines,"  and  all  fast-running  "  compounds,"  its 
addition  is  of  such  doubtful  utility,  on  the  whole,  that  it  is 
usually  omitted.  This  is  the  case  on  small  electric-light  en- 
gines and  on  the  enormous  triple-expansion  engines  of  trans- 
atlantic steamers  alike. 

158.  Jacketing  and  Superheating  have  been  already  seen 
to  be,  in  a  way,  incompatible.     Both  are  methods  of  reducing 
interior  wastes,  and  either  being  adopted,  the  desirability  of  the 
other  is  reduced.    There  is,  however,  this  difference  :  superheat- 
ing may,  and  sometimes  does,  entirely  suppress  initial  conden- 
sation ;  while  jacketing  cannot  do  this.     Yet,  even  with  highly 
superheated  steam,  there  must  atways  be  some  interior  waste 
by  storage  in  the  metal  and  subsequent  transfer.    Both  methods 
of  economizing  give  wastes ;    and  both  produce  gain,  but  in 
different  degree  ;  and,  of  the  two,  superheating  is  probably  ca- 
pable of  approximating  most  closely  to  the  ideal  case  ;    and 
even  moderate  superheating  reduces  the  total  of  these  losses 
below  minimum  jacket-waste,  and  thus  renders  the  jacket  use- 
less. 

159.  Jackets  on  High-speed  Engines  have  comparatively 
little  value  for  the  same  reason  as  in  the  case  of  superheating. 
The  cylinder-wastes  are  reduced,  by  high  speed  of  engine,  to 
so  small  a  quantity  that  this  excess  over  jacket-wastes  is  so 
small  as  to  be  of  comparatively  little  importance.      Where,  as 
is  now  often  the  fact,  these  engines  are  compounded,  the  still 


SUPERHEATING  AND  STEAM-JACKETIXG.  657 

further  reduction  of  wastes  and  the  addition  of  the  jacket  may, 
in  such  cases,  prove  entirely  useless,  practically. 

Thus,  the  Author  has  been  furnished  with  the  following 
record  of  test  of  a  high-speed  compound  engine  of  small  size^ 
working  with  and  without  the  jackets  in  operation.  The  gmall 
size  of  the  engine  makes  the  "water-rate" — Le.,  the  water  used 
per  horse-power  per  hour — rather  large  for  an  engine  of  this 
class,  as  well  as  giving  a  large  amount  of  engine-friction.  The 
jacket  evidently  has  no  practical  value  on  such  an  engine. 


Jacket  off.    Jacket  on. 

Boiler-pressure. 90  90 

Speed 343  343 

Brake  load 209'  209 

Duration  of  test,  hours 10  10 

Water  used  per  hour 1722  1686 

Vacuum None  None 

Initial  pressure 88  86 

Terminal  pressure. II  n 

Ratio  of  expansion 396  389 

High-pressure  M.  E.  P 44-77  43-97 

Low-pressure  M.  E.  P. J5-34  15JO4 

Indicated  horse-power. 66.81  65.57 

Brake  horse-power 54-99  54-99 

Loss  or  friction 11.82  10.58 

Percentage  of  loss. 17.7  16.13 

Indicated  water-rate 25.8  25.7 

Brake  water-rate,  Ibs.,  per  h.  p.  per  hour  31.3  30.66 

In  another  case,  the  water-rate  is  brought  down  to  20  or  21 
pounds  by  the  use  of  the  condenser,  and  it  is  found  that  the 
jacket  saves  I  or  2  pounds  on  these  figures.  In  still  another 
instance,  we  have  the  following : 

The  engine  was  a  "  tandem  compound,"  with  cylinders  8X 
12  and  13X12,  running  at  300  revolutions  per  minute:  steam 
at  about  95  pounds.  Each  test  was  for  one  hour. 


658  A    MANUAL   OF    THE   STEAM-ENGINE. 

(1)  First  hour,  steam-jacket  on  high-pressure  cylinder  only: 

I.  H.  P.,  64.46  ;     water  per  h.  p.  per  hour,  19.57  Ibs. 
Second  hour,  with  steam-jacket  on  both  cylinders : 

I.  H.  P.,  66.03  I     water  per  h.  p.  per  hour,  18.88  Ibs. 

Third  hour,  with  steam-jacket  on  both  cylinders : 

I.  H.  PC,  65.00  ;     water  per  h.  p.  per  hour,  18.44  Ibs. 

(2)  Same  engine,  same  conditions,  same  boiler-pressure. 
First  hour,  with  steam-jackets  on  : 

I.  H.  P.,  71.49  ;     water  per  h.  p.  per  hour,  19.59  Ibs. 

Second  hour,  without  steam-jackets  : 

I.  H.  P.,  77.57  ;     water  per  h.  p.  per  hour,  19.71  Ibs. 

It  will  be  noticed  that,  in  the  last  test,  the  load  on  the  en- 
gine was  greater  with  the  jacket  out  of  use  than  with  it  in  use, 
which,  however,  would  change  the  results  but  slightly. 

These  results  show  all  the  steam  used  by  the  engine,  the 
water  of  condensation  from  the  jacket  being  included  in  the 
figures. 

160.  The  Temperatures  and  Pressures  of  steam  in  the 
jacket  must  undoubtedly  have  an  important  influence  on  its 
economic  value.  Where,  as  is  usual,  the  same  or  a  slightly 
greater  pressure  is  carried  in  the  jacket  as  in  the  engine  during 
the  induction-period,  the  drain  of  heat  into  the  metal  must  be 
little  or  none,  after  the  first  effect  of  che  initial  condensation  is 
passed,  and  up  to  the  point  of  cut-off.  By  raising  the  pressure 
in  the  jacket,  as  is  sometimes  done,  by  the  use  of  an  auxiliary 
boiler,  or  by  throttling  the  steam  entering  the  cylinder,  a  dif- 
ference of  temperatures,  a  temperature-head,  may  be  obtained 
which  will  cause  a  more  prompt  restoration  of  the  chilled  cylin- 
der to  the  normal  maximum  temperature,  and  will  produce  a 
drain  of  heat  into  the  cylinder  throughout  the  induction-phase, 
an  increase  of  drying  and  in  work-effect  during  expansion,  and, 
also,  a  greater  waste  during  the  exhaust-stage. 

Evidently  this  may  be  productive  of  either  increase  or  dimi- 
nution of  efficiency  of  fluid,  accordingly  as  the  gains  or  the 
losses  shall  be  found  to  be  augmented  more  or  less,  relatively, 


SUPERHEATING  AND   STEAM-JACKETING.  659 

and  as  the  net  result  is  thus  rendered  more  or  less  favorable. 
Similarly,  a  reduced  pressure  in  the  jacket,  as,  for  example, 
when  the  boiler-steam  passes  through  it  on  its  way  to  the 
steam-chest,  will  modify  the  final  effect  either  the  one  way  or 
the  other.  The  conclusion  from  general  experience,  thus  far, 
would  seem  to  be  that,  within  the  usual  limits  of  these  varia- 
tions, as  hitherto  practised,  the  jacket  works  better  with  higher 
pressures  and  less  satisfactorily  at  lower,  assuming  the  engine 
receives  dry  steam.  To  jacket  with  exhaust-steam,  as  has  been 
actually  sometimes  done,  would  seem  to  be  an  absurdity. 

Some  time  prior  to  1855,  Mr.  D.  K.  Clark  proposed  supply- 
ing the  steam-jacket  from  an  independent  boiler  at  a  pressure 
exceeding  that  of  the  main  boiler,  and  this  was  done  by  Mr. 
Spencer  and  others.* 

Experimental  data  relating  to  the  economy  obtainable  by 
the  use,  in  the  jacket,  of  steam  of  considerably  higher  tempera- 
ture and  pressure  than  that  in  the  cylinder  are  rare.  Mr.  Guzzi, 
of  Milan,  in  1886-7,  employed,  thus,  steam  of  about  180  pounds 
pressure  where  the  working  steam  was  only  55.f  The  engine 
was  of  but  26  horse-power ;  the  weight  of  feed-water  demanded 
was  19.5  pounds  per  horse-power  and  per  hour,  as  compared 
with  23.5  with  boiler-steam  in  the  jackets. 

1 6 1 .  The  Quality  of  the  Steam  and  Condition  of  the  Sur- 
faces must  have  an  important  effect  upon  steam-jacket  action. 
While  superheating  steam  previously  to  its  entrance  into  the 
engine  may  so  reduce  interior  wastes  as  to  render  the  jacket 
unnecessary,  it  is  also  unquestionable  that  very  wet  steam  may 
exaggerate  wastes  to  such  extent  as  to  make  the  jacket  com- 
paratively impotent  in  effecting  the  result  to  accomplish  which 
it  is  employed.  Also,  should  either  the  conductivity  or  the 
heat-capacity  of  the  metal,  or  the  transmitting  power  of  its 
surface,  be  varied,  the  need  of  a  jacket  and  its  effectiveness,  if 
applied,  will  both  be  modified.  Low  conductivity  and  small 
specific  heat  are  the  characteristics  desirable  in  the  material  of 

*  The  Engineer;  Lond. ;  Feb.  17,  1860;  p.  106. 
f  Revue  Universelle  des  Mines;  Sept.  1887. 


66(3  A  MANUAL    OF   THE   STEAM-ENGINE. 

a  cylinder  without  jacket ;  while  large  conductivity  and  small 
heat-capacity  are  the  ideal  conditions  where  a  jacket  is  em- 
ployed. 

We  may  therefore  conclude  that  drynessof  steam  is  impor- 
tant in  order  that  it  shall  produce  minimum  tendency  to  waste  of 
heat  by  storage  in  the  metal  of  the  cylinder,  and  that  a  thin 
"  liner"  is  desirable  with  a  jacket ;  while  any  expedient  which 
will  reduce  the  absorbing  and  storing  power  of  the  interior  sur- 
faces of  the  cylinder- walls  will  prove  useful.  To  secure  the 
first  result,  liners  are  now  customarily  made  of  comparatively 
thin  steel.  Experience  shows  that  the  polishing  of  the  inner 
surfaces  of  the  cylinder,  coating  them  with  non-conductors,  or 
bathing  them  in  oil — a  somewhat  expensive  process — will  pro- 
duce the  last-mentioned  effect.*  It  is  probably  practicable 
to  find  methods  of  securing  a  gain  by  suitable  treatment  of 
the  heads  of  the  cylinder  and  the  sides  of  the  piston,  and  the 
working  of  the  engine  effects  the  polishing  of  the  cylinder, 
proper,  which  is  perhaps  next  best  to  giving  these  parts  non- 
conductivity. 

The  effective  action  of  the  jacket  cannot  even  begin  until 
the  process  of  evaporation  of  moisture,  by  its  heat-supply,  has 
ceased.  Hence  the  efficiency  attainable  by  its  action  depends 
upon  the  early  cessation  of  that  evaporation  during  the  induc- 
tion or  the  expansion  period,  and  the  prompt  conversion  of  the 
steam  into  the  superheated,  or  at  least  dry,  state. 

Incrustations  probably  often  exist  on  the  jacket  side  of  the 
cylinder-wall,  from  deposits  from  oil  or  remaining  from  ineffi- 
cient cleaning  of  the  casting  in  the  foundry,  which  seriously 
reduce,  in  such  cases,  the  effective  action  of  the  jacket. 

Where,  as  usually  in  multiple-cylinder  engines,  the  range  of 
expansion  is  considerable,  and  the  Rankine  and  Clausius  form 
of  cylinder-condensation  results  in  liquefaction  to  the  extent  of 

*The  Author  has  devised  a  system  of  treatment  of  interior  surfaces  with  first 
acid,  then  with  drying  oil  or  other  suitable  substance  having  low  conductivity 
and  specific  heat  per  unit  of  volume,  which  method  the  experiments  of  Profes- 
sor Carpenter  and  of  Mr.  Chamberlain  show  to  be  capable  of  reducing  their 
wasting  action  more  than  forty  per  cent.  See  Trans.  A.  S.  C.  E. ;  1890. 


SUPERHEATING  AND  STEAM-JACKETING.  66 1 

ten  or  fifteen  per  cent,  the  intermediate  receiver  has  an  office 
to  perform  as  a  separator  and  drying-chamber,  as  well  as  in  the 
adjustment  of  pressures ;  and  it  receives  the  products  of  this 
condensation  increased  by  all  that  due  to  the  cooling  through 
external  conduction  and  radiation  of  the  cylinder  from  which 
it  takes  the  exhaust. 

162.  Jacketing  the  Piston  is  sometimes  practised,  notwith- 
standing the  practical  difficulties  attending  it,  and  is  stated 
to  have  been  first  successfully  attempted  by  M.  Normand, 
of  Havre,  in  France,  and,  later,  by  Mr.  Davidson  in  Great 
Britain.  Where  the  system  of  piston-jacket  drainage  can  be 
made  certain  and  effective  in  its  operation,  this  will  prob- 
ably prove  advantageous  —  as  much  so  as  jacketing  the 
heads,  a  comparatively  common,  and  always  desirable,  ar- 
rangement. 

The  cylinder-heads  and  piston  are  the  parts  most  affected 
by  the  variations  of  temperature  which  cause  those  wastes  to 
check  which  jackets  are  introduced.  They  are  subject  to  as 
wide  a  range  of  variation  of  temperature  as  are  the  clearance 
and  port  spaces.  They  are  usually  comparatively  rough,  and 
therefore  peculiarly  active  transmitters  of  heat.  Again:  at 
the  point  of  cut-off  their  surfaces  usually  constitute  by  far  the 
larger  portion  of  all  areas  exposed  to  pressure  and  temperature 
changes.  The  advisability  of  jacketing  both  heads  and  of  ad- 
mitting steam  to  the  interior  of  the  piston  is  thus  sufficiently 
obvious ;  the  only  objection  and  drawback  being  the  difficulty 
of  supplying  steam  and  securing  thorough  drainage.  These 
conclusions  would  seem  to  be  also  justified  by  experience,  so 
far  as  it  goes. 

Where  the  heads  of  the  cylinders,  but  not  the  piston,  are 
jacketed,  it  is  obvious  that  reduced  clearances  should  give 
improved  performance ;  since  the  heat  in  the  head  would  act 
to  a  certain  extent  effectively  in  drying  the  surfaces  of  the  pis- 
ton when  close  together,  and  the  more  so  as  they  the  more 
closely  approach  each  other.  It  would  seem,  on  all  accounts, 
that  if  any  portion  of  the  cylinder  be  jacketed,  it  should  be  the 
heads  and  steam-passages. 


662  A    MANUAL    OF   THE   STEAM-ENGINE. 

163.  Proportions  of  Engines  having  Jackets. — Assuming 
the  jacket  to  be  of  good  design  and  construction  and  properly 
managed,  it  has  been  seen  that  its  activity  and  its  efficiency 
are  largely  determined  by  the  proportions  of  the  engine  and 
the  quality  of  the  steam  entering  the  working  cylinder.  Of 
the  latter,  enough  has  already  been  said.  The  relation  of 
diameter  to  length  of  stroke  evidently  determines  what  propor- 
tion of  heat-wasting  surface  exists  in  cylinder-heads  and  sides 
of  the  piston. 

Evidently,  to  secure  best  effect,  these  proportions  should 
vary  with  the  type  of  engine.  Jacketing  on  the  sides  and  not 
on  the  heads  is  best  where  diameter  of  cylinder  is  small  and 
the  stroke  long ;  if  the  heads,  and  especially  if  heads  and  pis- 
ton, be  jacketed,  on  the  other  hand,  the  reverse  proportions, 
larger  diameter  and  shorter  stroke,  give  better  effect. 

Clark  concludes,  after  a  comparison  of  jacketed  and  un- 
jacketed  cylinders,  both  on  long-  and  on  short-stroke  simple 
engines,  that  the  evidence  so  gathered  "  proves  what  has  long 
been  acknowledged — the  economical  advantage  of  superheat- 
ing the  steam  ;  and,  more  remarkably,  the  striking  disadvan- 
tage of  short-stroke,  as  versus  long-stroke,  cylinders.  .  .  .  The 
relatively  large  absorbing  surfaces  of  the  covers  and  the  piston 
of  short-stroke  engines  are  disturbing  influences  which  affect 
the  operation  of  the  steam  in  the  cylinder  to  a  greater  extent, 
proportionally,  than  in  long-stroke  cylinders."  *  He  adds  later  : 
"  Large  second  cylinders  proportionally  to  first  cylinders,  in  the 
ratio  of  4  or  4^  to  I,  may  be  employed  with  economy  when 
the  cylinders  are  thoroughly  steam-jacketed  ;  but  they  are 
unfavorable  for  economy  when  the  cylinders  are  only  partly, 
or  not  at  all,  jacketed. "f 

Mr.  Druitt  Halpin,  computing  the  quantities  affecting  cylin- 
der-wastes in  a  standard  triple-expansion  engine,  obtained  the 
following : 


*  Steam  engine  ;  vol.  I.  p.  577. 
f  Ibid.,  p.  581. 


SUPERHEATING  AXD   STEAM-JACKETLKG.  663 

S.S.Para,                                                High.  lnt«m.  Low. 

Diameter  of  cylinders,  inches 19  35  53 

Stroke,  inches. 33  33  33 

Steam  pressure  per  gauge,  IDS. 146 

"      temperature,  maximum,  Fahr. .     364° 

in  cylinders. 384°  266°  199° 

Diff.              "             "           "        .. 16°  98°  165° 

Volume  of  cylinders,  cu.  in. 9,356  31,750  72,804 

Area  of  surface  of  cylinders,  sq.  in 1,970  3,629  5,497 

Ratio.     ™luroe 4.75         8.75      13.25 

jacket-surface 

«      temperature-range 
volume  X  surface  * ' 

The  last-stated  quantities  are  taken  as  fairly  measuring  the 
relative  liability  to  waste  and  advisability  of  jacketing.* 

164.  The  Defects  of  Steam-jacketing  usually  result  in 
faulty  drainage.  In  some  cases,  no  effective  drainage  or  circu- 
lation of  steam  through  them  is  possible ;  in  other  cases,  this 
circulation  is  secured  by  carrying  the  steam  through  the  jacket  • 
into  the  cylinder,  with  all  its  burden  of  water  of  condensation ; 
a  process,  often  probably,  of  exaggeration,  rather  than  of  reduc- 
tion, of  wastes.  Provision  for  exit  of  air  is  often  not  well 
attended  to,  and  spaces  are  sometimes  found  hi  the  interior 
which  form  basins  holding  standing  pools  of  water  indefinitely. 
As  remarked  by  an  engineer  familiar  with  such  difficulties: 
"  To  secure  the  advantages  of  the  steam-jacket,  it  is  not  suffi- 
cient to  merely  place  around  the  cylinder  a  casing  that  may 
contain  steam.  Care  must  be  taken  that  this  jacket  always 
does  contain  steam.  Few  but  those  who  have  actually  tried 
it  fully  appreciate  how  soon  a  jacket  may  be  rendered  ineffec- 
tive by  the  accummulation  of  air  or  of  water."  f 

A  sensible  proportion  of  the  water  in  the  jacket  may  be 
due   to  external   radiation.     Experiments   on   the   engine   at 


*  Proc.  lost.  M.  E.,  1887 ;  p.  59. 
f  Lood.  Eng-g:  Aug.  3,  1877:  P-  88. 


664  A  MANUAL   OF   THE   STEAM-ENGINE. 

University  College,  London,  showed  that,  in  that  special  case, 
80  per  cent  of  this  water,  or  0.471  out  of  0.587  pound  per 
minute,  was  thus  produced.  Only  2O  per  cent,  0. 1 1 1  pound, 
or  0.6  pound  per  indicated  horse-power  per  hour,  was  due  to 
true  jacket  action.* 

The  failure  to  remove  the  sand  of  the  cores,  thoroughly, 
from  the  jacket-space  and  from  the  surface  of  the  enclosed 
cylinder  or  "  barrel  "  may  sometimes  produce  such  reduction  of 
heat-transmission  to  the  working  steam  as  to  reduce  the  effi- 
ciency of  the  jacket  or  possibly,  in  some  cases,  reverse  its  action 
as  an  economical  device. 

What  may,  perhaps,  be  termed  the  effect  of  a  negative 
jacket-action  is  illustrated  by  Clark's  experience  on  locomotives. 
The  office  of  the  jacket  is  to  supply  heat  to  the  cylinder  to 
keep  up  its  temperature  during  all  the  fluctuations  of  pressure 
of  the  working  fluid  within  it,  and  thus  partly  to  ameliorate 
the  wasteful  action  of  the  heat-conducting  material  of  which 
it  is  composed.  In  locomotive  practice,  the  cylinders  of  out- 
side connected  engines  are  exposed  to  the  refrigerating  influ- 
•  ence  of  the  air-currents  sweeping  past  them,  while  en  route, 
and  thus  to  the  precisely  opposite  action.  Clark  says : 

"  The  action  of  the  steam  in  the  outside  cylinder  is 
broadly  distinguished  from  that  of  the  steam  in  the  inside 
cylinder."  f 

165.  Experimental  Results  are  not  wholly  satisfactory, 
despite  the  fact  that  they  are  numerous  and  varied.^: 

Professor  Schroter,  experimenting  in  his  own  laboratory 
at  Munich  on  a  simple  engine  of  the  Sulzer  type,  28omm  in 
diameter  and  of  65omm  stroke  (u  inches  by  25!),  determined 
the  effect  of  its  jacket  at  varying  ratios  of  expansion,  the 
steam  passing  through  the  jacket  on  its  way  to  the  cylinder. 


*  Lond.  Eng'g;  Oct.  2,  1885. 

f  Railway  Machinery,  1851;  pp.  82-84.  On  the  Behavior  of  Steam,  Proc. 
Inst.  C.  E.;  No.  1910;  vol.  LXXII;  1882-3. 

JSee  Authorities  on  the  Steam-jacket;  R.  H.  Thurston;  Trans.  A.  S.  M.  E.; 
Nov.  1890. 


SUPERHEATING  AND   STEAM-JACKETING.  665 

One  head  was  also  jacketed.     The  points  of  cut-off  were  as 
below,  and  the  gains  by  the  jacket  are  stated  therewith  :  * 

53  Rev.  39  Rev. 

Cut-off..,.     O.I     0.2     O-3     04     O.5        O.I         O.2        0.3     0.4     0-5 

Gain  pr.ct.is./  12.25  8.96  4.57  (?)     18.85  16.80  14-00  8.72  6.05 

These  figures  indicate  a  gain,  at  high  ratios  of  expansion, 
of  15  to  nearly  20  per  cent,  the  largest  amounts  being  given  at 
the  lowest  speeds,  and  that  gain  progressively  decreasing  with 
reduction  of  values  of  the  ratio  of  expansion.  An  increase 
of  speed  of  about  30  per  cent  gives  an  economy  of  about  20 
per  cent  at  shortest  cut-offs,  and  of  nearer  50  per  cent  at  low 
expansions,  where  the  expenditure  of  steam  in  ratio  to  power 
is  greater,  while  the  percentages  of  total  waste  are  less. 

In  the  case  of  the  best  work  which  the  Author  has  yet 
(1891)  seen  reported.  Professor  Schroter  obtained  from  a  triple- 
expansion  engine  of  200  horse-power,  steam  at  156  pounds 
pressure,  the  remarkable  figure  of  12.2  pounds  of  dry  steam 
entering  the  engine  per  I.  H.  P.  per  hour.f  This  corresponds 
to  a  duty  of  a  trifle  over  162  million  ft.-lbs.  per  100  Ibs. 
coal  at  an  evaporation  of  10  to  i,  or  of  146  million  at  9  to  I. 
The  efficiency  of  machine  was  88  per  cent  nearly.  The 
jackets  condensed  a  large  percentage  of  the  steam,  thus  prov- 
ing their  effective  working.  The  total,  about  20  per  cent, 
was  distributed  thus:  In  the  first  cylinder-jacket,  2.2  per 
cent ;  second  and  intermediate  receiver,  6.4  per  cent ;  in  third 
and  receiver,  10.7  per  cent;  the  drain  of  heat  into  cylinders 
being  greater  as  their  mean  working  pressures  and  tempera- 
tures fell. 

M.  Schneider,  of  Creusot,  made  numerous  experiments, 
extending  over  a  period  of  six  months,  upon  a  Corliss  engine, 
at  the  Creusot  works,  the  results  of  which  were  reported  by  M. 
Delafond  in  the  following  year.£  In  these  experiments  careful 

*  Correspondence. 

tZeits.  des  Ver.  Deutscher  Ingenieure,  vol.  xxxiv.;  Load.  Eng.,  Dec.  5, 1890. 
p.  660, 

\  "Essais  effectues  sur  one  machine  Corliss;"  Annales  des  Mines,  Sep- 
tember, October,  1884. 


666  A   MANUAL   OF   THE   STEAM-ENGINE. 

examination  was  made  of  the  disputed  useful  effect  of  the 
steam-jacket,  with  what  M.  Delafond  considers  satisfactory 
results.  The  jacket  covered  the  cylindrical  portion  of  the 
engine  only. 

The  results  of  these  elaborate  and  carefully  conducted  in- 
vestigations, so  far  as  they  relate  to  the  steam-jacket,  are  the 
following: 

"  The  jacket  reduces  the  expenditure  the  more,  at  equal 
ratios  of  expansion,  as  the  pressure  is  higher ;  its  effect,  impor- 
tant at  7.75  atmospheres,  with  condensation,  becomes  very 
slight  at  2.5. 

"  The  economy  due  to  the  jacket  is  the  less  at  the  same 
pressure  as  the  effective  power  is  the  greater ;  i.e.,  as  the  ex- 
pansion is  less. 

"  It  is  found  advantageous  to  employ  in  the  jacket  steam 
of  higher  temperature  than  that  in  the  engine  cylinder." 

The  gain  by  the  jacket  in  these  experiments  was  usually 
not  far  from  15  or  20  per  cent  under  ordinary  conditions  of 
operation. 

Major  English  found  that  even  jacketing  the  steam-pipe  in 
engines  tested  by  him  sometimes  increased  their  efficiency  5 
per  cent  and  over,  so  sensitive  is  the  expansive  steam-engine 
to  variations  of  quality  of  steam.* 

One  of  the  most  satisfactory  of  recent  determinations  of 
the  value  of  the  steam-jacket  on  compounded  engines  is  that 
of  Professor  Osborne  Reynolds,  of  Owens  College,  Manchester, 
employing  the  triple-expansion  engines  of  the  Whitworth 
Laboratory,  f  (See  Frontispiece.) 

The  three  independent  engines  combined  in  the  compound 
machine  were  of  the  following  dimensions : 

Cylinder. 
Diam.  Stroke. 

No.  I 5    inches  10    inches 

"     2 8       "  10       " 

"     3 12       "  15       " 

Air-pump  on  No.  3 9       "  4^     " 

Feed-pump i£     "  2       " 

*  Trans.  Insi.  M.  E.,  1887.  f  Proc.  Brit.  Inst.  C.  E.,  Dec.  10,  1889. 


SUPERHEATING  AND   STEAM-JACKETING.  66/ 

All  were  jacketed,  sides  and  head ;  steam  was  carried  at 
200  pounds  per  square  inch,  and  boiler  pressure  was  maintained 
in  all  the  jackets. 

The  results  were  the  following,  with  and  without  the 
jackets  in  use : 

With  Jackets.  Without. 

Coal,  per  horse-power  per  hour. .    1.33  to    1.50      1.62  to    1.81 
Water 12.68"  14.10    15.90"  17.30 

The  effect  of  radiation  was  determined,  and  found  some- 
what considerable.  Deducting  this  waste,  the  figures  stand  : 

With  Jackets.  Without. 

Coal 1.21  to    1.30         i. 54  to    1.77 

Water 11.90"  12.30       15.10"   16.60 

This  is  a  most  satisfactory  approximation  to  the  ideal  en- 
gine and  to  minimum  wastes. 

In  this  remarkably  economical  engine  the  loss  by  shutting 
off  the  jackets  was  from  25  to  over  35  per  cent  in  fuel-con- 
sumption ;  or  from  25  to  30  per  cent  in  water-expenditure. 

Of  the  total  heat  received,  exclusive  of  radiation,  19.4  per 
cent  was  converted  into  work  with  jackets  in  action,  and  but 
1 5  without ;  a  difference  of  over  23  per  cent  of  the  first  quan- 
tity, or  29  of  the  latter.  The  ideal  engine,  under  similar  ther- 
modynamic  conditions,  would  have  utilized  23  per  cent. 

The  effect  of  the  jacket  on  the  high-pressure  cylinder,  where 
the  difference  of  temperature  between  jacket-steam  and  initial 
was  small,  was  found  to  be  slight  as  affecting  cylinder-conden- 
sation. In  No.  2,  the  effect,  with  a  difference  of  temperatures,  in 
this  respect,  of  80°  Fahr.,  that  condensation  was  reduced  from 
30  to  5  per  cent;  while  in  No.  3,  with  a  difference  of  180° 
Fahr.,  such  condensation  was  sensibly  zero  and  the  "  satura- 
tion expansion-curve,"  assumed  by  Rankine  to  be  attainable 
by  this  use  of  the  jacket,  was,  perhaps,  for  the  first  time  pro- 
duced. 

The  following  are  data  and  results,  reported  by  Mr.  Buel, 


668 


A    MANUAL   OF    THE   STEAM-ENGINE. 


as  obtained  in  trials  of  an  engine  corresponding  to  the  ideal 
case  summarized  in  the  Appendix:* 

NON-CONDENSING  ENGINE,  WITH  STEAM-JACKET  AND 
SATURATED  STEAM. 


Number  of 
Experiment 

Diameter  of 
Cylinder,  inches. 

Stroke. 
Inches. 

learance,  per  cent 
of  piston- 
displacement. 

Absolute  Initial 
Pressure,  pounds 
per  square  inch. 

Apparent  Cut-off, 
fraction  of  stroke. 

11 

K 

Cu  ^ 

Effective 
Horse-power. 

Steam 

hourly, 
per 
effective 
horse- 
power. 
Pounds. 

U 

I 

II8.8 

•13 

450 

152.6 

25-7 

2 

118 

.16 

450 

170.9 

25-4 

3 

92.4 

•23 

435 

I53-I 

23-5 

4 

22 

43-5 

3-7 

92.9 

•3 

439 

185.8 

24.1 

5 

118.5 

•58 

455 

211.  6 

24-8 

6 

49.9 

.1 

439 

134-7 

50.4 

The  influence  of  size  of  engine  on  the  necessity  and  effi- 
ciency of  the  jacket  is  well  shown  in  the  experience  of  makers 
of  slow-moving  multiple-cylinder  engines,  who  sometimes  find 
that  it  affects  the  economical  operation  of  their  small  engines 
appreciably,  while  insensible  in  its  action  on  large  machines. 
The  same  makers  find  it,  nevertheless,  necessary,  or  at  least 
advisable,  to  place  them  on  their  most  powerfulYnachines  on 
account  of  their  effectiveness  in  reducing  the  danger  arising 
from  the  presence  of  water  in  their  cylinders  when  the  exhaust 
is  closed  early  to  secure  full  compression. 

166.  Conclusion  relative  to  Jacketing. — From  what  has 
preceded,  it  is  sufficiently  obvious  that  if  jackets  are  used,  as 
is  advisable,  at  least  in  the  case  of  slowly  running  engines, 
care  should  be  taken  to  meet  the  following  essential  conditions 
of  efficient  and  economical  working: 

(1)  The  jacket  should  be  provided  with  ample  supply-pipes 
and  with  effective  traps  or  other  drainage  arrangements,  and  for 
air  as  well  as  water.     If  the  jacket  can  be  made  to  drain  back 
to  the  boiler,  that  plan  should  always  be  adopted. 

(2)  They  should  be  kept  supplied  with  steam  at  a  pressure 


Am.  Machinist  ;  Sept.  1888. 


SUPERHEATING  AND   STEAM-JACKETING.  669 

fully  equal  to  that  in  the  boiler.     It  is  probably  wise  to  jacket 
all  the  cylinders  of  a  multiple-cylinder  engine. 

(3)  All  surfaces  exposed  to  full-pressure  steam  sh  Duld  be 
jacketed,  if  practicable. 

(4)  The  jacket   itself   should  be  very  carefully  and  thor- 
oughly lagged,  and  so  made  secure  against  serious   external 
waste  of  heat. 

(5)  Provision  for  safe  expansion  and  contraction  should  be 
very  carefully  made. 

(6)  It  should  be  seen  that  the  jacket-steam  has  everywhere 
complete  contact    with  the  inner   or  working    cylinder,  and 
that  all  water  precipitated  therefrom  may  promptly  and  com- 
pletely drain  away. 

(7)  The  walls  of  the  cylinder  or  "  liner  "  should  be  as  thin  as 
practicable,  and  yet  safe ;  all  core-spaces  should  be  free  and 
clear ;  all  core-sand  thoroughly  removed  ;  no  pockets  should 
exist  in  which  water  may  gather ;  and  all  fits  and  joints  should 
be  made  with  extreme  care. 

A  jacket  through  which  the  steam  entering  the  cylinder 
should  pass  would  have  a  great  advantage  in  efficiency  of  heat- 
transfer  ;  but  unless  the  entrained  water  and  condensed  steam 
could  be  completely  removed,  it  would  cause  counterbalanc- 
ing and  probably  greater  losses,  as  compared  with  the  usual 
arrangement,  by  carrying  that  water  into  the  engine  to  exag- 
gerate wastes. 

In  any  case,  whenever  the  jacket-waste,  as  measured  by  the 
condensation  therein,  exceeds  the  amount  by  which  the  inter- 
nal waste  is  reduced  by  its  action,  the  jacket  is  useless,  or  even 
a  disadvantage. 

The  character  of  the  steam,  as  has  been  seen,  has  a  great 
influence  on  the  activity  and  economical  value  of  the  jacket, 
and  the  resultant  effect  is  due  to  quality  of  steam  quite  as 
much  as  quality  of  design  and  construction  of  jacket.  The 
main  points  are : 

(l)  If  the  steam  is  so  wet  that  it  and  the  cylinder-walls 
cannot  be  dried  before  the  end  of  the  expansion-period,  espe- 
cially if  the  jacket  is  thus  rendered  active  during  the  exhaust- 


6/0  A    MANUAL    OF    THE   STEAM-ENGINE. 

period,  it  may  waste  more  than  it  saves,  and  thus  may  have 
even  a  negative  value. 

(2)  If  so  dry  or  so  far  superheated  that  the  cylinder-waste 
would    be,  without  the   jacket,    no   greater   than   the  normal 
jacket-waste   with  the    same  steam,   the  value  of   the   jacket 
will  be  zero. 

(3)  If,    in  the  latter   case,  cylinder-wastes  without   jacket 
are,  as  is  usual,  greater  than  the  normal  jacket-waste  for  the 
same  engine,  with  the  same  steam,  the  net  value  of  the  jacket 
will  be  a  positive  quantity  proportional  to  the  magnitude  of 
this  difference. 

In  compound  or  multiple-cylinder  engines,  as  a  rule,  the 
temperature-head  driving  heat  from  the  jacket  into  the  cylin- 
der increases  as  the  pressures  successively  decrease,  in  the 
series  of  cylinders,  and  the  activity  of  its  action  is  thus  simi- 
larly increased.  It  may  sometimes  prove  that  the  plan  of 
securing  higher  pressures  in  the  high-pressure  engine  jacket  and 
graded  lower  pressures  on  the  others,  each  jacket  being  kept 
at  a  higher  temperature  than  the  steam  entering  its  own  cylin- 
der, may  prove  advantageous. 

The  jacket  may  prove  of  great  value  with  slow-moving 
engines  and  high  ratios  of.  expansion,  but  it  is  certainly  not 
usually  so  with  high  speeds  of  rotation  or  small  expansion. 
Since  the  active  useful  period  of  the  jacket  is  mainly  during 
the  early  part  of  expansion  only,  no  drain  into  the  cylinder 
being  possible  during  the  induction-period,  and  its  action  at 
the  end  of  expansion  and  during  exhaust  involving  waste,  the 
value  of  the  jacket  becomes  the  more  questionable  as  that 
active  useful  period  is  the  less. 

In  all  cases,  and  under  all  conditions,  the  use  of  a  steam- 
jacket  is  "  a  violation  of  a  fundamental  law  of  maximum 
efficiency  of  heat-engines,  which  requires  that  they  should 
receive  all  their  heat  at  the  maximum  and  give  it  out  at  the 
minimum  temperature,  and  not,  as  in  the  case  of  an  engine 
with  a  steam-jacket,  at  temperatures  between  these,  and  at 
times  when  the  heat  imparted  lessens  efficiency,  which  it  evi- 
dently must  do  at  and  near  the  end  of  the  stroke."  It  is  a 


SUPERHEATING  AND   STEAM-JACKETING.  67! 

necessary  evil,  justified  only  by  the  conditions  affecting  the 
use  and  the  construction  of  the  engine.  The  advantage  to  be 
derived  thus  varies  according  to  circumstances,  and  the  jacket 
may  not  only  sometimes  be  useless,  but  wasteful.  The  neces- 
sity for  a  careful  study  of  the  conditions  of  use,  of  care  in  its 
application,  and  of  exact  determination  of  its  value,  is  evident. 

167.  Superheated  Steam  as  a  Working  Fluid  can  prob- 
ably never  be  used  in  the  ordinary  steam-engine,  and  even 
superheating,  in  its  legitimate  function  of  reducing  liability  to 
interior  wastes,  is  employed  comparatively  infrequently.     It  is 
not  used  as  a  working  substance  for  the  reason  that,  in  order 
that  it  may  retain  the  gaseous  state  throughout  the  expansion- 
period,  it  must  be  superheated  initially  to  a  higher  temperature 
than  is  found  ordinarily  safe  or  practicable ;  or,  otherwise,  a 
way,  as  yet  undiscovered,  must  be  found  to  so  modify  the 
engine  itself  as  to  permit  its  safe   use  and  at  the  same  time 
to  prevent  those  wastes  of  heat  which  now  so  promptly  con- 
vert the  steam,  at  entrance,  from  the  superheated  to  the  satu- 
rated or  wet  condition. 

Could  it  be  employed  as  a  working  fluid,  however,  its  phys- 
ical characteristics  would  be  more  nearly  those  of  the  gases  ; 
it  would  insure,  possibly,  a  similarly  high  thermodynamic 
efficiency,  and  would  possess  the  characteristic  advantage  of 
high  tension,  at  the  same  time  with  high  temperatures,  initially, 
and  would  thus  permit  the  use  of  a  comparatively  small  volume 
of  engine,  and  thus  the  attainment  of  that  high  efficiency  of 
mechanism  which  is  now  the  distinguishing  excellence  of  the 
steam-engine.  That  this  may  some  time  be  accomplished  may 
be  perfectly  possible.  In  such  event  the  engine  would  com- 
bine the  high  thermodynamic  efficiency  of  the  gas-engine  with 
the  high  efficiency  of  machine  of  the  contemporary  steam- 
engine.  According  to  Hirn,  steam  becomes  steam-gas,  and  so 
remains,  when  the  superheating  exceeds  about  9°  C.  (16°  F.). 
Siemens  found  this  margin  to  be  18°  F.  at  the  boiling-point 
under  atmospheric  pressure. 

168.  The    Steam-engine  using  Superheated  Steam  is 
simply  an   engine  in  which  the  working   fluid,    by  previous 


6/2  A   MANUAL    OF   THE   STEAM-ENGINE. 

superheating,  is  rendered  a  more  satisfactory  working  sub- 
stance, with  a  certain  nearly  unaltered  range  of  temperature 
and  expansion  ;  one  in  which  the  expansion  is  rendered  more 
nearly  adiabatic,  and  the  conditions  of  maximum  thermody- 
namic  efficiency  are  more  nearly  attained.  The  condensation 
of  steam  at  entrance  is  reduced  in  amount  ;  but,  ordinarily,  at 
least,  the  fluid  is  still  more  or  less  wet  at  the  point  of  cut-off, 
and  continues  nearly  at  the  saturation-point  throughout  its 
whole  expansion-period.  Superheating  is  thus,  as  commonly 
practised,  simply  a  method  of  economizing  by  reduction  of 
interior  waste. 

The  higher  the  temperature  of  superheating  is  carried 
above  that  of  saturation,  within  usually  practicable  limits,  the 
more  complete  is  this  improvement  of  working  quality  of  the 
steam,  the  less  the  waste,  and  the  higher  the  efficiency  of  the 
working  fluid.  Could  this  elevation  of  temperature  be  carried 
far  enough,  the  steam  might  surrender  all  heat  demanded  from 
it  to  raise  the  walls  of  the  cylinder  up  to,  or  above,  the  tempera- 
ture of  saturation,  without  itself  becoming  condensed,  and  it 
might  thus  eliminate  that  kind  of  waste  entirely,  substituting 
for  it  the  comparatively  small  cylinder-wastes  of  a  gaseous 
working  substance.  Could  the  "adheating"  be  carried  still 
further,  the  working  fluid  would  be  a  gas  of  high  tension,  but 
of  low  temperature  as  compared  with  the  gases  worked  in  the 
other  forms  of  heat-engine. 

Superheating  the  steam  transferred  from  boiler  to  engine 
thus  results  in  the  supply  of  a  fluid  which  may  surrender  a  cer- 
tain portion  of  heat,  measured  by  the  product  of  its  specific 
heat  as  a  gas  into  the  range  of  superheating  and  into  its 
weight,  to  the  metal  of  the  working  cylinder  without  the  pro- 
duction of  initial  condensation.  If  this  quantity  is  equal  to  or 
greater  than  the  loss  of  heat  during  expansion  and  exhaust, 
there  will  be  no  initial  condensation,  and  the  waste  from  the 
high-pressure  cylinder  will  be  nearly  that  due  to  the  passage  of 
a  gas  through  it  under  similar  conditions  of  temperature  and 
expansion, — a  comparatively  small  quantity,  since  any  substance 
in  the  gaseous  state  possesses  low  conductivity  and  slight 


SUPERHEATING  AND   STEAM-JACKETING.  673 

power  of  absorption  and  storage  of  heat.  Should  the  super- 
heating be  in  excess  of  this  amount,  the  steam  will  not  begin 
to  condense  until  a  later  period,  perhaps  not  at  all,  the  only 
demand  being  now  for  heat  to  supply  the  amount  required  to 
keep  the  steam  dry  and  saturated  while  expanding  and  doing 
work.  If  the  superheating  be  less  than  the  first-mentioned 
quantity,  initial  condensation  will  be  reduced,  but  not  entirely 
prevented.  It  is  probably  never  the  fact,  in  practice,  that  it  is 
possible  to  secure,  safely  and  economically,  so  much  superheat- 
ing as  is  needed  to  keep  the  steam  dry  throughout  the  stroke.* 
In  any  case  of  use  in  the  multiple-cylinder  engine,  the 
quantity  of  heat  represented  by  the  superheating  will  be  a 
gauge  of  the  amelioration  of  wastes  by  internal  transfer  of 
heat  in  every  cylinder  of  the  series.  The  steam  leaving  the 
high-pressure  cylinder  will  be  to  that  extent  drier  than  it 
would  otherwise  be ;  and  this  will  be  true  of  the  succeeding 
cylinder  or  cylinders.  Were  there  no  other  disappearance  of 
heat  than  that  due  to  cylinder-condensation,  superheating  at 
the  first  of  the  series  would  give  superheating  at  each  of  the 
others.  In  so  far  as  condensation  doing  work,  such  as  was 
pointed  out  by  Rankine  and  Clausius,  takes  effect,  and  so  far 
as  other  wastes  by  transfer  without  transformation  occur,  to 
that  extent  will  the  gain,  as  observed  in  successive  passages 
from  cylinder  to  cylinder,  be  reduced ;  though  the  improve- 
ment of  the  working  conditions  will  be  none  the  less  real. 
Each  cylinder  will  have  wetter  steam  than  the  preceding,  in 
proportion  as  the  condensation  doing  work  and  the  losses  by 
conduction  and  radiation  increase,  as  a  total,  cylinder  by  cyl- 
inder. Superheating  at  the  high-pressure  cylinder  will  produce 
a  favorable  effect  all  through  the  series,  including  the  low-pres- 
sure cylinder.  Cylinder-condensation  will,  nevertheless,  cumu- 
latively increase  through  the  series,  in  consequence  of  the  fact 
that  the  wetter  the  steam  entering  any  one  cylinder  the  more 
the  condensation  and  the  wetter  that  leaving  it,  both  by  this 

*  In  one  case  reported  to  the  writer  an  initial  superheating  of  500°  F.  was 
required  to  give  50°  F.  superheating  at  exhaust ;  100°  F.  has  usually  been 
considered  a  practical  maximum  superheat. 


6/4  A    MANUAL    OF    THE    STEAM-ENGINE. 

initial  increase  of  humidity  and  by  the  additional  moisture 
coming  from  the  Rankine  and  Clausius  phenomenon,  and  from 
the  loss  by  transfer  to  surrounding  bodies.  This  last  action 
will,  however,  be  the  less  observable  and  the  less  important  in 
its  effect  as  the  moisture  of  the  entering  steam  and  the  mag- 
nitude of  the  waste  by  initial  condensation  become  greater. 

The  compound  engine  offers  peculiar  facilities  for  super- 
heating effectively,  since  the  steam  may  be  reheated  between 
the  cylinders,  and  thus  kept  comparatively  dry  with  lower 
maximum  temperature  than  in  the  simple  engine  ;  or,  other- 
wise stated,  with  the  same  range  of  temperature,  the  working 
substance  is  a  more  perfect  fluid  for  its  purpose.  This  has 
been  effectively  practised  by  Cowper  in  Great  Britain,  and  by 
Corliss  and  by  Leavitt  in  the  United  States.  The  best  work 
on  record  has  since  been  reported  where  this  expedient  has 
been  adopted, 

In  some  instances,  as  in  the  Worthington  "  high-duty  " 
engine,  the  "  reheating  "  is  obtained  by  the  use  of  "  prime  " 
steam  from  the  boiler  in  a  "  re-heater  "  constructed  like  a  sur- 
face-condenser, the  water  of  condensation  flowing  back  to  the 
boiler  at  nearly  the  temperature  of  the  latter. 

Reported  experiments  by  Mr.  Barrus  on  engines  using 
superheated  steam  lead  him  to  question  its  production  of  an 
economy  in  usual  cases,  even  of  effective  drying,  exceeding 
about  ten  per  cent.  His  data  show  the  effect  of  a  small  range, 
as  from  15°  to  25°  Fahrenheit,  to  be  slight  ;  while  superheating 
60°  to  80°  reduces  the  cylinder-wastes  one  half  or  two  thirds  : 
results  fairly  to  have  been  anticipated  in  view  of  general  ex- 
perience and  the  economics  of  the  case.  For  such  cases  as  the 
latter  he  obtains  as  the  internal  waste 


per  cent; 

a  =  0.7,  nearly,  for  the  best  cases,  when  for  saturated  steam 
a  =  O.iO  or  a  =  0.15.  For  the  former  class  we  find  a  =  0.9  to 
a=Oi2  where,  with  saturated  steam,  a  —  0.12  or  (7  =  0.15. 
This  gain  by  superheating  is  thus  made  not  far  from  one  half 


SUPERHEATING  AND   STEAM-JACKETING.  675 

the  total  internal  wastes,  or,  in  common  cases,  about  ten  per 
cent  net  on  total  expenditures  of  steam. 

169.  The  Limit  in  Superheating  is,  to-day,  considered  to 
be  practically  somewhere  inside  of  the  temperature  500°  F. 
( 260°  C.),  or  within  a  range  of  not  much  above  100°  F.  (56°  C.) 
above  the  now  usual  maximum  temperature  of  saturation.  If 
this  amount  of  adheating  can  be  secured,  steadily  and  with 
certainty,  no  serious  difficulties  are  anticipated ;  but  at  higher 
points  on  the  scale  the  burning  out  of  superheaters  and  the 
difficulties  of  cylinder-lubrication  are  such  as  are  likely  to  in- 
timidate both  engineer  and  owner. 

The  desirable  limit  of  superheating  is  determined,  for  the 
purposes  now  in  view,  by  the  amount  of  initial  condensation  to 
which  the  steam  is  liable  if  supplied  in  the  saturated,  or  the  wet, 
state.  Assuming,  for  example,  that  each  pound  of  wet  steam 
entering  the  engine,  bringing  with  it  1200  thermal  units  from 
the  fuel,  is  subject  to  loss  of  20  per  cent  of  its  latent  heat  by 
cylinder-condensation,  storing  about  250  B.  T.  U.  in  the  metal 
of  the  engine  :  since  the  specific  heat  of  gaseous  steam  is,  ac- 
cording to  Regnault,  0.4705,  it  is  seen  that  the  amount  of 
superheating  required  in  order  that  it  may  surrender  this  quan- 
tity of  heat  without  condensation  on  admission  must  be  ap- 
proximately 

250r=52i°Fahr.; 


0.4805 

which  is  far  beyond  the  practically  advisable  limit  as  fixed  by 
experience  to  date. 

Fortunately,  however,  this  is  not  necessary,  and  very  much 
less  adheating  is  amply  sufficient  to  accomplish  the  purpose 
in  view,  and  a  small  addition  by  superheating,  as  by  jack- 
eting, suffices  to  greatly  reduce  or  even  suppress  initial  con- 
densation. All  that  is  necessary,  in  this  case,  is  to  supply  an 
excess  sufficient  to  meet  the  demand  due  to  interior  wastes  of 
a  fluid  of  the  character  of  that  actually  at  the  moment  worked 
in  the  engine-cylinder.  The  drying  and  the  superheating  of 
the  steam  continually  improve  the  working  of  the  engine  in 


6/6  A    MANUAL   OF    THE  STEAM-ENGINE. 

two  distinct  ways:  (i)  giving  a  better  working  substance,  and 
thus  initially  reducing  interior  wastes ;  (2)  at  the  same  time 
meeting  more  completely  the  demand  for  heat  to  bring  up  the 
temperature  of  the  metal  to  that  of  the  prime  steam  before 
the  entrance  of  the  latter  into  the  cylinder  ;  thus,  each  process 
conspiring  with  the  other,  the  final  effect  is  large  economy 
with  small  expenditure. 

It  is  found  that  in  engines  of  moderate  size — -as  200  or  300 
I.  H.  P. — superheating  80°  F.  to  100°  F.  will  sometimes  check 
all  sensible  condensation.  This  indicates  that  superheated 
steam  is  in  such  cases  productive  of  cylinder-waste  to  the 
extent  of  not  more  than  about 

100  X  0.4805 


or  less  than  5  per  cent  ;  initial  condensation  being  entirely 
prevented.  Against  this  saving  by  the  reduction  of  waste 
perhaps  by  about  25  —  5  =  20  per  cent,  must  be  charged  the 
cost  of  superheating.  This,  when  the  extra  heat  is  obtained 
at  the  chimney-flue,  will  be  only  the  financial  charge  for 
first  cost  and  maintenance  of  superheaters,  and  by  simple 
extension  of  heating  surface,  and  will  be  only  its  proportion  of 
the  cost  of  steam-production,  in  other  cases  ;  or 

1000  +  48 

i  =  0.048, 

IOOO 

to  give  a  gross  gain  of  about  25  per  cent  in  steam  by  the  ex- 
penditure of  5  per  cent  additional  fuel,  or  a  net  gain  of  20  per 
cent  ;  a  not  infrequently  reported  case. 

The  experiments  of  Mr.  G.  B.  Dixwell  show  that  the 
amount  of  superheating  required  to  prevent  cylinder-con- 
densation is,  as  is  readily  seen  must  be  the  fact,  variable 
with  the  ratio  of  expansion,  with  the  quantity  of  steam 
used  and  the  proportion  of  surfaces  exposed  ;  these  varying  with 
the  point  of  cut-off.  He  found  that  in  a  small  engine,  steam 


SUPERHEATING  AXD   STEAM-JACKETING.  &JJ 

entering  the  engine  at  550^  F..the  temperature  retained  at  two- 
thirds  stroke  without  cut-off  was  500"  :  while  cutting  off  at  one- 
third,  the  temperature  dropped  to  274'.  Mr.  Dixweii  found  the 
higher  temperature  perfectly  safe,  even  at  low  ratios  of  expan- 
sion, and  considered  the  comparatively  high  absorbing  and  radi- 
ating power  of  the  vapor  of  water  an  important  element  in  pro- 
ducing its  economic  effects.*  The  gain  obtained  by  the  reduc- 
tion of  cylinder-condensation,  amounting  to  69  per  cent,  was 
computed  at  55  per  cent,  only  about  20  per  cent  of  its  true 
value  being  expended  in  its  extinction  :  while  the  gain  in 
power  was  at  the  same  time  16  per  cent.  The  fact  that  a 
temperature  of  superheat,  safe  at  high  ratios  of  expansion, 
might  not  be  safe  at  low  ratios,  was  very  clearly  exhibited-f 

The  extent,  however,  to  which  superheating  is  required  to 
check  a  known  amount  of  cylinder-condensation,  as  already 
seen,  cannot  as  yet  be  computed :  but  it  will  be  something 
intermediate  between  that  giving  heat-storage  in  the  fluid 
equivalent  to  that  observed  in  the  metal  and  zero.  The  pre- 
cise location  of  this  minimum  is  presumably  determined  by  the 
size  and  physical  characteristics  of  the  engine.  Recorded  data 
have  led  the  Author  to  assume  that  less  than  one  half  this 
maximum  will  often  suffice.  It  may  be  computed  thus : 

Let  /  =  latent  heat  of  the  saturated  steam ; 
m  =  that  fraction  initially  condensed ; 
Cp  =  048,  its  specific  heat  at  constant  pressure ; 
f  =  range  of  superheating  required  ; 
a  =  coefficient. 

Then 

f  =  ^=2amt,  nearly. (l) 

If  a  =  efe3$  as  above  assumed, 

f  =  ml,  nearly. (2) 

*  Him  had  already  set  this  maximum  safe  temperature  at  230*  C  (446*  F.). 
f  On  Cylinder-condensation  :  Trans.  Society  of  Arts ;  Boston.  1875- 


678  A  MANUAL    OF   THE   STEAM-ENGINE. 

For  example,  let 

/,  =    90  Ibs.  absolute  ; 
/=89oB.T.  U.; 

m  =  0.25  ;     a  =  0.5  ; 

then 

t'  —  ml=  0.25  X  890  =  223°  F.,  nearly. 

Thus,  roughly  speaking,  superheating  about  ten  degrees  for 
each  one  per  cent  initial  condensation  is  considered  sufficient. 

A  large  engine,  working  with  dry  steam  and  at  moderate 
speed,  should  not  waste  over  ten  or  fifteen  per  cent  by  this 
process ;  in  which  case  the  superheating  demanded  would  be 
computed  as  about 

/'  =  0.15  X  890  =  134°  Fahr.,  nearly. 

When  the  available  range,  /,  of  superheating  is  given,  the 
condensation  may  be,  on  the  above  assumptions,  reduced  by 
the  quantity 


Thus,  when  t'  =  100°  F.  and  m  =  0.25, 

m'  =  t'  -±  I  =  100  -=-  890  =  o.i  i, 

and  the  cylinder-condensation  may  be  reduced  to  something 
like 

m  —  m'  —  0.25  —  o.i  i  —  0.14; 

or,  in  the  case  of  the  larger  engine,  completely  with  a  surplus 
to  extend  the  period  of  pre-condensation  in  the  forward  stroke, 
in  the  first  case,  and  to  0.15  —  o.ii  '=  0.04  in  the  second.  It 
is  to  be  remembered,  however,  that,  even  with  complete  sup- 
pression of  condensation  by  superheating  the  steam,  heat-waste 
still  goes  on,  to  some  extent,  by  storage  and  transfer,  as  before. 
A  good  illustration  of  the  computation  of  efficiency  and 
steam-consumption  in  the  ideal  case,  in  which  it  is  assumed 
that,  to  suppress  initial  condensation,  the  superheating  must 
give  a  surplus  of  heat  precisely  equivalent  to  the  anticipated  or 
actual  waste  of  the  same  engine  using  saturated  steam,  will  be 
found  in  the  Appendix,  with  all  its  nomenclature,  formulas, 
data,  and  results.  The  following  is  a  comparison  of  computed 


SUPERHEATING  AND   STEAM-JACKETING. 


679 


with  actual  results  obtained  by  test  of  engines  presumed  com- 
parable : 

GAIN  BY  SUPERHEATED  STEAM  IN  NON-CONDENSING 
ENGINES  WITH   UNJACKETED  CYLINDERS. 


COMPUTED  RESULTS. 


RESULTS  FROM  EXPERIMENTS  OF  U.  S.  N. 
BOARD,  1877. 


T  = 

Pounds  of  Steam  hourly  per  ettec- 
tive  horse-power.                   II    «.   . 

founds  of  Steam  hourly  per  indi- 
cated horse  -power. 

=  2 

=  3 

fcU 

Satn-    !   Super-      nHfer 
rated        heated       "„' 

Percent  'i    ]?.3. 
ofdif-        

Satu-       Super- 
rated    ;    heated 

Differ- 

Percent 
of  dif- 

Steam. 

Steam          cute. 

ference. 

Steam. 

Steam. 

ence. 

ference. 

F.  S.* 

40.7 

38.8      1.9 

4-9 

1 

39-3 

36.6 

2-7 

7-4 

69 

48.2 

35-2 

13 

37 

i 

30-3 

26.6 

3-7 

13.9 

.46 

42.2 

31-7 

io.5 

33-1 

i 

2&.(J 

23.7 

4-9 

20.7 

i 

2S. 

22.1 

5-9 

26.7 

-25 

45-3 

35-8 

9-5 

26.6 

i 

30.2 

22. 

8.2 

37-3 

i 

34-9 

24-2 

10.7 

44-2 

VI 

42.2 

26.1 

16.1 

61.7 

"  F.  S."  =  full  stroke. 

The  only  special  assumption  made  in  the  ideal  case  is  that, 
as  in  the  ideal  jacketed  engine,  condensation  is  prevented  and 
the  steam  is  dry  and  saturated  at  the  end  of  the  expansion- 
period. 

SUPERHEATED-STEAM  CONDENSING  ENGINES  WITH 
UNJACKETED  CYLINDERS. 


THEORETICAL  RKSUXTS. 


PRACTICAL  RESULTS. 


Pounds  of  Steam  hourly  per  effec- 

<M 

tive  horse-power. 

i 

15 

Satu- 
rated 

Super 

heated 

S£-  ^-' 

Steam. 

Steam, 

ence-       ference. 

F.  S. 

35-9 

33-2 

2-7 

8.1 

t 

34-7 

31-2 

3-5 

II.  2 

i 

26.6 

22-4 

4-2 

:;.- 

i 

24-5 

19-3 

4.6 

23-8 

i 

23-4 

17-3 

6.1 

35-3 

i 

23.4 
24-6 
24.8 

15.9 
15-7 
13-9 

7-5 
8.9 
10.9 

47-2 
56.7 
78.4 

Pounds  of  Steam  or  Coal  hourly 
_  .              per  indicated  horse-power. 

||        ^ 

Super- 

Percent 

£••  **>    !     rated 

heated 

Diner-      Q^  dif- 

Steam. 

Steam. 

ence. 

ference. 

.65 

3-71 

2-99 

-72 

24-1 

.60 

3.07 

2-74 

•  33 

12.  1 

.58 

31-4 

26.1 

5-3 

20.3 

.50 

32.7 

25.1 

7.6 

30.3 

•-: 

3-38 

2.91 

-47 

16.2 

•35 

2-73 

2-33 

.40 

17.2 

.32 

30.6 

28.4 

2.2 

7-8 

68o 


A    MANUAL    OF    7 HE   STEAM-ENGINE. 


The  next  table  is  given  for  the  case  of  condensing  engines 
by  Mr.  Buel ;  and  the  following  cases  are  from  Bourne  :* 

GAIN  BY  USE  OF  SUPERHEATED    STEAM   IN  MARINE   ENGINES. 


Total  Coal—  Pounds. 

Vessel. 

Saturated 
Steam. 

Super- 
heated 
Steam, 

Differ- 
ence. 

Per  cent 
of 
difference. 

Alhambra,  Southampton  to  Lisbon  and  re- 

turn   
Colombo,  Southampton  to  Alexandria  and 

405,440 

275,520 

129,920 

47.2 

return  

2,287,280 

613,520 

26.8 

Norman,  Southampton   to  Cape    of  Good 
Hope  and  return  
Ceylon,  Southampton   to   Alexandria    and 

1,189,440 

365,120 

3°-7 

return    

3,364,480 

2,201,520 

1,072,960 

46.8 

Since  these  dates,  however,  the  increasing  pressures,  ad- 
vances in  general  efficiency  and  especially  high  temperatures 
and  wide  range  of  expansion,  which  have  become  common, 
have  greatly  reduced  the  margin  for  gain  by  superheating.  In 
multiple-cylinder  engines,  especially,  the  adoption  of  re-heating 
methods,  between  cylinders,  by  jackets  and  even  by  "  live," 
boiler,  steam,  afford  gains  of  important  amount,  and  without 
the  disadvantages,  costs,  and  risks  of  direct  superheating. 

It  is  evident  that,  as  long  since  observed  by  Professor 
Hirsch,  a  most  serious  obstacle  to  the  employment  of  super- 
heated steam  exists  in  the  difficulty  of  regulating  the  quantity 
of  added  temperature.  It  is  also  obvious  that,  to  secure  every 
desired  favorable  condition,  a  method  must  be  found  of  appor- 
tioning the  degree  of  superheating  to  the  varying  demands  of 
the  engine,  as  determined  by  variation  of  the  ratio  of  expan- 
sion, from  time  to  time,  and  by  the  quality  of  steam  entering 
the  superheater. 

170.  Experience  and  Testimony  derived  from  many  ex- 
periments prove  the  value  of  moderate  superheating.  Mons. 
Hirn  reports,  as  the  results  of  trials  in  which  he  was  aided  by 


*  Treatise  on  the  Steam-engine,  by  John  Bourne;  1859. 


SUPERHEATING  AND   STEAM-JACKETING. 


68 1 


Messrs.  Dwelshauvers-Dery,  Grossteste,  and  Hallauer,  the  fol- 
lowing figures,  checked  by  Cotterill : 


SUPERHEATING. 

Extent.  /,  r 

Steam  superheated 157°  F.  61  4 

o°  54  4 

95°  56  7 

o°  55  7 


Per  cent 
of  waste. 

7-8 
I5.6 
I2.4 

21.8 


The  engines  built,  in  1832,  for  H.M.S.  Dee  demanded 
3.9  pounds  of  coal  per  I.  H.  P.  per  hour  with  saturated  steam, 
but  only  2.74  pounds  at  a  temperature  exceeding  that  of  satu- 
ration by  1 88°,  the  pressure  being  but  9  pounds.  The  Ceylon 
in  1860  gained  over  25  per  cent  by  superheating  about  100° 
F.;  the  Alhambra  gained  over  25  per  cent ;  the  Nepaul  about 
50  per  cent.* 

The  following  table,  compiled  by  Mr.  Dixwell  from  the  ex- 
periments of  Isherwood,  Emery,  and  Loring,  shows  well  the 
advantages  of  superheating  steam  within  the  safe  limit  and  at 
moderate  pressure.  It  thus  appears,  as  remarked  by  Mr.  Dix- 


Boiler- 

Pounds 

pressure 

of  Coal 

Name  of 
Steamer. 

Kind  of 
Engine 

Kind  of 
Steam  used. 

above 

Atmos- 

Actual 
Cut-off. 

consumed 
net  horse- 

Lbs per 

power 

sq.  in. 

per  hour. 

Michigan.  .  . 

Simple 

Saturated 

21 

•29 

4-5 

Mackinaw.    . 

" 

" 

35 

•43 

3-49 

Eutaw  .... 

" 

" 

27 

•54 

3-84 

Dexter  .... 

" 

" 

67 

.29 

3-4 

Dallas  

" 

" 

32 

•31 

3-8 

Bache  

j  Compound  ) 

M 

80 

.20 

2.66 

(    Jacketed     f 

Rush  

•' 

" 

69 

.16 

2.71 

Georgeanna. 

Simple 

Superheated 

33 

.31 

2.58 

Adelaide  

" 

" 

34 

•39 

2.45 

Mackinaw..  . 

c* 

" 

39 

•29 

2.48 

Eutaw  

28 

•54 

2.99 

Proc.  Brit.  Inst.  C.  E.;  vol.  xix.  p.  473. 


682  A  MANUAL    OF   THE   STEAM-ENGINE. 

well,  that  the  Georgeana,  Adelaide,  Mackinaw,  and  Eutaw, 
working  with  superheated  steam  at  moderate  pressures  and 
without  jackets,  surpassed  the  performances  of  jacketed  com- 
pound engines  working  with  much  higher  pressures  and  much 
greater  expansion. 

Conclusions  relative  to  superheating  may  evidently  be  arrived 
at,  and  without  question,  favorable  to  the  moderate  use  of 
superheating.  It  is  certain  that,  as  long  since  pointed  out  by 
Him,  this  method  is  more  thorough  in  its  reduction  of  cyl- 
inder-wastes than  jacketing,  or  even,  if  it  can  be  carried  suffi- 
ciently far  with  safety  in  the  simple  engine,  than  "  compound- 
ing." It  gives  dry  steam  initially,  and  throughout  the  expan- 
sion-period, and  is  not  productive  of  loss  during  the  exhaust- 
period,  a  phase  in  the  engine-cycle  during  which  wastes  by  the 
jacket  are  especially  active  where  it  has  not  left  the  steam  and 
the  walls  of  the  cylinder  dry  at  the  end  of  expansion.  The 
jacket  keeps  these  surfaces  approximately  at  the  boiler  tem- 
perature, even  during  this  last  most  wasteful  part  of  the  whole 
revolution  ;  while  superheated  steam  produces  its  effects  just 
when  and  where  they  are  needed,  and  does  not  thus  exaggerate 
losses  during  exhaust. 

Where  the  superheating  is  effected  by  the  saving  of  heat 
which  would  otherwise  have  passed  up  the  chimney,  as  is  often, 
perhaps  usually,  the  case,  the  gain  at  the  engine  is  a  real  gain. 
When,  however,  the  superheater  simply  produces  dry  and 
superheated  steam  where  it  would  otherwise  have  been  wet, 
and  by  the  application  of  heat  that  might  otherwise  have  been 
employed  in  the  boiler  in  the  production  of  saturated  steam, 
the  apparent  gain  must  be  reduced  by  this  expenditure  and  the 
net  and  real  saving  is  correspondingly  lessened.  This  net  sav- 
ing is  to  be  measured  in  fuel,  rather  than  steam,  consumption. 
A  net  gain  amounting  to  from  50  to  75  per  cent  the  apparent 
saving  has  been  attained  in  practice,  in  such  cases,  by  a  reduction 
of  cylinder-wastes  to  a  very  small  quantity,  as  to  five  per  cent, 
or  even  less. 

There  exists,  for  every  engine,  a  set  of  conditions,  and 
especially  a  quality  of  steam,  which  make  the  jacket  most 


SUPERHEATING  AND  STEAM-JACKETING.  683 

effective.  With  sufficiently  superheated  steam,  the  jacket  is 
not  needed  at  all :  it  would  add  nothing  to  the  efficiency  of  the 
engine ;  with  wet  steam  it  might  be  possible  that  the  loss  from 
the  jacket  during  the  terminal  portion  of  the  expansion-period, 
and  throughout  the  exhaust,  might  exceed  the  gain  in  the 
earlier  part  of  the  active  period  of  jacket-action,  and  during 
the  compression.  With  intermediate  conditions,  a  maximum 
gain  by  the  jacket-action  might  be  observed.  This  maximum 
may  be  expected  to  be  found  when  the  steam  is  at  least  fairly 
dry  and  the  ratio  of  expansion  considerable. 

Once  the  surfaces  become  dry,  they  can  yield  but  little 
heat  to  the  enclosed  vapor,  and  the  jacket  can  then  promptly 
bring  them  up  to  approximate  the  temperature  of  the  entering 
steam.  This  action  is  that  desired  of  the  jacket,  in  fact,  and 
the  more  completely  it  is  effected  and  the  less  the  waste  of 
heat  in  the  process  the  better. 

171.  Compression  and  Clearances  have  rather  definite 
relations ;  nevertheless  they  are  not  related  by  purely  kinematic 
principle  ;  even  if  the  usual  treatment,  by  such  a  process,  have 
any  really  important  bearing.  Were  there  no  exchange  of 
heat  to  be  anticipated,  between  the  working  fluid  and  the  walls 
of  the  cylinder,  the  proper  treatment  would  be  to  secure  such 
compression  as  would  just  fill  the  "dead-spaces'*  to  initial 
pressure.  But  not  only  does  this  transfer  occur  and  thus  modify 
the  case :  but  the  purely  dynamic  exigencies  of  operation  may 
enter  as  important  factors  in  determining  these  relations. 

The  "  clearance"  in  the  steam-engine  is  the  small  space  nec- 
essarily left  between  the  piston  and  head,  at  the  end  of  stroke, 
to  evade  danger  of  their  being  brought  into  actual  contact, 
through  wear,  accident,  or  carelessness  in  adjustment  of  length 
in  taking  up  wear  on  the  connecting-rod  "  brasses,"  or  in  other 
bearings  "  in  series"  with  it.  The  "  dead-spaces"  include  this 
clearance  and  the  port-spaces ;  which  latter  are  often  large. 
The  total  varies  from  below  2  per  cent  up  to  6,  8,  or  even  10 
per  cent  of  the  volume  of  the  cylinder.  Since  these  spaces 
must  be  filled  with  steam  at  every  stroke,  they  constitute  a 


684  A    MANUAL   OF   THE   STEAM-ENGINE. 

source  of  waste ;  except  they  are  filled  from  the  back-pressure 
steam  by  compression. 

Thus  the  waste  due  to  clearance  maybe  reduced  and  in  some 
cases  made  zero  by  suitable  compression.  Where  expansion 
is  incomplete,  it  will  be  found  that,  dynamically,  the  best 
result  is  secured  when  the  compression  is  somewhat  in  excess 
of  the  expansion-ratio,  and,  under  usual  conditions,  not  far 
from  50  per  cent  higher.*  The  thermal  effect  in  reduction  of 
internal  wastes  is  sufficiently  important,  however,  to  make  it 
advisable  to  aim  at  compressing,  in  most  cases,  probably,  well 
up  toward  boiler-pressure,  regardless  of  this  aspect  of  the 
problem.  The  dynamic  loss,  in  engines  with  large  clearance, 
as  6  to  10  per  cent,  may  be  as  much  as  10  and  15  per  cent 
without  compression,  and  but  one  third  these  figures  with  best 
adjustment. 

Zeuner's  principle,  affecting  the  action  of  the  clearance  and 
port  spaces,  is  the  following : 

In  any  case,  complete  compression,  if  practised,  annuls  the 
wasteful  effect  of  those  spaces  with  complete  expansion. 

Complete  expansion  occurs  when  the  pressure  at  its  end 
is  equal  to  the  back-pressure  ;  complete  compression  is  that 
which  carries  the  final  pressure  of  compression  up  to  the 
initial  pressure  of  admission.  Assuming  that  the  law  of  com- 
pression is  the  same  as  that  of  expansion,  and  also  assuming 
the  law  of  Mariotte  : 

Let  vl  =  the  volume  of  steam  entering  at  the  initial  press- 
ure /, ; 

v  =.  the  volume  of  the  dead-space ; 
PO  —  the  back-pressure. 

The  expansion  will  be  complete  when  the  pressure  at  the 
end  of  expansion  is  equal  to  /0,  which  requires  that  the  vol- 
ume at  that  point  shall  be  greater  than  at  the  beginning  of 

*  See  Cotterill;  p.  258. 


SUPERHEATING  AND   STEAM-JACKETING.  685 

expansion   in  the   proportion    -'.      In  a  cylinder  having  no 
clearance,  the  work  per  stroke  of  piston  is,  in  such  case. 


When  there  exists  a  dead-space,  r,  the   initial  volume  of 

p 
steam,  i\ ,  first  fills  a  portion,  v  —  v—,ol  this  space,  and  then 

drives   the    piston    through   a    volume,   t\  —  v  -f-  v—  ,    during 

ft 
admission.     The  work  at  full  pressure  is 

/•»•—/•»+ A* 

The  total  volume  of  steam  at  the  end  of  the  admission  is 

v,  -  «'^  ; 
while  the  work  of  expansion  is  measured  by 

log  j  (A*'.  +  A*0- 

The  volume  of  steam  at  the  commencement  of  the  exhaust 
is 

Ai 


the  volume  at  the  beginning  of  the  compression  is,  in  order  that 

it  shall  be  complete,  evidently  v  -'. 

A 

The  work  of  the  back-pressure  is  then 

^°    "     ~~  V  ~  V        =  **Vl  ~  P<?>  ~  P*V  ' 


686  A    MANUAL    OF   THE   STEAM-ENGINE. 

and  the  work  of  the  compression  will  be 

A*  log*. 

The  net  amount  of  work  done  is  thus,  finally, 


^-r-A^  +  iA^i+A*') 

~~  Piv\  —  Piv  —  P<P  —  PoV  ^g 


It  is  perfectly  obvious,  however,  that  the  action  of  the 
cylinder-walls  may  completely  invalidate  all  conclusions  drawn 
from  this  purely  kinematic  principle. 

Where  it  is  necessary  to  take  cognizance  of  the  clearance 
and  its  effect,  it  is  obvious  that  r,  the  true  ratio  of  expansion, 
has  the  relation  to  the  apparent  ratio,  r',  as  practically  meas- 
ured on  the  guides  at  the  instant  of  seating  of  the  cut-off  valve, 
for  example, 


cr* 


where  c  is  the  clearance-ratio. 

The  volumes  and  weight  of  vapor,  as  shown  by  the  indi- 
cator, will  be  greater,  in  the  case  of  an  engine  with  clearance, 
in  the  proportion  i  -f-  cr',  where  c  is  the  clearance-fraction. 
It  is  obvious  that  the  volume  traversed  by  the  piston  to  do  the 
same  work  must  be,  with  clearance,  greater  in  the  proportion 


SUPERHEATING  AND   STEAM-JACKETING.  687 

-,  and  either  the  size  of  cylinder  or  speed  of  piston  corre- 

spondingly increased.  The  efficiency  will  also  be  diminished 
in  a  slightly  less  ratio  than  that  of  increased  steam  used,  unless 
full  compression  be  adopted  ;  in  which  case  no  such  loss  occurs. 
A  comparison  of  the  weight  of  steam  demanded  in  the 
steam-engine  at  various  ratios  of  expansion,  as  affected  by 
clearance,  and  neglecting  the  influence  of  compression,  is  easily 
made. 

Let   r  =  ratio  of  expansion  ; 

c  =  ratio  of  clearance  to  stroke  ; 
s  =  stroke  of  piston  ;  A  =  its  area  ; 
iv  =  specific  weight  of  steam. 

Then  the  ratio  of  weight  of  steam  to  work  done  will  be 


for  the  engine  without  expansion, 


for  the  case  of  expanding  steam  ;  /,  and  /,  being  the  pressures 
at  the  beginning  of  expansion  and  during  exhaust,  measured 
from  a  vacuum,  and  n  is  the  ratio  of  the  mean  effective  press- 
ure to  the  difference/,  —  /,,  the  initial  effective  pressure. 
The  ratio  of  these  two  quantities,  (i)  and  (2),  is 


r"  - 
- 


The  following  tables  give  values  of  »  and  of  r",  as  calcu- 
lated by  Professor  Schroter.* 

*  Baverisches  Industrie-  und  Gewerbeblatt;  1881;  Heft  VL 


688 


A   MANUAL   OF   THE   STEAM-ENGINE. 


§     II      II      II      II      II      Ij     I 


1  II 


1  1 


00 
*S  "co 


O  O         mo 


* 


co  co       co  co 


«    T         t^O         T  r»         NT         O 


d  '     T 


TO        O   O         COO         « 
i-i  d       o'  d       d  <>      d 


r^-T       Oco       oc<         mM 
in  In        in  In        in  In        in  In 


in        °.  "^ 

d      >So 


(•in        co  T        M   co 
•>O         mo         inO 


O        00        00        00        o"  O        00 


q  co      c>  co     oo  e» 

T  in        co  in        co  in 


aa 


"     8 


!  1 


SUPERHEATING  AND  STEAM-JACKETIXG. 


689 


F 

II  11  1  1 

1  1 

•  I 

IS 

d 

f  M 

II  1  1  II 

-. 

if 

!  5* 

I  1  1 

II  II  II 

if 

=  3 

IS 

od 

~ 

II  II  1  !• 

i 

•n 

-~ 

—  C- 

1  1 
I 


< 

H 

£ 


f  1 1  1 1 


£  §S  SK  SI.  SS 

d  do  od  do-  do 


•»    o 

S  I 

S 


s  i 


:  :   : 


~  5f  S I  f  §  I  i1  |S  25  SS 

=   :  =   :  :   :  =   :  :   :  :   :  =   :  : 


d   do   do   d  d   =  ="   do"   =  d   d  o" 

— s? — ?^ — ^ — ^^ — 5^ — 5^ — ?s~ 

:T   f 'i   'i  ='   :' t   d  d   ~'z'z   :  *   =  1" 


o  II 

z   z  z 


z  z 


oo  ~^  5^  55  55  55  55  55 

d   =  d   d =   do   do   do   d  d   d d 


J  f  I   II   II   M   M   M   M 


II  II  II 


690  A    MANUAL   OF   THE  STEAM-ENGINE. 

The  main  value  of  high  compression,  as  is  seen  in  some 
types  of  engine,  certainly,  is  not  to  secure  that  nice  adjustment 
which  would  prevent  a  slight  waste  of  power  due  to  maladjust- 
ment of  the  ratios  of  expansion  and  compression,  but  to  secure 
a  smooth-running  engine  by  "  cushioning,"  in  such  manner  as 
to  take  up,  by  the  spring  thus  produced,  that  impact  and  jar, 
that  "  pound,"  otherwise  liable  to  occur  with  annoying,  if  not 
dangerous,  consequences,  every  time  the  crank  swings  past  the 
centre.  In  high-speed  engines  the  designer  carefully  adjusts 
the  volume  of  clearance  to  be  adopted,  with  this  end  in  view, 
making  the  "  dead-space  "  comparatively  large  to  insure  that 
the  work  of  compression  shall  furnish  the  needed  means  of 
absorption  of  the  energy  of  retardation. 

Still  another  and,  in  respect  to  efficiency,  even  more  influ- 
ential factor  in  the  determination  of  the  magnitude  of  the 
ratio  of  compression  is  the  fact  that  the  heat  of  compression 
tends  to  check  cylinder-condensation,  and  that  it  may  be  made 
really  effective.  This  would  dictate  that  compression  should 
be  carried  fully  up  to  boiler-pressure,  in  order  that  the  surfaces 
which  are  productive  of  interior  waste  may  be  heated  as  nearly 
as  possible  to  such  a  temperature  as  will  reduce  that  loss  to  a 
minimum. 

From  this  point  of  view  no  computation  is  required,  or  is 
yet  possible,  that  shall  exactly  determine  the  magnitude  of 
these  effects.  It  is,  however,  obvious  that  compression  to 
boiler-pressure  is  always  desirable,  and  that  the  volume  of  dead- 
spaces  should  be  such  as  will  make  the  work  of  compression 
approximately  equal  to  so  much  of  the  stored  energy  of  the 
reciprocating  parts  as  is  required  to  be  absorbed.* 

*  Leloutre  remarks:  "I  can  easily  demonstrate,  by  an  immense  number 
of  diagrams  and  of  calorimetric  observations  made  on  a  large  scale,  that  the 
law  of  Mariotte  is  radically  false  in  its  application  to  the  steam-engine.  This 

law  is  expressed  by  the  equation  — *=  -— ^.     Rankine  was  the  first,  I   think, 

Pn         /  Vm\lfl1 

to  propose  the  expression   — —  =  IT^/      •     More   recently   MM.    Him   and 
Cazin,  in  the  courses  of  thoroughly  scientific  investigations,  have  found  the 


SUPERHEATING  AND  STEAM-JACKETING.  69! 

It  is  evident,  further,  that  compression  is  a  necessary  and 
an  effective  adjunct  to  all  other  methods  of  economizing; 
although  the  magnitude  of  the  dead-spaces  and  the  waste  by 
clearance  is  a  matter  of  less  importance  with  the  multiple- 
cylinder  engines. 

So  essential  is  the  use  of  compression  to  insure  smooth 
action  in  high-speed  engines  with  their  large  inertia-effects  that 
their  usually  large  clearances  are  sometimes  even  purposely 
exaggerated  to  obtain  ample  cushioning.  In  such  makes  of 
engine  the  clearances  are  carefully  proportioned  with  this  pur- 
pose in  view.  Thus  Messrs.  H.  VVestinghouse  and  Rites  intro- 
duce a  "  clearance-chamber  of  carefully  determined  proportions 
between  the  two  cylinders  of  the  single-acting  compound  en- 
gine, which  space  is  constantly  open  to  the  small  cylinder,  in 
order  that  the  initial  and  compression  pressures  may  be  made 
equal.  The  action  of  the  engine  is  that  characteristic  of  the 
Woolf  or  receiyerless  engine,  and  the  result  of  this  arrange- 
ment is  that  the  compression  in  the  small  cylinder  is  made 
independent  of  the  load,  but  variable  with  the  steam-pressure, 
this  compression  always  beginning  when  the  low-pressure 
expansion  begins,  producing  the  distribution  shown  in  Fig. 
159,  the  diagram  being  that  used  in  designing  the  engine. 

In  this  diagram  three  variations  of  load  are  shown,  respec- 
tively, by  the  heavy,  light,  and  light-dotted  lines,  the  compression 


value,  for  superheated  steam,     *-  =    -^'     Butin  "^e  application  of  these 

last  formulas  to  cur  industrial  motors  they  will  be  found  even  more  incorrect 
than  the  law  of  Mariotte.  Through  numberless  researches  I  have  reached  the 
following  conclusion:  There  is  no  fixed  taw  of  expansion  in  these  engines;  or, 
rather,  the  general  law,  if  one  can  be  established,  varies  in  its  effects  from  one 
stroke  of  the  piston  to  another.  ...  I  have  already  demonstrated,  in  a  report 
on  the  superheated-steam-engine  of  Mons.  Him,  that  the  succession  of  press- 
ures during  the  expansion  is  represented  very  exactly  by  the  general  formula 

**  =  I  —  -I  f  in  which  the  index  a  is  generally  less  than  i,  and,  consequently, 
pm  *  V»' 

that  the  machine  has  slightly  more  power  than  the  constructors  consider  them- 
selves able  to  guarantee."  (Bulletin  de  la  Societe  Industrielle  de  Mulhouse; 
1873.) 


692 


A    MANUAL   OF   THE   STEAM-ENGINE 


of  each  commencing  at  c,  b,  and  a,  respectively,  but  following 
the  same  curve,  and  terminating  in  each  case  at  the  same  initial 
pressure,  M,  In  like  manner,  with  the  steam-pressure  raised 
to  N,  we  get  the  heavy-dotted  diagram,  in  which  cut-off  having 
taken  place  earlier,  compression  would  commence  earlier  at  d, 
but  terminating  at  the  new  initial  pressure,  TV.  Whatever  be 
the  exhaust-pressure  at  the  commencement  of  compression  in 
the  small  cylinder,  due  to  changes  of  load  or  of  boiler-pressure, 
it  is  automatically  compensated  by  shifting  the  point  of  com- 


FIG.  159.— FULL  COMPRESSION. 

pression  itself  to  such  a  position  as  will  insure  final  pressure 
equal  to  that  of  the  admitted  steam.  Expansion  in  the  large 
cylinder  should  commence  coincidently  with  compression  in 
the  small  cylinder. 

This  result  is  arrived  at  by  the  simple  combination  of  cor- 
rect valve-travel  and  proportion,  with  a  specific  and  constant 
clearance-volume  in  the  small  cylinder. 

In  this  case,  also,  the  clearance  and  compression  are  ad- 
justed to  compensate  that  loss  of  pressure  between  the  cylin- 
ders due  to  cylinder-condensation  in  the  initial  stage  in  the 
low-pressure  engine. 


SUPERHEATING  AND  STEAM-JACKETING.  693 

Where  the  two  pistons  are  secured  on  the  same  rod,  as  in 
most  tandem  compound  engines,  the  smooth  running  of  the 
engine  is  facilitated  by  the  aid  given  in  the  cushioning  of  the 
steam  in  the  high-pressure  cylinder, -wheiv. as.  in  condensing 
engines,  large  compression  in  the  low-pressure  cylinder  becomes 
difficult. 

Compression  was  not  used  by  Mr.  Corliss  in  his  engines, 
whatever  their  speed.  Mr.  Henthorn  advises,  for  Corliss  en- 
gines, a  compression  not  to  exceed  the  terminal  pressure  on  the 
expansion  line  for  condensing  engines,  and  an  excess  over  this 
pressure  of  about  five  pounds  for  non-condensing  engines.* 

The  loss  of  work  by  the  clearance  and  the  cushion-steam  is 
readily  computed  as  a  purely  dynamic  quantity  ;  but  the  real 
loss  by  clearance  and  the  thermodynamic  gain  by  high  com- 
pression are  not,  as  yet,  capable  of  computation  with  accu- 
racy. 

If  the  pressure  and  volume  of  the  steam  at  exhaust  are/,, 
v , ,  the  back-pressure  /, ,  and  the  volume  of  the  clearance-space 
vt ,  the  pressure  and  volume  of  the  cushion-steam  at  the  begin- 
ning and  end  of  compression,  and  the  ratio  of  compression,  re- 
spectively, /,^, ,  ppt ,  and  rc ,  the  work  of  compression  is,  very 
nearly, 

Ue  =  /,?'j  ( i  -f-  log,  rc) 

+  *>*$••          ••: 

hyperbolic  expansion  being  assumed.     The  work  of  expansion 
of  the  cushion-steam  is 


*  The  Corliss  Engine:  Henthorn  and  Thurber;  N-  Y.,  E.  P.  Watson.  i8gi. 


694 


A   MANUAL    OF   THE  STEAM-ENGINE. 


The  difference  in  work  lost  by  incomplete  expansion  of  the 
cushion-steam  is 


When,  to  insure  best  thermal  action  or  effective  cushioning, 
the  compression  is  made  complete  and/4  =/,, 


t  -  Uc'  =  /,*,  (log,  4  -  log,  4)  ; 


With  complete  expansion,  rc  =  r  ;  with  clearance  reduced 
to  zero,  vt  =  o  ;  in  either  case  Uc  —  UJ  =  o. 

The  effect  of  clearance  in  producing  a  difference  between 
the  real  and  the  apparent  ratio  of  expansion  is  exhibited  by  the 
following  diagram  and  tables  which  were  prepared  by  Mr.  Buel.* 


Perfect    Vacuum 


1   2  3   45   6   T  8   9  10  11  12  13 14  15  16  17  18  19  20  21 22  23  24 
FIG.  160. — EXPANSION-CURVES. 

A  clearance  of  5  per  cent  is  assumed.     For  the  effect  of  clear- 
ance  on  the  cut-off  and  ratio  of  expansion,  see  Appendix. 

*  Am.  Machinist;  Apr.  14,  1888,  p.  2. 


SUPERHEATING  AND  STEAM-JACKETIXG. 


695 


Fig.  160  is  a  diagram  showing  the  expansion  of  steam  in 
hyperbolic  curves,  at  the  points  of  cut-off  noted,  the  initial 
pressure  being  100  pounds  per  square  inch : 

(1)  In  a  cylinder  with  5  per  cent  clearance  (curves  in  full 
lines). 

(2)  In  a  cylinder  with  no  clearance-spaces  ('curves  in  broken 
lines). 

In  the  following  table  the  numbers  in  column  4  are  mean 
pressures,  corrected  for  back-pressure,  for  stroke  plus  clearance, 
and  the  numbers  in  column  5  are  the  mean  effective  pressures 
in  column  4,  corrected.  Compression  to  initial  pressure  reduces 
the  mean  effective  pressure,  but  the  steam  in  the  clearance- 
space  is  saved.  This  case  is  illustrated  in  the  diagram  by  the 
curve  KA,  the  clearance  being  AG. 


THEORETICAL  RESULTS  OF  Uasc  STEAM  ExrxsarELT— CORRECTED  FOR  BACK 
CLEARANCE  AXD  Ccsmox. 


:•:  Btalfai 


Costtooo*  to  £3  efeanam  sgwcet 


82.5  1.000.  1.00  1.050 

.762  S7.0  79.5  •  78.5  .952  1.051  jMf 

.524  86.2  68.7    67.1  .813  1.23     J — 

,  .365  73.3  55.8    53.6 ,  .650  1.54     .590 

|J8f  64.41 46.9  '  44.2  .5361.87     .561 

La06  53.2  35.7  i  32.5  .394   2.54     .550 

I  JOTI  46.5  29.0*25.5  .309   3.24     .567 

.!•::  38.8  •::  s    ::.4  :::  ±  74 


=  r        a  a       |j:=c  ^ 


.-•.  20.( 

.645  35.5 

.562  43.S 

.534  46.6 

.524  47.6 

.540  46.0 

•  •  » 


1.00 
1.05 


•-•-  " 

77.9' 1.000 

73.9  .949 

62.5  .802*1.25 
49.0 1  .629    1.59 

39.6  j  .508 '1.97 
27.9  j  .358   iW 
20.9  .969    3.T3 
ItAI  .164    6.10 


.5*) 

.-_•- 
.465 
.466 


I? 
II 


21.2 
37.5 
47.0 
50.7 
53.5 

'-:    I 


Another  method  of  treatment  is  the  following :  The  quan- 
tity of  steam,  q.  entering  the  cushion-spaces  is  the  difference 
between  that  required  to  fill  them  at  boiler-pressure,/,,  and 
that  compressed  into  them,  reduced  to  the  same  pressure ;  Le^ 
if  f,  is  the  "  dead-space," 

q  =  re  —  v, . 


696  A    MANUAL   OF   THE   STEAM-ENGINE. 

But,  assuming  hyperbolic  expansion, 


which  value  becomes  o  when  the  compression  is  complete,  and 
vc  —  v,. 

The  total  steam  admitted  up  to  the  point  of  cut-off  is 


The  larger  the  ratio  of  expansion  and  the  greater  the  vol. 
ume  vc,  the  more  serious  is  the  loss  due  to  incomplete  expan- 
sion of  the  cushion-steam  and,  the  clearance  being  given,  the 
useful  effect  of  increasing  pressure  becomes  less  and  less  as  the 
pressure  rises. 

The  greater  the  back-pressure,  the  less  the  ratio  needed  or 
desirable,  either  to  effect  complete  compression  or  to  annul 
the  waste  by  cooling.  Non-condensing  engines  are  given  in- 
significant  ratios  of  compression  as  compared  with  those  re- 
quired for  complete  compression  in  condensing  engines.  Other 
things  equal,  the  higher  the  initial  pressure,  the  less  should  be 
the  clearance.  Large  port  and  clearance  spaces  increase  the 
cost  of  the  engine,  as  they  decrease  the  net  useful  work  of  the 
machine,  both  by  actual  reduction  of  the  indicated  work  and 
by  increasing  the  waste-work  due  to  friction. 


SUPERHEATING    AtfJ)   STEAM-JACKETING.  697 

EXPANSION   OF  STEAM. 


offl. 

Initial 

Mean  total 

Quantity 

Per  cent 

r 

pressure,  pi. 

pressure,  /„. 

of  steam. 

saving. 

I 

IOO 

IOO 

IOOO 



1 

u 

96.4 

780 

22.0 

i 

M 

84-7 

590 

41.0 

i 

U 

70.0 

477 

52.3 

£ 

M 

59-7 

420 

58.0 

i 

U 

46.5 

358 

64.2 

i 

M 

38.5 

325 

67.5 

rS 

tt 

29.0 

288 

71.2 

Same,  allowing  17^  Ibs.  back-pressure : 

A 
i  100  82.5  1000  — 

£  "  78.9  780  22 

i  "  67.2  615  38.5 

i  52-5  523  47-7 

|  "  42.2  488  51.2 

*  "  29.0  473  52.7 

i  "  21.0  490  51.0 

r?  "  11.5  596          40.0 

172.  The  Binary-vapor  System  is  a  method  of  what  may 
be  termed  "  compounding  "  engines  with  transfer  of  heat  and 
without  transfer  of  working  fluid  from  the  high-  to  the  low- 
pressure  element  of  the  series.  The  general  principles  are 
thus,  in  the  main,  the  same  as  in  the  usual  form  of  multiple- 
cylinder  engine ;  but  with  important  differences  of  result  due 
to  practical  differences  of  physical  conditions  of  environment 
and  of  operation. 

While  the  principle  of  Carnot,  asserting  that,  thermodynami- 
cally,  all  working  substances  have  the  same  value  of  efficiency 
of  fluid  when  working  through  the  same  range  of  temperature 
in  adiabatic  expansion,  in  the  ideal  engine,  it  happens  to  be 
the  fact  that  it  is  often  practically  impossible  to  obtain  the 
ideal  conditions  of  maximum  efficiency  in  all  cases.  Some 
fluids  are  more  liable  to  loss  of  heat  in  actual  working 


698  A   MANUAL   OF   THE   STEAM-ENGINE. 

through  internal  and  external  conduction  and  radiation,  than 
others  ;  and  the  pressures  of  the  various  possible  working  sub- 
stances at  any  temperatures  vary  enormously  ;  vapors  of  ether 
and  chloroform,  for  example,  having  much  higher  pressures 
than  steam. 

A  defect  in  the  action  of  steam,  as  commonly  used,  is  that, 
at  high  temperature,  it  has,  if  saturated,  dangerously  and  even 
uncontrollably  high  pressures ;  while,  at  low  temperatures,  its 
pressure  falls  below  that  of  the  atmosphere  and  compels 
the  use  of  an  expensive  and  cumbersome  system  of  condensa- 
tion if  we  seek  to  transform  low-temperature  heat  into  work. 
The  binary-vapor  system  is  one  in  which  this  latter  difficulty 
is  sought  to  be  remedied  by  using  a  volatile  fluid  as  the  con- 
densing medium,  so  that  the  latter  may  be  vaporized  at  a  good 
working  pressure  by  the  condensation  of  the  former  and  may 
then,  in  turn,  be  used  in  a  supplementary  engine,  transforming 
a  new  and  sometimes  large  quantity  of  thermal  into  dynamic 
energy.  Thus  a  kind  of  "  compounding  "  results  in  the  substitu- 
tion of  a  second  engine,  "  in  series  "  with  the  first,  for  a  con- 
densing apparatus.  This  added  machine  must  necessarily  also 
be  made  a  surface-condensing  engine  in  order  that  its  always 
costly  and  sometimes  dangerous  working  fluid  may  be  saved  and 
used  over  and  over  again.  By  the  use  of  such  a  system,  the  gain 
due  to  decreased  cylinder-condensation  and  increased  range  of 
expansion,  combined,  may  prove  to  be  considerable,  when 
compared  with  the  economy  of  the  ordinary  steam-engine. 

The  following,  adopting  Rankine's  methods,  is  the  theory 
of  this  case  :  * 

Let/,  be  the  absolute  pressure  of  the  steam  at  its  admis- 
sion; 

?>j ,  the  volume  of  i  Ib.  of  it  when  admitted  ; 
rv^ ,  the  volume  to  which  it  expands. 

Let  //,  denote  the  available  heat  expended,  in  foot-lbs.  per 

Ib.  of  steam  ; 
U,  the  energy  exerted  on  the  piston  by  I  Ib.  of  steam. 

*  Rankine  ;  p.  145. 


SUPERHEATING  AND  STEAM-JACKETING.  699 

Then  the  heat  rejected  by  each  Ib.  of  steam,  and  given  up 
to  the  ether,  is 

H9  =  Ht-U.     .......    (i) 

To  find  what  volume  will  be  filled  with  ether-vapor,  the  ex- 
penditure of  heat  per  cubic  foot  of  ether-vapor,  at  the  pressure 
under  which  it  is  evaporated,//,  is  necessarily  lower  than  the 
temperature  at  which  the  steam  is  condensed  : 


T"^     .....    (2) 

where 

j.i 
L  =  T'  -j^r;  is  the  latent  heat  of  evaporation  of  one  cubic 

foot  of  ether-vapor  under  the  given  pressure  ; 
Jc1  =  399.1  foot-lbs.  per  degree  Fahrenheit,  is  the  specific  heat 

of  liquid  ether  : 

iy  is  the  weight  of  one  cubic  foot  of  ether-  vapor; 
T'  is  the  temperature  at  which  the  ether  is  evaporated,  and 
T'"  that  at  which  it  is  condensed. 

The  initial  volume  of  the  ether  evaporated,  per  Ib.  of  steam 
condensed,  is 


Let  ft'  denote  the  intended  final  pressure  of  the  ether- 
vapor,  and  p'"  its  mean  back-pressure  ;  about  5  Ibs.  on  the 
square  inch.  Then  by  means  of  the  formulae  for  steam,  already 
given,  substituting  the  constants  which  apply  to  ether,  we  may 
obtain  : 

The  ratio  of  expansion,  r/,  and  the  final  volume,  r'uf,  of  the 
ether  evaporated  per  Ib.  of  steam  ;  the  energy  exerted  by  that 
ether,  £/"',  and  the  ratio 

rV 


is  that  of  the  volume  of  the  ether-cylinder  to  that  of  the  steam- 
cylinder.  In  practice,  those  cylinders  are  usually  of  equal 
size,  or  the  ether-cylinder  somewhat  larger. 


700  A   MANUAL   OF   THE   STEAM-ENGINE. 

The  heat  per  Ib.  of  steam,  abstracted  by  the  cold  water  in 
the  ether-condenser,  is 

H.-U-U'  ........     (4) 

The  mean  effective  pressures  in  the  steam  and  ether 
cylinders  are 

U  U' 

and     —  -,.      .......    (5) 

rvl  rti 

But  the  amount  of  energy  obtained  by  the  addition  of  the 
ether-engine  to  the  steam-engine  might  be  obtained  by  con- 
tinuing the  expansion  of  the  steam. 

The  following  are  means,  computed  from  results  given  in 
the  report  of  M.  Gouin,  on  the  performance  of  the  steam  and 
ether  engines  of  the  Bre'sil  : 

Pressures  in   Pounds  on  the  Square  Inch. 
In  Boiler  or  Back-  Mean 

Evaporator.          pressure.         Effective. 

Steam  ............  43.2  7.6  n.6 

Ether  .............    31.2  5.3  7.1 

Total  M.  E.  P.  reduced  to  the  area  of  one  piston, 
the  areas  and  strokes  of  the  pistons  having 
been  the  same  .  .  .  ...............  .  ......  18.7 

It  appears  that  the  proportions  of  the  power  obtained  in 
the  cylinders,  respectively,  were  : 

11.6 
Steam  .........................      —=—  =  .62 

18.7 


Ether 


The  gain  of  power  by  the  addition  of  the  ether-engine 
is  not  so  great  as  this  shows  ;  because,  had  the  steam-cylinder 
been  used  alone,  the  back-pressure  would  have  been  in  all 
probability  about  4.6  instead  of  7.6  ;  so  that  the  mean  effective 
pressure  in  the  steam-cylinder  would  have  been  14.6  instead  of 


SUPERHEATING  AND   STEAM-JACKETING.  7OI 

1 1.6  ;  and  the  proportion  of  the  power  of  the  steam-engine  to 
that  of  the  binary  engine  would  have  been 

14.6  _ 

leaving 

1.00-77  =  . 23 

of  the  power  of  the  binary  engine,  as  the  gain  due  to  the  ether- 
engine. 

The  consumption  of  fuel  was  either  2.8  or  2.44  Ibs.  of  coal 
per  indicated  horse-power  per  hour,  according  as  certain  ex- 
periments made  under  peculiarly  adverse  circumstances  were 
included  or  excluded.  Rankine  adds  : 

"  The  binary  engine  is  not  more  economical  than  steam- 
engines  designed  with  due  regard  to  economy  of  fuel ;  but  by 
the  addition  of  an  ether-engine,  a  wasteful  steam-engine  may 
be  converted  into  an  economical  binary  engine" — a  conclu- 
sion which  is  sufficiently  obvious  from  the  fact  that  such 
figures  are  considered  rather  high  for  the  ordinary  compound 
steam-engine. 

A  binary-vapor  engine,  tested  by  Mr.  Haswell,  in  which  the 
auxiliary  fluid  was  carbon  disulphide,  gave  the  following  re- 
sults in  a  trial  in  which  the  operation  of  the  engine  was  con- 
tinued five  hours,  which,  as  that  period  involved  the  cleaning 
of  the  fire,  was  held  to  afford  time  for  a  test.* 

The  reported  data  are  as  below : 

Pressure,  steam — boiler 75.8  pounds 

"          shell.. 15.3       " 

"     vapor — engine 76          " 

"         "         mean,  by  indicator. .  31.35     " 

Water  evaporated 571  cubic  feet 

Revolutions  per  minute IOO 

Vacuum 9.85  pounds 

Coal  consumed 600 

Horse-power  indicated 86.64 

*  Trans.  Am.  Soc.  C.  E.;  1887;  also  Steam-engine  and  Boiler  Trials:  p.  454. 


7O2  A    MANUAL   OF   THE   STEAM-ENGINE. 

From  which  it  appears  that  steam  at  a  pressure  of  75.8 
pounds  per  square  inch  passed  through  the  automatic  regulat- 
ing valve  to  the  shell  surrounding  the  generator  at  the  reduced 
pressure  of  15.3  pounds,  due  to  a  temperature  of  250.4  degrees, 
produced  a  vapor  in  the  generator  of  76  pounds. 

The  consumption  of  coal  was  thus  reported  as  1.385  pounds 
per  indicated  horse-power  per  hour. 

These  results  confirm  the  indications  of  thermodynamic 
science,  that  substantially  as  good  work  may  be  done  with 
other  vapors  as  with  steam  ;  but  the  steam-engine  has  actually 
given  as  good  economical  results  as  those  here  reported,  and 
has  many  practical  points  of  superiority.  This  trial  was,  how- 
ever, too  short  to  be  taken  as  fully  satisfactory,  and  the  history 
of  these  devices,  so  far  as  known,  does  not  seem  to  encourage 
an  expectation  of  the  displacement  of  the  steam-engine  by 
their  introduction. 

The  data  and  results  obtained  by  Mr.  Barrus,  by  three  tests 
of  a  Campbell  ammonia-engine  and  boiler,  as  reported  to  the 
Campbell  Engine  Co.,  April  1887,  were  as  follow  : 


DIMENSIONS   OF  BOILER  AND   ENGINE. 

Boiler — One  horizontal-return  tubular,  set  in  brick-work. 

Diameter  of  shell 42  in. 

Length  of  shell 10  ft. 

Inside  diameter  of  tubes 1.75  in. 

Area  of  water-heating  surface 369.3  sq.  ft. 

Area  of  steam-heating  surface 318.8      " 

Area  of  grate-surface . . . , 9.17    " 

Collective  area  for  draught  through  67  tubes 1.12    " 

Ratio  of  water-heating  surface  to  grate-surface 40.3  to  I 

Ratio  of  steam-heating  surface  to  grate-surface 33.6  to  I 

Height  of  smoke-stack  above  grate 30  ft. 

Engine — Porter-Allen  automatic  cut-off,  single  cylinder. 

Diameter  of  cylinder 1 1.5  in. 

Stroke  of  piston 20      " 


SUPERHEATING  AND  STEAM-JACKETING.  703 

DATA  AND  RESULTS  OF  TESTS. 

Date 1887,  March  8,  March  9,  April  16. 

Duration  of  test hrs.  8  10  7.45 

Percentage  of  ashes,  etc....  per  cent  9.9  8.2 

Coal  per  hour  per  sq.  ft.  of 

grate Ibs.  19.09  15.27  16.07 

Boiler-pressure  above  at- 
mosphere   100  95.5  86.6 

Temp,  of  feed-liquid  en- 
tering boiler deg.  F.  167.6  167 

Temp,  of  gases  entering 

stack "  390  394 

Vacuum  in  feed-well inches  1 1.5         n 

Revolutions  of  engine  per 

minute revolu.  205.2  204.5  201.5 

Indicated  horse-power  de- 
veloped by  engine H.  P.  61.80  57-53  54 

Proportion  of  stroke  com- 
pleted at  cut-off .189  .211 

Proportion  of  stroke  com- 
pleted at  release .773  .791 

Proportion  of  return  stroke 
uncompleted  at  compres- 
sion    .307  .342 

Coal  consumed  per  indi- 
cated horse-power  per 
hour Ibs.  2.832  2.433  2.729 

All  the  fluids  which  have  been  proposed  or  employed  as 
substitutes,  wholly  or  in  part,  for  steam,  have  been  seriously 
objectionable  on  the  score  of  either  cost  or  danger  and  usually 
both.  None  has  yet  been  found  satisfactory  in  these  re- 
spects. 

Comparison  of  results  of  experience,  as  illustrated  by  the  pre- 
ceding facts  and  figures,  leads  to  such  final  conclusions  as  fol- 
low: 


704  A   MANUAL    OF   THE   STEAM-ENGINE.-. 

(1)  Experiment,  experience,    and    the   philosophy   of   the 
steam-engine  combine  to  indicate  that  the  limit  of  possible 
advance  in  their  economical  application  is  now  so  nearly  ap- 
proached that  further  progress  must  be  expected  to  be  both 
slow  and  toilsome. 

(2)  That  the  range  left  for  such  further  improvement  upon 
the  best  and  most  efficient  of  existing  engines  is  probably 
small,  and  the  difficulties  arising  in  the  attempt  to  reduce  it 
are  increasing  in  a  higher  ratio  than  progress  in  its  reduction. 

(3)  That,  while  wasteful  engines  may  be  improved  by  vari- 
ous expedients,  including  the  substitution  of  other  working 
fluids  than  steam,  either  wholly  or  partly,  no  other  vapor  has 
yet  been  found  to  give  an  economical  performance  exceeding, 
on  the  whole,  or  even  equalling,  that  obtained  with  the  best 
steam-engines. 


CHAPTER  VII. 
THE    MAXIMUM    EFFICIENCIES   OF    THE    STEAM-EN'GIXE. 

173.  The  Mathematical  Theory  of   Efficiencies    has 
been  comparatively  little  studied.     The  thermod ynamic  theory, 
and  the  efficiency  of  the  ideal  engine  free  from  all  other  than 
thermodynamic  wastes,  has  been  fully  developed  by  Clausius 
and  Rankine  and  their  successors  :  but  neglect  of  experimental 
and  mathematical  investigation  of  the  physics  of  the  case,  and 
consequent   ignoring  of   the  practically  important   conditions 
distinguishing  the  real  from  the  ideal  case,  has  often  led  to  seri- 
ous misconceptions,  and  to  enormous  losses  of  money,  in  the 
attempt  to  realize  in  practice   the   advantages   indicated    as 
attainable  by  the  pure  thermodynamic  treatment.    In  the  estab- 
lishment of  a  correct  and  practically  applicable  theory  of  effi- 
ciencies, it  is  not  only  essential  that  the  physical,  as  well  as  the 
purely  thermodynamic,  conditions  of  working  should  be  taken 
into  the  account :  but,  also,  that  the  several  efficiencies  should 
be  very  carefully  distinguished,  and  that  the  finance  of  prac- 
tical operation  should  be  no  less  carefully  studied.     The  latter 
division  of  the  subject,  in  fact,  includes,  and  depends  upon,  all 
the  preceding,  and,  to  the  user  of  the  engine,  presents  the  con- 
trolling considerations  and  the  essential  problem. 

174.  The  Several  Efficiencies  of  the  Steam-engine.* — 
In  the  design  of  the  steam-engine  the  engineer  has  frequent 
occasion  to  solve  certain  problems  relating  to  its  economical 
performance,  to  determine  what  proportions  of  engine  and 
boiler  are  best  adapted  to  give  maximum  economy  of  fuel  or 
of  money  under  certain  conditions  precisely  defined  in  advance. 

*  Trans.  Am.  Soc.  M.  E.  ;  1882. 

70S 


7O6  A   MANUAL   OF   THE   STEAM-ENGINE. 

Such  problems  may  usually  be  solved  by  the  determination  of 
the  ratio  of  expansion  producing  maximum  economy  under 
the  given  conditions. 

Several  problems  of  this  character  may  be  classed  together, 
all  of  which  relate  to  one  or  another  of  the  "  Several  Efficien- 
cies of  the  Steam-engine,"  as  the  Author  has  called  them. 

These  are : 

(1)  Tliermodynamic  Efficiency  of  Fluid. — This  is  measured 
by  the  ratio  of  work  done  by  the  working  substance  to  the 
mechanical  equivalent  of  the  heat  expended  on  it  to  do  that 
work.     In  the  perfect  engine-cycle  this  efficiency  is  measured 

by  the  quantity  — -;    the   range  of    temperature  worked 

through,  divided  by  the  maximum,  initial,  absolute  temperature 
of  the  fluid  entering  the  cylinder  of  the  engine. 

To  obtain  a  measure  of  the  thermodynamic  efficiency  of 
the  working  substance,  as  has  already  been  seen,  it  is  only 
necessary  to  measure  the  work  done,  as  by  the  measurement 
of  the  indicator-diagram,  and  compare  its  amount  with  the 
mechanical  equivalent  of  the  heat  expended  in  its  perform- 
ance. In  the  case  of  the  steam-engine,  this  requires  the  deter- 
mination of  the  volume  of  steam  and  its  weight,  at  the  point 
of  cut-off,  the  determination,  by  computation  or  from  the 
tables,  of  the  quantity  of  heat  required  in  its  production  from 
the  feed-water,  and,  finally,  the  division  of  the  work  shown  in 
the  diagram  by  this  quantity.  This  is  substantially  the  method 
adopted  by  Rankine,  in  the  first  construction  of  the  thermo- 
dynamic theory  of  the  heat-engines. 

In  real  engines  great  losses  occur  by  incomplete  expansion 
and  by  direct  transfer  of  heat  from  induction  to  exhaust  with- 
out production  of  work. 

(2)  Actual  Efficiency  of  Working  Substance. — This  is  here 
considered  to  be  that  observed  in  the  actual  operation  of  the 
engine  as  the  ratio  of  heat  conveyed  into  the  engine  by  the 
working  fluid,  and  acting   purely  thermodynamically,  to  the 
total  heat  entering  the  system. 

Various  working  fluids  have  different  values  in  this  respect. 


MAXIMUM  EFFICIENCIES  OF   THE   STEAM-EA'CIXE.     JO? 

Thus  a  gas  has  little  conducting  or  radiating  power,  can  sur- 
render but  little  heat  and  can  absorb  but  little,  in  its  contact 
with  the  parts  of  the  machine  in  which  it  is  employed,  while  a 
saturated  vapor  like  steam  may  take  it  up  with  comparative 
freedom  when  in  contact  with  hotter  substances,  and  can  reject 
it  with  enormous  rapidity  if  brought  in  juxtaposition  with  a 
cold  body.  The  latter  is  a  less  efficient  vehicle  of  heat  for 
thermodynamic  purposes  than  the  former,  and,  in  this  respect, 
a  much  less  satisfactory  working  substance.  The  "  actual 
efficiency  of  the  working  substance  "  is  lower  with  saturated 
than  with  superheated  steam,  and  with  steam  than  with  gas. 
It  varies  with  every  known  working  substance. 

(3)  Efficiency  of  the  Machine. — This  is   measured   by   the 
ratio  of  the  quantity  of  work  yielded  to  the  "  machinery  of 
transmission  "  to  that  done  upon  the  piston  by  the  working 
fluid. 

This  is  the  ratio  of  the  "  dynamometric  power"  to  the  indi- 
cated power,  and  is  less  as  the  waste  in  engine-friction  is  greater. 

(4)  Efficiency  of  the  Engine. — In  some  cases  the  product  of 
the  total  efficiency  of  the  fluid  by  the  efficiency  of  the  machine 
is   called   the    Efficiency  of  the    Engine  or  Efficiency  of   the 
System.     It  measures  the  ratio  of  the  work  performed  by  the 
engine,  externally,  to  the  work-equivalent  of  the  heat  supplied 
it. 

(5)  The  Efficiency  of  the  Furnace  is  the  ratio  of  quantity  of 
heat  transferred  to  the  working  substance  to  that  developed 
by  combustion  of  the  fuel. 

(6)  The  Efficiency  of  Combustion,  or  ratio  of  heat  produced 
by  combustion  to  that  latent  in  the  fuel. 

(7)  The  Total  Efficiency  of  the  Apparatus,  or  of  Plant,  as 
the  Author  would  term  it,  is  the  product  of  these  several  par- 
tial efficiencies,  and  is  the  fraction  of  the  total  calorific  power 
of  the  fuel  which  is  delivered  to  the  machinery  of  transmission 
as  mechanical  energy.     It  is  a  maximum  when  each  of  its  fac- 
tors is  a  maximum. 

(8)  The  Efficiency  of  Capital,  or  the  Commercial  Efficiency 
of  Steam  Machinery,  is  measured  by  the  amount  of  capital  re- 


70S  A    MANUAL   OF   THE   STEAM-ENGINE. 

quired,  or  the  total  running  expenses,  per  unit  of  time,  for  a 
given  power  required  and  obtained  ;  i.e.,  it  determines  how 
small  a  sum  will  provide  a  given  amount  of  power,  and  ivhat 
size  of  engine  must  be  selected  for  the  given  work,  a  problem  first 
enunciated  by  Rankine.* 

Each  of  the  above  efficiencies  is  made  a  maximum  by  a  set 
of  conditions  the  determination  of  which  constitutes  an  im- 
portant problem  in  the  science  of  engineering.  Each  must  be 
solved,  and  in  a  certain  definite  order,  in  the  application  of 
steam-power  to  any  given  case.  The  determination  of  the  effi- 
ciency of  fluid  is  included  in  the  problem  relating  to  efficiency 
of  engine,  and  this  and  all  other  efficiencies  are  included  in  the 
last, — the  efficiency  of  capital, — which  cannot  be  exactly  deter- 
mined unless  they  are  first  ascertained. 

(9)  In  addition  to  the  above,  another  problem  may  present 
itself  to  the  user  of  power,  although  seldom  to  the  designer,  or 
to   any   one  proposing  to  purchase  a  steam-engine ;  viz.,  the 
determination  of  the  maximum  economy  of  a  given  plant ;  i.e., 
how  the  most  work  may  be  obtained  for  the  unit  of  cost  from 
a  given  engine  already  constructed.     This  is  entirely  a  different 
problem  from  the  preceding  ;  its  solution  leads  to  very  differ- 
ent results,  and  does  not  usually,  if  ever,  determine  maximum 
commercial  efficiency.     This  problem  relates  to  what  may  be 
called  the  "  Maximum  Commercial  Efficiency  of  a  Given  Plant" 

(10)  It  may,  finally,  be  necessary  to  determine  still  another 
question  :  "  What  is  the  Maximum  Amount  of  poiver  that  can 
be  profitably  obtained  from  a  Given  Plant?"     This  is  a  more 
commonly  familiar  problem  than  the  last,  and  in  most  cases  of 
more  direct  and  practical  importance. 

The  solution  of  all  these  problems  in  the  case  of  the  real 
engine  and  for  the  purposes  of  the  designing  engineer,  of  the 
builder,  or  of  the  proprietor,  is  complicated  by  the  presence 
among  the  data  to  be  introduced  of  the  varying  thermal  inter- 
nal wastes.  As  has  already  been  stated,  however,  and  as  will 


*  Trans.  Royal  Society  of  Edinburgh;   1851;  vol.   xxi.     Rankine's  Miscel- 
laneous Papers  ;  No.  xvi.  p.  295.     Shipbuilding,  Appendix  ;  p.  292. 


MAXIMUM  EFFICIENCIES  OF   THE   STEAM-ENGINE.     709 

be  again  shown  later,  the  engineer  is  always  able  to  say,  in  ad- 
vance, how  these  variations  of  wastes  will  affect  the  problem, 
and  can  say  in  advance,  with  some  degree  of  approximation, 
what  will  be  the  probable  size  of  the  engine,  and  the  slight  un- 
certainty arising  from  a  first  approximation  based  on  data  ob- 
tained in  this  manner  becomes  insensible  with  a  second  ap- 
proximation obtained  by  repeating  the  process  of  computation 
or  graphical  construction,  as  presently  described  and  illus- 
trated. 

175.  Maximum  Thermodynamic  Efficiency,  or  the  effi- 
ciency of  the  working  fluid  operating  under,  purely  thermody- 
namic  conditions,  is,  as  has  been  seen,  entirely  independent  of 
the  nature  of  the  fluid  selected,  and  is  dependent  simply  on 
the  limits  of  temperature  adopted  and  the  character  of   the 
cycle  employed.     With  the  cycle  of  maximum  efficiency,  as 

T  —  T 
the    Carnot  cycle,  the  measure   is   invariably  — '— — -;  with 

other  methods  of  operation  this  efficiency  is  measured  by  the 
ratio  of  work  done  by  the  fluid,  and  of  heat  thermodynamically 
transformed  in  its  performance,  to  the  quantity  of  heat  sup- 
plied from  the  source  during  the  same  period  :  this  period 
being  that  of  a  cycle  or  of  some  stated  number  of  complete 
cycles.  The  processes  by  which  this  ratio  is  calculated  have 
been  already  given  and  examples  presented,  illustrating  their 
use  and  practical  application. 

176.  Estimates    of  Heat,  Steam,  and  Fuel   are    easily 
made.     Were  it  possible  to  utilize  all  heat  stored  in  the  steam 
supplied  to  the  engine,  under  the  usual  conditions  of  practice, 
there  would  be  demanded  but  about    2|  pounds  (about  one 
kilogram)  of  feed-water,  or  of  dry  steam,  per  horse-power  per 
hour.     The  horse-power    is  the  equivalent  of  1,980,000  foot- 
pounds (or  in  metric  H.  P.  270,000  kilogram-metres  per  hour, 
equal  to  2565.5  B.  T.  U.  per  hour  or  43  units,  nearly,  per  min- 
ute (metric  :  637  calories  per  hour,  or  10.6  per  minute).    Assum- 
ing the  total  available  heat  to  be  1 1 50  B.  T.  U.  per  pound  as 
a  maximum,  the  steam  of  ordinary  pressure  demanded  in  a 
perfect  engine  of  efficiency  unity  would  thus  be  between  2.2 


7IO  A    MANUAL    OF    THE    STEAM-ENGINE. 

and  2.25  pounds  (one  kilog.,  nearly)  per  horse-power  per  hour. 
Dividing  the  quantity  2.2  pounds  (i  kilog.)  by  the  thermody- 
namic  efficiency  of  fluid  will  give  the  weight  of  steam  de- 
manded at  that  efficiency,  and,  assuming  a  maximum  pract\- 
cally  attainable  evaporation  of  9  or  10  to  I,  the  weight  of  coal 
required  is  obtained  by  dividing  this  weight  of  steam  by  9  or 
10  for  condensing  or  for  non-condensing  engines,  respectively. 

Thus :  a  steam-engine  receiving  steam  at  a  pressure  100 
pounds  above  vacuum,  and  condensing  it  at  a  temperature 
corresponding  to  4  pounds,  the  ratio  of  expansion  being  5,  has 
a  thermodynamic  efficiency  of  0.15,  nearly  ;  it  would  demand 
about  15  pounds  of  feed-water  per  horse-power  per  hour,  and 
about  1.7  pounds  of  coal. 

A  non-condensing  engine  similarly  operated  would  have  an 
efficiency  of  fluid  o.io,  nearly,  would  use  about  22  pounds  of 
steam  and  2.2  pounds  of  fuel,  the  engine  being,  as  before,  ther- 
modynamically  perfect.  If,  in  the  latter  case,  the  steam-pres- 
sure were  ten  atmospheres,  this  efficiency  would  become  0.125, 
nearly,  and  the  steam  and  fuel  consumption  18  pounds  and  1.8 
pounds,  respectively. 

With  larger  ratios  of  expansion  the  efficiencies  would  be 
increased  and  the  expenditure  of  steam  and  fuel  correspond- 
ingly reduced. 

The  Gain  by  Expansion,  in  an  engine  free  from  the  wastes 
which  characterize  the  steam-engine  as  actually  used  or  for 
an  ideally  perfect  case,  is  seen  in  the  table  on  p.  711,  which 
assumes  hyperbolic  expansion. 

Thus  it  is  found  that  the  gross  or  "  absolute"  work  done  by 
a  pound  of  steam,  or,  as  assumed  in  the  table,  by  that  giving 
loo  units  of  power,  at  full  stroke,  increases  enormously  with  its 
use  expansively,  doubling  at  one-third  stroke  ;  and  becoming 
three  times  the  initial  amount  at  r  =  8,  and  four  times  at 
r  —  20.  But,  as  will  be  seen  when  studying  the  losses  of  the 
actual  engine,  these  gains  are  rarely  even  approximately  real- 
ized. The  extent  and  the  nature  and  effect  of  the  losses  in 
real  engines  have  been  already  fully  indicated. 


MAXIMUM  EFFICIENCIES  OF   THE   STEAM-ENGINE.     Jll 
GAIN  BY   EXPANSION. 


Point  of  Cut-off. 


::    Efr 


Work  and 

Power. 


!,« 

.. 

J 

2*S  6 

.« 

--V 

5 

i 

3X9  7 

H 

I         «« 

?        « 

V*        " 

16 

^77  2 

M 

18 

i        " 

** 

The  values  in  the  last  column  of  the  table  are  evidently 
proportional  to  the  quantity, 

_/.('+  log.*) 

/.-        -  - 


The  true,  net,  work  of  the  engine  would  be  proportional  to 


-A; 


where  pb  is  the  mean  back-pressure. 

Were  it  possible  to  expand  steam  in  a  non-conducting 
cylinder,  the  adiabatic  curve  would  differ  slightly  from  the 
hyperbola,  and  the  relative  work  of  the  steam  would  corre- 
spondingly differ,  giving  figures  as  follow,  for  ideal  non-con- 
densing engines : 

WORK  OF  ADIABATIC   F-XPANSION. 


Point  of  Cnt-off 

Value  of  U  per  pound 

Steam  per  H.P.  per  hour. . 


* 

285    1-459    I-667 
[23-8      21.4  1l8.« 

115  !     107  ',    96 


I 

1.905 
16.4 
9i 


2.278    2.85 
15.4       :: 
61          23 


712  A    MANUAL   OF   THE   STEAM-ENGINE. 

177.  The  Actual  Efficiency  of  Working  Substances  has 

been  seen  to  be  very  greatly  less  than  the  thermodynamic 
efficiency,  in  any  real  engines ;  the  difference  being  mainly  due 
to  wastes  of  heat  by  internal  storage,  conduction,  and  radia- 
tion. As  shown  by  experimental  investigations,  such  as  have 
been  already  described,  the  magnitudes  of  these  wastes  vary 
with  the  area  of  the  confining  walls  of  the  working  cylinder, 
and  the  differences  of  temperatures  produced,  and  probably 
nearly  as  the  square  roots  of  the  times  of  exposure  of  the 
working  fluid  to  refrigerating  influences. 

It  is  becoming  practicable  to  determine,  approximately,  the 
amount  of  waste  to  be  anticipated  when  the  size  of  engine 
arid  the  conditions  of  its  operation  are  known.  This  quantity 
being  added  to  that  demanded  by  the  thermodynamic  action 
of  the  engine,  the  total  weight  of  steam  required  is  obtained, 
and  the  quotient  of  the  work  done,  or  its  heat-equivalent,  by  the 
work-equivalent,  or  the  total  heat  supplied,  as  just  indicated, 
is  the  measure  of  the  actual  efficiency  of  working  substance  in 
the  real,  as  distinguished  from  the  ideal,  engine. 

Thus:  in  the  cases  considered  in  the  preceding  section,  the 
ideal  condensing  engine  has  a  thermodynamic  efficiency  of 
about  0.15,  and  requires  about  14.7  pounds  of  steam,  or  1.47  of 
coal,  per  hour  and  per  horse-power  ;  but  its  exhaust-wastes, 
due  to  internal  conduction  and  loss,  may  amount  to  one  third 
of  all  steam  entering  the  engine,  fifty  per  cent  of  the  thermo- 
dynamic requirement,  or  to  about  ten  pounds  of  steam  and 
one  pound  of  coal,  making  the  total  25  pounds  of  steam  and 
2.5  of  fuel,  nearly ;  which  are  very  common  figures  for  good 
engines  of  moderate  size.  Similarly,  the  non-condensing 
engine,  requiring,  thermodynamically,  18  pounds  of  steam,  or 
1.8  pounds  of  fuel,  if  subject  to  similar  losses,  would  actually 
demand  32  and  3.2  pounds.  The  actual  efficiency  thus  be- 
comes, for  the  condensing  engine  o.io,  and  for  the  non-con- 
densing engine  0.065,  instead  of  0.15  and  o.io,  as  for  the  ideal 
case. 

Relative  Actual  Efficiency  is  the  efficiency  actually  attained, 
as  compared  with  the  computed  ideal  efficiency.  It  is  here 


MAXIMUM  EFFICIENCIES  OF   THE   STEAM-EXG1XE.     ?I3 

—  —  0.667  for  the  one,  and  -^  =  0.65,  for  the  second  of  these 

two  examples. 

178.  Estimating  Consumption  of  heat,  of  steam,  and  of 
fuel,  for  the  actual  case,  becomes  a  very  simple  matter,  approx- 
imations such  as  may  be  based  upon  the  researches  already 
described  being  accepted.  The  engineer  may  desire  either  to 
estimate  the  probable  total  absolute  weight  of  steam  condensed 
in  the  cylinder  :  or  he  may,  for  purposes  to  be  presently  de- 
tailed at  some  length,  find  it  desirable  to  estimate  this  waste 
as  percentage  or  as  a  function  of  the  ratio  of  expansion,  simply, 
where  all  other  conditions  are  constant,  and  the  expansion-ratio 
is  the  only  variable  :  thus  making  two  cases. 

The  weight  of  steam  condensed  may  be  estimated  as  a 
function  of  range  of  temperature,  or  pressure,  of  area  of  in- 
ternal surfaces,  and  of  time  of  exposure,  or  speed  of  engine. 
It  may  also  be  reckoned  as  a  fraction  of  the  thermodynamic 
consumption  of  steam,  and  in  terms  of  the  ratio  of  expansion. 

The  Relative  Actual  Efficiency  of  the  working  fluid  is  thus 
from  0.90  to  0.75  for  these  cases, 

The  quantity  of  heat,  of  steam,  or  of  fuel,  being  estimated 
thermodynamically,  as  already  indicated  in  the  preceding  sec- 
tion and  the  last  chapter,  the  quotient  of  the  quantities  so  ob- 
tained by  a  known  relative  actual  efficiency  of  a  working  sub- 
stance gives  the  amount  of  heat,  of  steam,  or  of  fuel,  to  be  ac- 
tually consumed. 

Thus,  if  the  efficiency,  calculated  from  the  thermodynamic 

conditions,  be  0.15  :  the  heat  demanded  being  ^-p   =  285 

2566 
British  thermal   units  per  horse-power  per  minute   or 

2.2 
=  17,107  per  hour;  the  steam  called  for  amounting  to    =— 


O.22 

=  14.7  pounds  per  hour  ;  and  the  fuel  amounting  to    —  =  1.5 


pounds,—  the  product  of  these  quantities  by  the  reciprocal  of  the 


714  A   MANUAL   OF   THE   STEAM-ENGINE. 

relative  actual  efficiency,  --  =  i.ni,  gives  for  the  real  de- 

mand per  indicated  horse-power  18,817  thermal  units;  15.1 
pounds  of  steam;  and  1.67  pounds  of  coal  —  figures  often  at- 
tained by  modern  engines. 

The  net  efficiency  of  the  fluid  is  thus  found  to  be,  for  this 
case,  the  "  indicated  power"  being  considered, 

E  —  0.15  X  0.90  =  0.167. 

It  should  be  remembered  that  this  efficiency  of  the  fluid 
employed  as  the  medium  of  energy-transformation  is  deter- 
mined both  by  the  physical  properties  of  the  substance  and  by 
the  conditions  of  its  employment  in  the  engine. 

179.  The  Efficiency  of  the  Engine,  as  a  Machine,  and  be- 
low unity,  as  has  been  seen,  is  less  as  the  friction  of  its  moving 
parts  is  greater.  It  has  been  further  seen  that  this  friction 
may  probably  be  usually  taken  as  sensibly  constant  for  all 
loads,  and,  for  any  given,  or  for  the  rated,  load,  as  a  determ  in- 
able  fraction  of  the  resistance  or  power.  In  its  absolute 
amount,  it  may  be  taken  as  equal  to  the  product  of  a  nearly 
constant  friction-pressure,  as  it  may  be  termed,  into  the  area 
and  speed  of  piston  ;  and  the  work  of  friction  is  the  product  of 
that  intensity  of  pressure,  pf,  into  the  volume  ASN  traversed 
by  the  piston  in  the  given  time.  This  pressure  being  taken  as 
/y,  we  have 

Uf=pfAS 

as  the  work  of  friction  per  stroke  of  piston,  and  the  efficiency 
of  the  machine  as 


This  efficiency  usually  varies  from  Em  =  0.80,  in  small  en- 
gines, to  above  Em  =  0.90,  in  large  engines  of  the  best  con- 
struction. The  smaller  values  are  the  more  common. 

The  total  efficiency  of  the  engine  is  the  continued  product 


MAXIMUM  EFFICIENCIES  OF   THE   STEAM-EA'CIXE.     ^5 

of  the  thermodynamic  efficiency,  the  relative  actual  efficiency. 
and  the  efficiency  of  the  machine.  For  the  case  last  con- 
sidered, this  becomes 

Et  =  Et  X  Er  X  Ef  =  0.15  X  0.90  X  0.95  =  0.129. 

For  a  more  common  case,  in  which  these  values  are  much  less, 

Et  =  0.08  X  0.75  X  0.90  =  0.054  ; 

and  only  about  one  eighteenth  the  energy  supplied  by  the 
steam-boiler  is  here  converted  into  useful  work  ;  such  as  is 
measured  by  the  absorbing  dynamometer  and  known  as  the 
"  dynamometric  power,"  the  D.  H.  P.,  as  often  symbolized 
when  given  in  horse-power. 

T/tf  Actual  Demand  of  the  engine,  as  measured  in  heat, 
steam,  and  fuel,  is  thus  known  to  be  often  much  greater  than 
the  quantity  computed  for  the  ideal  engine,  and  is,  as  already 
seen,  readily  estimated  by  multiplying  the  values  for  the  ideal 
case  by  the  reciprocal  of  total,  final,  efficiency.  Thus,  for  the 
last  example,  we  have 

2566 
Heat  per  horse-power  per  hour  -  —     =     49>37<>  ; 

Steam"  "   "  ^  =  4°-4: 


And,  for  the  case  next  preceding, 

Heat-    jfl    =     '9.89.B.T.U, 
Steam,  -—     =     17,054  Ibs.: 


7l6  A    MANUAL   OF   THE   STEAM-ENGINE. 

In  the  best  of  modern  engines,  the  thermodynamic  effi- 
ciency is  about  0.20;  the  wastes  are  reduced  to  about  one 
tenth  the  total  thermodynamic  expenditure,  making  the  rela- 
tive actual  efficiency  0.90  ;  the  efficiency  of  the  machine  is  not 
far  from  0.95,  and  the  total  real  efficiency  of  the  system  is  thus 

Et  —  0.20  X  0.90  X  0.95  =0.17, 
and  the  actual  consumption  is 

Heat,    -^     -     1  5,094  B.  T.  U.; 
Steam,  -—     =     12.94  Ibs.; 


Fuel,     222.     =     1.29  Ibs* 

The  common  non-condensing  mill-engine  has  often,  as  ac- 
tually operated,  a  total  efficiency  of  about 

Ee  =  o.io  X  0.75  X  0.90  =  0.068, 
and  the  expenditures  are,  per  H.  P.  per  hour, 

Heat,    |||     =     38,030  B.  T.  U.; 
Steam'bS     =     32-35  Ibs.; 
Fue1'  =     3-24  Ibs. 


The  efficiency  of  boiler  here  assumed  is  rarely  attained, 
however,  and  taking  the  steam  evaporated  at  nine  times  the 
weight  of  fuel,  instead  of  ten,  the  three  cases  would  give,  re- 
spectively, 2.99,  1.45,  and  3.6  pounds  of  coal  per  horse-power 
of  work  done  and  per  hour  ;  which  are  figures  now  familiar  to 
the  experienced  engineer. 

*  This  is  the  figure  actually  attained,  since  the  above  was  written,  by  a  large 
Corliss  engine  designed  by  Mr.  Reynolds. 


MAXIMUM  EFFICIENCIES  OF   THE   STEAM-EXGIXE.     ^\^ 

Accepting  Rowland's  value  of  the  mechanical  equivalent  of 
heat  as  778,  the  quantities  above  computed  become 

Heat  per  H.  P.  per  hour,  — '—-  —  =  47.056  ; 

steam"  ••  "  ••    S  =4o: 

Coal    -      -       »      -  °-'8 

and 

Heat,    -      —  = 


Steam,  i!j=,.  68  Ibs.; 

Fuel-  57itrM3lbs-: 

for  the  first  two  cases,  respectively  :  and 

Heat,    ~~=  14,941  B.T.U.; 


Fue1' 
and 


Heat-  =  37,367  B.T.U.; 


-j  18 

Steam,  —    —  =  29  Ibs.  ; 
0.068 


0.218 
Fue1'  =  2- 


for  the  second  pair. 


71 8  A    MANUAL   OF   THE   STEAM-ENGINE. 

180.  Thermal  Lines  and  "  Curves  of  Efficiency,"  as  the 

Author  has  called  the  latter,  may  be  now  studied  for  the  case 
of  the  actual  engine.* 

It  has  been  shown  that  friction  and — often  to  a  vastly 
greater  extent — cylinder-condensation,  due  to  expansion  of  a 
heated  fluid  in  a  working  cylinder  made  of  a  material  of  high 
conducting  power,  modify  the  methods  of  expansion  and  of 
expenditure  of  heat  so  greatly  that  the  ratio  of  expansion  for 
maximum  efficiency,  in  unjacketed  engines,  is  small,  although 
its  value  would  otherwise  be,  often,  several  times  greater  than 
it  actually  is.  It  was  also  shown  that  these  modifying  con- 
ditions very  differently  affect  different  kinds  of  steam-engine 
and  different  engines  and  also  individual  engines,  at  various 
pressures  and  piston-speeds.  It  has  become  evident  that  in  no 
case,  in  steam-engines  as  to-day  constructed,  can  the  expansion, 
line  or  the  curve  of  mean  pressures  for  varying  ratios  of  expan- 
sion be  such  as  would  be  obtained  in  a  non-conducting  cylinder. 
Steam  must  always  be  more  or  less  condensed  at  the  beginning, 
and  must  always  carry  away  heat  by  its  re-evaporization  at  the 
end  of  the  stroke.  The  steam-jacket  checks  the  first  operation, 
but  accelerates  the  last,  and,  with  wet  steam,  may  possibly  even 
increase  the  evil  that  it  is  designed  to  prevent. 

The  actual  expansion-line  is  not  only  modified  in  position 
and  in  form  by  the  conductivity  of  the  cylinder,  but,  also, 
although  perhaps  less  seriously,  by  the  quantity  of  water  con- 
tained in  the  mass  of  fluid  at  the  instant  of  closing  the  expan- 
sion-valve. 

The  expansion-curve  may  be  often  closely  represented  by 
a  regular  curve  of  the  hyperbolic  class,  p^v*  =  pvn,  the  ex- 
ponent n  varying  with  the  proportions  of  steam  and  water  in 
the  mixture  at  the  commencement  of  the  expansion,  which  is 
assumed  to  take  place  in  a  non-conducting  cylinder.  Table 


*  On  the  Ratio  of  Expansion  at  Maximum  Efficiency  in  Steam-engines; 
Trans.  Am.  Soc.  Mech.  Engrs.,  1881;  Jour.  Franklin  Institute,  May  1881.  On 
the  Behavior  of  Steam  in  the  Steam-engine,  and  on  Curves  of  Efficiency;  Jour. 
Franklin  Institute,  Feb.  1882. 


MAXIMUM  EFFICIENCIES  OF  THE  STEAM  EXGIXE.  719 
1 1 1,  appended,  gives  the  values  of  the  ratio  of  mean  pressure  to 
initial  pressure, ^,  for  various  mixtures  from  steam  1.00,  water 

o,  to  steam  0.50,  water  0.50,  assuming  the  formula  to  be  prac- 
tically accurate  within  that  range.  With  these  are  given  the 
adiabatics  for  superheated  steam,  n  =  1.333.  Table  III  also 

gives  the  values  of  ~-  for  steam-expansion  in  a  jacketed  metal 

cylinder,  in  which  it  is  kept  just  dry  and  saturated  by  heat 
from  the  jacketed  sides  and  ends ;  the  values  for  wet  air  com- 
pressed in  air-compressors,  in  which  n  is  frequently  found  to  be 
1.2 ;  and  for  peculiar  cases  in  actual  steam-engines  in  which 
leakage  or  re-evaporation,  or  both,  raise  the  terminal  pressures 
greatly,  giving  n  =  0.50,  n  =  0.75.  Table  IV,  similarly,  gives 

the  ratios  — . 
A 

It  is,  as  yet,  impossible  to  predict  which  of  these  curves  will 
be  found,  in  any  case,  and  the  engineer  is  compelled  to  rely 
entirely  upon  the  "  indicator"  for  information  of  this  character. 
The  greatest  possible  variety  of  curves  are  found  to  occur  in 
such  cases.*  but  they  approach  the  adiabatic  more  nearly,  as 
the  steam  is  drier  and  as  the  speed  of  piston  is  increased,  rarely 
departing  far  from  the  common  hyperbola  in  good  engines. 
Perfectly  dry  or  superheated  steam,  in  fast-running  engines, 
gives  a  curve  most  closely  approaching  the  adiabatic ;  but  the 
deviation  is  more  marked  as  the  speed  of  engine  is  decreased, 
and  as  the  amount  of  moisture  in  the  steam,  initially,  increases. 
The  Emit  may  be  taken  as  pv  —  /tr, ,  on  the  one  side,  and  to 
p?%  =  PJP&  on  the  other  :  the  latter  being  the  rare  case  some- 
times met  with  of  an  unjacketed  engine  working  at  a  piston- 
speed  below  50  feet  per  minute  (under  15  metres),  and  with  a 

*  An  indicator-diagram  lying  before  the  Author  gives  n  =  i.ooi  at  the  begin- 
ning of  the  stroke,  «  =  0.94  at  the  middle,  and  m  =  0.89  at  the  end.  The  com- 
pression-line starts  with  *=  1.52  and  varies  thus,  *  =  i.2o.  9=90.6  to  the  end. 
where  »=O-77,  showing  that  the  mean  temperature  of  the  surfaces  in  contact 
with  steam  is  above  that  of  the  vapor  during  the  first  half  of  the  period  of  com- 
pression, and  below  that  of  the  fluid  during  the  second  half. 


720 


A   MANUAL   OF   THE   STEAM-ENGINE. 


high  ratio  of  expansion  ;  while  the  former  is  a  very  usual  limit- 
ing value  with  well-constructed  jacketed  engines  at  good  speed. 


'"Hi  kill    1 

Where  the  steam  contains  much 
::::    actual  engines  often,  especially 

--  occurs,  lies   entirely  above  the 
--  curve  of  Mariotte,  the  value  of  n 

r  —  cases,  the  line  may   fall   under 

I  .  V  V  \  V  .    >1  _  _  .  

1        K 
Ijjijijjjjijiijjljjljji 

•<0p^---  IjEJj 

^  but  rise  far  above  it  toward  the 
curve  more  nearly  parabolic  in 

^  . 

1      iN.      i  i    i    i  !    i  !  i  i    Mil    j      |    i  i  i 

gft:W=g%Tf:::::!---;:4j: 

.30    jl|    -L-  

JyitirllJIIIIIIIIIjlllljllllJ 

:::::::::::::!«:  1|:S:=::^SS; 
::±  ::::::::::::::  :::::::::  ::::  ::::: 

1 

15 

FIG.  161. — CUF 


MEAN  PRESSURE. 


MAXIMUM  EFFICIEXCIES  OF  THE   STEAM-EXGI\E.     /2I 


appearance,  and  also  with  a  mean  value  of  a  less  than  unity. 


The  values  of  r~  giv< 
P\ 


I 


in  the  tables  are  plotted  in  Figs,  161 

and  162. 

These  curves  of  mean  pres- 
sure are  valueless,  usually,  for 
direct  application,  but  the  en- 
gineer will  find  them  useful  in 
the  construction  of  probable 
mean-pressure  curves  for  pro- 
posed engines;  and  by  properly 
applying  them  he  may  obtain 
practically  valuable  curves  of 
efficiency  for  any  given  class  of 
engines. 

Referring  to  Fig.  163,  sop- 
pose  a  pound,  a  cylinderful,  or 
other  unit  of  quantity  of  stecm 
and  water  to  be  drawn  from 


"^        ^        -       3      ^ 


722  A   MANUAL    OF   THE    STEAM-ENGINE. 

the  boiler,  carrying  10  per  cent  its  total  weight  of  water,  90  per 
cent  being  saturated  steam,  and  to  have  a  pressure  which  may 
be  called  i.oo.  When  separated  from  the  boiler  and  carried 
into  the  cylinder  it  will  retain  the  pressure  i.oo  and,  worked  at 
full  stroke,  will  do  the  work  i.oo.  If  supplied  with  additional 
heat  until  completely  dry,  the  work  becomes  i.n  at  full  stroke 
and,  if  worked  at  different  ratios  of  expansion,  such  steam  will 
give  a  series  of  mean  pressures  represented  by  the  curve  of  effi- 
ciency, Alt  Fig.  163,  as  obtained  from  the  expansion-curves 
whose  equation  is/^1-135  =  constant,  provided  expansion  occurs 
in  a  non-conducting  cylinder  where  no  condensation  can  occur 
except  such  as  is  due  to  performance  of  work.  Expanded  wet, , 
as  drawn  from  the  boiler,  the  mean  pressures  of  curve  B — from 
pv1-12*  =  constant,  which  is  deduced  by  Zeuner  for  x  =  go — are 
proportional  to  the  work  done  by  the  mixture  if  worked  with- 
out change  of  proportion  other  than  occurs  by  production  of 
work.  If,  again,  the  same  weight  were  drawn  from  the  boiler 
at  the  pressure  assumed  and  in  the  same  proportions — steam 
90,  water  10 — and  if,  on  entering  the  cylinder,  initial  condensa- 
tion should  double  the  quantity  of  water  present,  the  work  at 
full  stroke  would  be  .90  and  the  mixture  would,  at  other  ratios 
of  expansion,  the  proportion  remaining  unchanged,  give  rela- 
tive quantities  of  work  measured  by  the  ordinates  of  curve  C: 
pv™*  =  constant.  It  now  contains  steam  81,  water  19.  Simi- 
larly, the  proportion  of  water  present  being  increased  by  initial 
condensation  from  the  original  amount  carried  out  of  the  boiler, 
so  as  to  reduce  the  work  of  unity  of  weight  to  .80,  .70,  .60,  .50, 
etc.,  at  full  stroke,  the  curves  of  efficiency  become  as  shown  in 
Fig.  163,  curves  D,  E,  F,  etc.,  successively,  down  to  the  base- 
line where  condensation  has  become  complete  and  the  work  of 
expansion  of  the  water  may  be  neglected.  (See,  also,  §  187.) 

Such  are  the  curves  of  efficiency,  of  work,  and  of  mean 
pressures  to  be  obtained  where  steam  is  expanded  in  a  non- 
conducting cylinder.  They  are  easily  deduced  and  easily  con- 
structed, and,  by  reference  to  Zeuner's  formula,  the  engineer 
can  determine  them  with  a  satisfactory  degree  of  accuracy  for 
all  cases  which  are  likely  to  arise  in  his  practice.  Studying  the 


I  0 


FIG.  163.—  CURVES  OF  EFFICIENCY. 


MAXIMUM  EFFICIENCIES  OF   THE  STEAM-ENGINE.     ?2$ 

behavior  of  steam  in  a  metallic  cylinder,  we  find  vitally  differ- 
ent conditions  and  results ;  but  given  the  law  of  variation  of 
composition  of  the  mixture  with  change  of  point  of  cut-off,  or 
of  ratio  of  expansion,  it  is,  nevertheless,  practicable  to  deter- 
mine curves  of  efficiency,  and  to  deduce  values  of  the  best 
ratio  of  expansion  for  any  given  case,  as  illustrated  in  the  suc- 
ceeding section.  In  the  actual  engine,  steam  entering  from  the 
boiler — at  the  instant  of  starting  the  piston  forward — consists 
of  a  mixture  of  steam  and  water,  of  which  the  proportions  are 
determined  by  the  character  of  the  boiler-steam  and  the  amount 
of  initial  condensation.  As  the  piston  moves  forward,  this 
proportion  becomes  independent  of  all  external  conditions  at 
the  instant  of  the  closing  of  the  steam-valve.  From  this  point 
on,  the  interchange  of  heat  between  the  steam  and  the  sur- 
rounding walls  of  the  cylinder  produces  a  continuous  change 
of  proportion  until  the  exhaust-valve  opens. 

Thus,  assuming  steam  to  enter  at  a  pressure  of  i.oo,  and  to 
contain  10  per  cent  water,  its  curve  of  efficiency  *  starts  on 
curve  B  and  gradually  shifts  from  curve  to  curve — as  seen  on 
the  plate,  curves  K,  L,  and  J7 — more  or  less  rapidly,  as  cylinder- 
condensation  takes  place  to  a  greater  or  less  extent,  the  real 
curve  of  efficiency  usually  crossing  C,  D,  E,  etc.,  and  taking  the 
general  form  indicated  by  lines  K,  L,  O,  and  P.  With  con- 
siderable expansion  and  wet  steam,  the  expansion-line  may 
again  rise  during  any  one  stroke,  by  re-evaporation,  toward  the 
end  of  the  stroke  to  such  an  extent  as  to  somewhat  increase 
the  mean  pressures,  but  this  case  is,  apparently,  not  a  very 
common  one.  The  amount  of  that  condensation  is,  evidently, 
some  function  of  the  ratio  of  expansion  in  every  engine,  aqd 
the  Author  has  been  accustomed  to  take  it  as  varying  approxi- 
mately as  some  power  of  r.  Lines  K,  Z,  and  M,  which  are  pre- 
sented simply  in  illustration,  represent,  respectively,  the  curves 
of  efficiency  when  the  total  loss  by  cylinder-condensation,  kc , 
varies  approximately  as  Vr,  and  when  Ae  =  o.i  i  r,  he  —  0.2  tV, 

*  The  curve  of  efficiency  and  of  mean  pressures  must  not  be  confounded 
with  the  expansion-line  representing  the  varying  relations  of  pressure  and 
volume  during  the  stroke. 


724  A    MANUAL    OF   THE   STEAM-ENGINE. 

hc  =  0.3  Vr,  nearly ;  values  in  per  cent  of  total  steam  demanded 
not  uncommon  in  engineering  practice.  The  abscissas  of  the 
curves  are,  as  before,  measures  of  weights  of  steam  used.  If, 
in  any  case,  condensation  were  so  to  vary  that  no  gain  should 
be  derived  from  expansion — and  such  cases  are,  within  a  limited 
range  of  expansion,  sometimes  nearly  approximated  to — the 
curve  of  efficiency  would  become  a  straight  line,  N,  the  "  line 
of  constant  efficiency,"  Fig.  163.  The  curves  O  and  P  are 
obtained  by  altering  the  vertical  scales  of  L  and  M,  so  as  to 
give  them  a  common  initial  point  with  B  and  K  at  /  =  100, 
and  thus  enabling  the  reader  to  compare  the  differences  of 
form  of  the  several  lines,  and  of  the  two  kinds  of  curve  more 
satisfactorily.  It  will  be  seen,  later,  on  comparing  the  second 
of  the  two  kinds  of  curve  with  those  derived  from  experiment 
on  working  engines,  and  to  be  presented  later,  that  the  curve 
of  efficiency  here  obtained  by  induction  is  of  precisely  the  same 
character  as  that  given  by  direct  experiment. 

Referring  once  more  to  the  set  of  curves  of  efficiency, 
Fig.  163,  we  may  deduce  the  same  conclusions  from  graphical 
construction,  and  obtain  results  far  more  easily  and  rapidly. 

Pb 

Selecting  values  of  —  such  as  are  often  obtained  with  non-con- 

p. 

densing  and  with  condensing  engines^  respectively, —  —  =  .20; 

— -  =  .10, — we  may  determine  ratios  for  maximum  efficiency  of 

engine  thus:  From  the  points  .20  and  .10  on  the  axis  of  ordi- 
nates  on  the  scale  measuring  total  work  per  stroke,  draw  lines 
tangent  to  the  several  curves,  as  RT,  RV,  SV,  SW,  etc.,  etc. 
The  points  of  tangency  being  found,  the  values  of  their  abscissas 
measure  the  quantities  of  steam  to  be  used  per  stroke  to  give 
maximum  engine  efficiency,  since  the  ordinate  of  any  point 
divided  by  the  abscissa  is  a  measure  of  the  ratio  of  work  done 
to  steam  expended  in  doing  it,  and,  for  the  assumed  back- 
pressures, the  net  amount  of  work  per  unit's  weight  of  steam 
is  a  maximum  at  the  points  just  identified.* 

*  This    principle   was    pointed    out    by    Rankine.      See    his    Miscellaneous 
Papers,  p.  295,  and  Shipbuilding,  Appendix. 


MAXIMUM  EFFICIENCIES  OF    THE   STEAAf-EXGIXE.    725 

On  making  the  construction  it  will  be  found  that  these 
maxima  are  found  for  very  nearly  the  same  values  of  abscissa 
and,  therefore,  for  the  same  ratio  of  expansion,  nearly,  what- 
ever the  dryness-fraction  of  the  steam  used  in  the  non-conduct- 
ing cylinder.  But,  drawing  tangents  RK,  RY,  SX.  SZ.  etc.,  to 
curves  K,  C,  and  J/,  to  determine  the  best  ratios  for  the  metallic 
steam-cylinder,  values  are  formed  for  r  far  removed  from  those 
just  obtained  for  the  non-conducting  cylinder,  and  also  differ- 
ing among  themselves  greatly  with  the  proportion  of  water 
present.  In  the  cases  shown  on  the  plate,  the  ratio  for  the 
non-condensing  engine  is  decreased  to  two  thirds,  and  for  the 
condensing  engines  to  less  than  half  that  found  best  for  the 
non-conducting  cylinder.  It  is  to  be  remembered  that  the 
quantity  of  steam  used  per  stroke,  although  in  direct  propor- 
tion to  the  distances  "  followed  "  by  the  steam  up  to  point  of 
cut-off  in  the  non-conducting  cylinder,  may  be  in  widely  differ- 
ent proportion  with  the  metal  cylinder.  In  the  latter  it  varies 
from  nearly  an  equal  proportion  at  full  stroke  to.  often,  a 
double  proportion  at  high  ratios  of  expansion. 

iSi.  The  Ratio  of  Expansion  at  Maximum  Efficiency. 
—  In  all  heat-engines  the  method  of  transformation  of  heat-ener- 
gy into  useful  mechanical  work  has  been  seen  to  be  the  fol- 
lowing :  * 

A  certain  mass  of  the  working  fluid  is  heated  from  a  tem- 
perature which  is  usually  not  far  from  that  of  the  atmosphere 
up  to  some  higher  temperature.  This  is  accompanied  by  a 
definite  increase  of  volume,  or  of  pressure,  or  of  both,  and  in 
the  case  of -liquids  by  a  change  of  physical  state  after  passing 
a  certain  point  which  is  variable,  but  definite  for  each  press- 
ure ;  this  latter  temperature  is  the  boiling  point,  and  the 
change  is  that  known  as  vaporization.  Evaporation  being 
complete,  the  mass  is  expanded  in  the  working  cylinder  of  the 
engine  until  it  has  attained  a  certain  larger  volume,  z-t ,  the 
magnitude  of  which  is  r  times  that  of  the  initial  volume,  «•, , 
with  which  expansion  began.  We  thus  have  the  "ratio  of 

*  See  Journal  Franklin  Institute  ;  May  1881. 


726  A    MANUAL    OF   THE   STEAM-ENGINE. 

expansion"  r  =  — .     When  expansion  is    complete,  the  whole 

volume,  vt,  of  steam  or  gas  at  the  pressure/.,  is  rejected  from 
the  cylinder  into  a  condenser  or  into  the  atmosphere,  and  the 
piston  which  it  has  impelled  through  the  total  volume,  z>a  f 
returns  to  the  starting-point,  resisted  by  the  "  £af£-pressure," 
/„,  of  the  condenser  or  of  the  atmosphere.  During  the  latter 
operation  all  heat  which  has  not  been  transformed  into  work 
is  rejected,  and  an  additional  amount  is  expended,  which  is 
equivalent  to  the  work  done  by  the  piston  upon  the  fluid  dur- 
ing its  expulsion.  This  operation  is  that  which  has  already 
been  more  than  once  described. 

This  process  is  thus  graphically  represented  :  In  Fig.  164, 
the  fluid,  initially  in  the  state  measured  by  the  pressure  a£  or 
a'E'  and  volume  Oa  or  Oa',  is  heated,  sometimes  at  constant 
volume,  as  Oa,  and  sometimes  with  compression,  as  from  Oa' 
to  a  higher  temperature,  the  pressure  and  volume  varying  as 
shown  by  EA  or  by  E'A.  Heated  next  at  constant  pressure 
or  at  constant  temperature,  the  mass  expands,  doing  work,  to 
B  or  to  B'.  At  this  point,  vl ,  pl ,  the  supply  of  heat  ceases  and 
the  fluid  expands  "  adiabatically,"  transforming  into  mechani- 
cal energy  all  the  heat  demanded  as  equivalent  to  the  work 
measured  by  the  area  bBcC,  and  drawing  upon  its  own  stock  of 
heat  to  supply  this  demand.  At  the  end  of  this  stage  the  fluid 
has  a  lower  temperature  and  a  pressure  and  a  volume,  cC,  Oc 
(Pii  ^a>)  determined  by  that  temperature  and  the  value  of 

r  =  — -,  and  which  are  indicated  by  the  location  of  the  point 

V1 

C.  Rejecting  heat  at  constant  volume,  vt,  pressure  falls  to  D, 
/3 ,  and  then  rejection  of  heat  continuing  at  constant  pressure, 
/8 ,  the  volume  is  reduced  to  that  with  which  it  started. 

The  total  or  gross  work  done  is,  in  gas-engines,  measured  by 
the  area  ABCcaA,  in  steam  and  vapor  engines  by  this  area 
increased  by  a  very  considerable  amount— the  measure  of 
internal,  of  molecular,  work  which  cannot  appear  on  the  indi- 
cator-diagram. 

The  net  work  done  is  measured  by  the  area  included  in  the 


MAXIMUM  EFFICIENCIES  OF   THE   STEAM-ENGINE.     727 

indicator-diagram  ABCDEA.  This  work  is  the  equivalent 
of  all  heat  transformed  into  mechanical  work  or  energy.  Ttu 
efficiency  of  the  fluid  is  the  ratio  of  net  work  done  to  total 
heat  received  by  the  fluid,  and  is  a  maximum  when  the  area 
ABCDE  is  a  maximum,  assuming  the  ratio  of  expansion  alone 
to  vary.  It  is  evident  that  this  maximum  is  determined,  there- 
fore, by  the  conditions  which  make  the  area  bBcC  a  maxi- 
mum, which  conditions  are  very  simple  in  the  hot-air  engine, 
and  are  easily  expressed,  while  in  the  steam  and  in  vapor 
engines  they  are  very  difficult  of  determination  and  expression 
in  consequence  of  their  extreme  variability.  But  the  efficien- 
cy of  the  fluid  is  but  one  factor  Y 
in  the  determination  of  the  ratio 
of  expansion  for  maximum  econ- 
omy. The  heat  in  the  fluid  is 
compelled  to  do  its  work,  not 
simply  through  that  fluid  as  a 
transmitting  mechanism,  but  also 
through  a  machine  which,  as  an  \Q  a.  a7" 

apparatus      intended     tO     imprison  F'S-  164.— INDICATOR  DIAGRAM  WORK  OF 

and  direct   so  subtle   and  elusive 

a  form  of  energy  as  heat,  is  extremely  imperfect,  and  which 
has  the  additional  and  very  serious  defect  of  being  itself 
cumbersome  and  difficult  to  start  and  to  keep  in  motion 
without  considerable  loss  of  power  within  itself. 

The  useful  work  of  the  machine  is  that  which  it  transmits 
beyond  its  own  boundaries  to  other  mechanisms,  and  this  is  a 
maximum  at  that  ratio  of  expansion  which  gives  energy  to  the 
machinery  of  transmission  beyond  the  engine  at  least  cost  in 
heat  expended.  This  efficiency  of  the  system  is  therefore  the 
product  of  the  factors,  total  efficiency  of  the  fluid  and  actual 
efficiency  of  the  engine  considered  as  a  piece  of  mechanism. 

Taking  first  the  purely  ideal  case  in  which  the  mechanism 
is  assumed  to  be  perfect  and  the  ratio  of  expansion  the  only 
variable  element,  we  may  by  examining  Fig.  165  see  at  once 
what  should  be  the  value  of  that  ratio. 

It  is  obvious  that  the  ratio  of  expansion  simply  determines 


728 


A    MANUAL    OF   THE   STEAM-ENGINE. 


how  far  the  transformation  of  stored  heat-energy  existing  at  B 
shall  be  continued  by  transformation  into  work  during  the 
expansion  of  the  working  fluid.  It  is  equally  obvious  that  this 
expansion  should  continue  until  the  gain  of  work  by  further 
expansion  is  more  than  balanced  by  losses  avoidable  by  ter- 
mination of  that  process. 

Where  the  only  loss  is  due  to  a  fixed  back-pressure,  FD  = 
ps ,  it  is  seen  that,  were  expansion  to  cease  at  C,  the  work  which 
would  have  been  done  had  the  expansion-line  BC  extended 
to  the  right  beyond  C,  is  lost,  and  that  the  counterwork  of 


FIG.  165.— ENGINE  CYCLES. 


back-pressure  beyond  that  point  is  gained  ;  but  the  former 
exceeds  the  latter,  and  the  net  result  is  a  loss  by  incomplete 
expansion.  On  the  other  hand,  were  the  ratio  of  expansion 
increased  so  that  the  expansion-line  becomes  B"  £,  the  back- 
pressure line  is  reached  at  D' ;  and,  beyond  this  point,  we  note 
a  gain  of  work  done  usefully,  which  is  measured  by  the  area 
D'EFF'D ',  while  a  loss  accrues  by  back-pressure  measured 
by  D'DFF'D'.  We  thus  again  meet  with  a  net  loss  which  is 
represented  by  D'DED',  and  expansion  has  evidently  been 

carried  too  far.  Making  the  value  of  r=—  such  that  expan- 
sion reaches  the  back-pressure  line  at  D  and/2  becomes  equal 
to  /„ ,  we  meet  with  neither  kind  of  loss,  and  it  follows  that 


MAXIMUM  EFFICIENCIES  OF   THE   STEAM-EXGINE.     J2$ 

expansion  should   in  this  ideal  case  be   continued  until  the 
expansion-line  meets  the  back-pressure  line. 

This  may  be  readily  shown  by  other  methods  :  It  was 
shown,  nearly  two  generations  ago,  by  Sadi  Carnot,  that  max- 
imum efficiency  of  fluid  is  attained  when  expanding  between 
the  widest  possible  limits  of  temperature.  It  is  now  well 
known,  and  it  is  shown  by  every  elementary  treatise  on  physics, 
or  mechanics,  or  thermodynamics,  and  on  heat-engines,  that 
the  efficiency  of  the  fluid  in  any  heat-engine  is  measured  by 

the  expression  — l—^ — *,  in  which  7*,  and  7",  are  the  temperatures 

of  reception  and  rejection  of  heat  measured  from  the  "  abso- 
lute "  zero.  But  this  maximum  range  of  temperature  corre- 
sponds to  the  maximum  attainable  range  of  pressure,  and,  the 
upper  limit  being  fixed,  this  range  is  determined  by  the  value 
of  r  and  is  a  maximum  when  p^  =  /,  and  expansion  continues 
to  the  back-pressure  line.  A  general  analytical  demonstration 
is  obtained  in  the  following  manner  :  Problem  :  Given/,,  vlt 
v*  >  P*  >  to  find  the  value  of  the  ratio  of  expansion,  r,  which 
will  make  the  net  work  done  a  maximum  for  the  Ideal  Case. 
This  work,  ABODE,  figure,  is  measured  by 


-pf>**         ....       (I) 


and  is  a  maximum  when  the  variable  part    /   ' pdv  —  /,z>,  is  a 

maximum. 

The  method  of  variation  of  /  with  variation  of  v  is  deter- 
mined by  various  conditions  which  do  not  affect  the  analysis. 
Let  this  relation  be  such  that  we  may  write,  as  experiment  in- 
dicates that  we  may  with  practically  close  approximation, 


*V=A*V  =  const. ;       =  r. 


73°  A  MANUAL    OF   THE   STEAM-ENGINE. 

Thus  we  have 


or,  for  hyperbolic  expansion,  where  n  —  i, 

WH  =fllv1  (i  -f-  log*  r)  —  /3z'2 (3) 

Determining  the  maximum  for  the  first  and  usual  case,  we 
get 

— j-^  =  af  I  ^  v.  -4-^-LJ ^-^ P«rv. ) .  — ,-  =  O : 

alir  X^1  n  —  i  ^3     V    «V 

whence 


Hence 


and  the  ratio  of  expansion  for  maximum  efficiency  of  fluid  is 
that  which  makes  the  terminal  direct  pressure  equal  to  the 
pressure  resisting  the  motion  of  the  piston,  and  irrespective  of 
the  method  of  variation  of/  with  v,  or  of  the  value  of  n. 

This  analysis  must  be  modified  when  the  expansion-line  is 
taken  as  an  equilateral  hyperbola  ;  in  which  case  we  have  n  =  i 
and/,^,  =A7V  This  case  is  often  assumed  in  the  theory  of 
gas  and  air  engines,  as  it  is  in  those  cases  that  of  isothermal 
expansion  ;  but  it  is  probably  rarely  observed  in  actual  prac- 
tice, and  perhaps  never  occurs  in  steam  and  vapor  engines.  In 
simple  computations  of  work,  however,  the  assumption  does 
not  lead  to  serious  error,  and,  so  expanding  the  working  fluid, 
the  energy  exerted  by  it,  up  to  the  point  of  cut-off,  is  equal  to 
the  lost  work  due  to  back-pressure  ;  the  net  work  done  is 
measured  by  the  total  area  under  the  expansion-line  of  the 


MAXIMUM  EFFICIENCIES  OF   THE   STEAM-ENGINE.     731 

indicator-diagram,  and  the   efficiency  is   proportional   to   the 
hyperbolic  logarithm  of  r. 
Thus  we  have 

w*  =  A",  (i  +  log,  r)  - 


whence  we  again  find 

A -A- 

The  following  are  values  of  n  for  various  cases  commonly 
taken  in  these  discussions : 

VALUES  OF  n  IN  p~S  =  CONSTANT. 

Air,  isothermal  expansion i.o 

"  adiabatic  "  1 .4 

"  wet  and  adiabatic 1.2 

Gases  generally,  isothermal i.o 

adiabatic 1.4 


in  explosive  gas-engines, 


Steam,  dry  and  saturated . 


adiabatic, 


Steam,  0.76 ;  water,  0.24. 


superheated 


.6 
.046 

•135 
.in 

•333 
Steam  and  water  generally 1.035  H 

But  in  all  real  engines  we  have  a  resistance  to  the  motion 
produced  by  the  expanding  fluid,  which  is  composed  of  two 
parts :  an  actual  back-pressure  on  the  piston,  pb=  /,,  as  in  the 
ideal  case  above,  and  a  resistance  due  to  friction  of  engine, 
including  pumps  and  all  attachments.  It  is  evident  that,  as 
this  latter  resistance,//,  like  the  back-pressure, pb,  is  a  constant 


732  A    MANUAL    OF    THE   STEAM-ENGINE. 

source  of  lost  work,  we  must  terminate  the  expansion  as  soon 
as  it  produces  a  greater  loss  of  power  or  of  work  than  is  gained 
by  further  expansion.  In  fact  :  given  a  certain  value  for  the 
sum  of  these  resistances,  pb  -}-//,  we  may  consider  the  whole 
as  back-pressure,  if  we  choose  ;  and  it  is  a  matter  of  indiffer- 
ence, so  far  as  the  determination  of  the  ratio  of  expansion  is 
concerned,  what  are  their  individual  magnitudes. 

To  determine  /&+//,  the  sum  of  resistances  due  to  back- 
pressure,^, and  to  the  frictional  and  other  resistances  —  as  of 
pumps,  etc.  —  denoted  by//,  take  an  indicator-card  from  the 
engine  unloaded.  Its  mean  pressure  measures  the  friction,//, 
of  the  unloaded  engine,  and  this,  sometimes,  probably,  increased 
by  a  fraction  of  the  pressure  added  by  the  load,  is  the  value  of 
//.  Or,  still  better,  determine  the  indicated  and  the  dynamo- 
metric  power  of  the  engine  simultaneously  ;  their  difference  is 
lost  work,  and  the  value  of  //,  corresponding  to  that  work,  is 
that  required. 

Hence,  for  actual  engines,  where  no  other  cause  of  loss 
exists  of  any  appreciable  magnitude,  we  may  write 


(6) 


and,  by  the  process  already  outlined,  we  obtain  a  maximum 
and  deduce 


Hence  :  Where  the  lost  energy  and  work  is  that  due  to  back- 
pressure and  to  friction  of  engine,  the  ratio  of  expansion  should  be 
such  as  to  carry  the  expansion-line  down  to  the  mean-pressure  line 
of  the  engine-diagram  taken  without  load. 

The  useful  work  is,  as  before,  the  gross  work  done  during 
expansion  ;  and,  thus  adjusted,  the  net  useful  work  and  the 
efficiency  are  nearly  proportional  to  log*  r.  This  conclusion  is 
obviously  true,  whatever  the  value  of  n  or  the  character  of  the 
expansion-line. 

Thus,  as  stated  by  Rankine,  "  the  greatest  useful  work  is 
obtained  by  making  the  expansion  cease  when  the  forward- 


MAXIMUM  EFFICIENCIES  OF   THE   STEAM-ENGINE.     733 

pressure  is  just  equal  to  the  back-pressure,  added  to  a  pressure 
equivalent  to  the  friction  of  the  engine."  * 

For  all  actual  steam  and  other  engines  still  further  and  still 
greater  modification  is  necessary,  since  in  such  engines  the 
departure  from  the  ideal  conditions  first  assumed  is  so  great  as, 
in  most  cases,  to  lead  to  radically  different  ratios  of  expansion. 
Even  in  the  gas-engines,  the  action  of  the  working  fluid,  as 
assumed  above,  is  very  greatly  modified  by  such  variations 
from  the  ideal  conditions  as  are  here  referred  to. 

For  any  given  engine,  there  is  always  a  certain  ratio  of  ex- 
pansion appropriate  to  every  steam-pressure,  and  which  gives, 
on  the  whole,  the  most  economical  performance.  Every 
engine  must  therefore  be  most  carefully  proportioned  to  the 
usual  conditions  of  its  operation. 

The  best  ratio  of  expansion,  kinematically,  when  the  ex- 
pansion-curve is  defined  by  the  expression  pmift  =  const.,  is 


and,  for  engine-efficiency,  friction  being  considered, 


r/«(-«Jf. 


The  defining  equation  usually  takes  the  form/'V  +  I  =  const.; 
when  we  have 


It  may  evidently  be  concluded  from  what  has  preceded : 
(i)  That  the  work  done  in  a  non-conducting  cylinder,  the 
fluid  expanding  adiabatically,  varies  so  little  with  the  propor- 
tion of  water  present  that  this  variation  may  be  neglected  by 
the  engineer,  and  he  may  assume  the  performance  of  work  to 

*  Life  of  John  Elder;  1871;  p.  16. 


734  A    MANUAL    OF   THE   STEAM-ENGINE. 

be  such  as  would  come  of  hyperbolic  expansion ;  while  the 
heat  thus  expended  may  be  computed,  as  in  the  thermc- 
dynamic  case,  from  the  quantity  of  work,  when  the  latter  is 
known. 

(2)  That,  in  cylinders  of  metal,  the  work  done  at  any  given 
point  of  cut-off  is  nearly  the  same  as  in  the  non-conducting 
cylinders;   but  that  the  quantity  of   heat  and  of  steam  ex 
pended  in  doing  it  are  increased,  and   usually  very  greatly 
increased,   by   cylinder-condensation,    if   ordinary   nearly  dry 
steam  is  used,  or  by  other  methods  of  storage  and  transfer  of 
heat   to  the   exhaust,  and   consequent  waste,  if   superheated 
steam  or  other  gaseous  working  fluid  is  employed. 

(3)  That  the  ratio  of  expansion  at  maximum  efficiency  of 
fluid  would  be  but  slightly  changed  by  ordinary  variations  in 
the  proportion  of  water  entrained  by  the  steam,  if  it  were 
worked  in  a  non-conducting  cylinder,  and  the  value  of  that 

P 
ratio,  re,  is  very  nearly  -+ ,  the  quotient  of  initial  pressure  by 

the  sum  of  the  cylinder  back-pressure  and  other  wasteful  re- 
sistances. 

(4)  That  the  ratio  of  expansion  at  maximum  efficiency  of 
fluid,  when  steam  expands  in  a  metallic  cylinder,  is  affected  by 
the  introduction  of  water  entrained  by  the  steam  ;  and  this 
difference  is  increased  and  usually  is  made  a  serious  one  by 
the  occurrence  of  cylinder-condensation,  or  other  method  of 
transfer  of  heat  to  the  exhaust.     This  ratio  becomes,  in  this 

case,  much  less,  usually,  than  re  =  ^ . 

Pb 

(5)  That  the  quantity  of  fluid  used  per  stroke,  in  the  non- 
conducting cylinder,  is  in  direct  and  exact  proportion  with  the 
volume  of  the  cylinder  open  to  the  supply-pipe  at  the  instant 

of  closing  the  expansion-valve,  and  is  measured  by  -,  the  re- 
ciprocal of  the  ratio  of  expansion. 

(6)  That  the  volume  of  steam  worked  per  stroke,  in  the 
metal  cylinder,  is  not  in  direct  proportion  to  volume  of  cylinder 
open  to  steam  at  the  point  of  cut-off ;  but  that  it  is  often  very 


MAXIMUM  EFFICIENCIES  OF   THE   STEAM-ENGIXE.     73$ 

greatly  in  excess  of  the  latter  quantity,  and  is  in  greater  excess, 
as  the  ratio  of  expansion  is  increased,  indefinitely. 

(7)  That   the    ratio  of   expansion   is  not  a  gauge  of   the 
volume  of  steam  demanded  from  the  boiler,  and  paid  for  by 
the  proprietor  of  the  apparatus,  when  the  metal  cylinder  is 
employed ;  but  that  the  volume  of  steam  used,  and  quantity 

of  heat  demanded,  must  always  exceed  the  proportion  —  in  real 

engines. 

(8)  The  Curve  of  Variation  of  Efficiency — of  which  the  ab- 
scissas measure  varying  quantities  of  steam  used  in  a  given 
steam-cylinder,  while  the  ordinates   are   proportional   to   the 
quantities  of  work  done  by  those  amounts  of  steam — is  a  curve 
of  entirely  different  character  and  form,  and  often  widely  dif- 
ferent in  location,  with  the  actual  engine,  from  the  curve  of 
adiabatic  mean  pressures,  or  other  curve  of  mean  pressures 
exhibiting  the  work  done  by  various  quantities  of  steam  ex- 
panding in  a  non-conducting  vessel. 

(91  That  no  predetermination  of  the  efficiency  of  any  pro- 
posed engine,  whether  of  fluid,  of  machine,  or  of  capital,  can 
be  made  unless  the  elements  of  the  true  curve  of  efficiency 
can  be  obtained  for  the  assumed  case 

(10)  That  the  most  certain  and  the  most  satisfactory  solu- 
tion of  any  problem  of  efficiency  will  be  that  obtained  by  first 
securing  the  data  for  the  curve  of  efficiency,  from  actual  en- 
gines, operated  in  the  manner  proposed  for  the  case  taken. 

(n)  That,  having  obtained,  by  experiment  upon  any  en- 
gine, the  true  "  Curve  of  Efficiency,"  as  defined  by  the  Author, 
the  efficiency  of  fluid,  of  engine,  and  of  capital  expended  to  do 
a  given  amount  of  work,  and  the  quantity  of  work  to  be  ob- 
tained most  cheaply  from  a  given  engine,  may  all  be  obtained 
for  any  given  set  of  conditions :  and  the  ratio  of  expansion  at 
maximum  efficiency,  of  fluid,  of  engine,  and  of  capital,  and  the 
ratio  of  expansion  which,  with  a  given  "  plant,"  gives  most 
work  for  a  dollar  of  total  expense  of  operation,  may  all  be  de- 
termined with  a  degree  of  exactness  only  limited  by  the  mag- 
nitude of  the  errors  of  observation. 


73^  A   MANUAL    OF   THE   STEAM-ENGINE. 

To  construct  the  theory  of  cases  of  non-adiabatic  expansion, 
the  Author  has  taken  the  following  method:*  We  may  take 
two  distinct  cases:  (i)  That  in  which,  as  when  the  cylinder  is 
unjacketed  and  unprotected  against  radiation  and  the  ratio  of 
expansion  small,  so  little  re-evaporation  occurs  that  it  may  be 
neglected  ;  (2)  That  in  which,  as  in  most  cases  familiar  to  the 
engineer,  and  especially  in  jacketed  cylinders  with  considerable 
expansion,  nearly  all  condensation  occurs  before  the  point  of 
cut-off  is  reached,  and  re-evaporation  takes  place  throughout 
the  remainder  of  the  stroke. 

Case  i.  —  It  has  been  seen  that  the  form  of  the  adiabatic 
expansion-line  may  be  obtained  from  approximate  expressions 
of  the  form  pvn  =  p1i>1n;  p^  =  plr~n. 

Since  loss  of  pressure  occurs  in  the  metallic  cylinder  by  a 
transfer  of  heat,  taking  place  by  initial  condensation  and  later 
re-evaporation,  and  since  the  amount  of  this  loss  is  determined, 
in  any  given  cylinder,  by  the  magnitude  of  the  ratio  of  expan- 
sion, we  may  write 


The  values  as  well  as  the  form  of  this  function  of  r,  f(r) 
above,  are  not  yet  exactly  ascertained.  The  Author  has  found 
that  for  the  ordinary  values  of  the  ratio  of  expansion  we  may 
assume,  as  an  approximation,  f(r)  =  arm  ;  m  being  taken  con- 
stant. 

In  this  expression  a,  for  any  engine,  has  a  value  which  is  de- 
termined by  the  condition  of  the  steam  at  entrance  into  the  cy- 
linder, and  is  connected  with  the  exponent  n  by  some  definite, 
though  as  yet  unascertained,  relation.  The  value  of  m  is  de- 
pendent upon  the  character  of  the  engine  and  the  method  of 
its  operation,  so  far  as  they  determine  the  variation  of  the 
proportions  of  steam  and  water  during  expansion.  Given  the 
values  of  n  and  of  a,  m  becomes  determinable.  We  have 

*  On  the  Behavior  of  Steam  in  the  Steam-engine,  etc.  Trans.  N.  Y.  Acad. 
Sci.,  1882  ;  Jour.  Franklin  Inst.,  Feb.  1882. 


MAXIMUM  EFFICIENCIES  OF  THE   STEAM-ENGINE.    737 


where  A  is  the  terminal  pressure,  a  quantity  always  known 
when  either  it  or  r  is  obtained  by  experiment. 

The  equation  for  the  expansion-line,  the  working  substance 
being  enclosed  in  a  metallic  cylinder,  is  then 


The  work  done  by  expansion  is 


The  net  work  is 


in  which  /4  is  the  back-pressure  plus  friction  and  useless  re- 
sistance. 

The  terminal  pressure  is  given  above.  Making  r  =  i,  we 
obtain  from  that  equation  A  =  A(*  —  a)  =  A'»  showing  that 
A  is  not  the  initial  cylinder-pressure,  A  '>  but  the  pressure  which 
the  same  weight  of  steam  would  have  given  if  working  at  the 
same  volume  and  without  condensation  in  the  same  cylinder  : 
A  exceeds  A'  in  the  ratio  I  :  I  —  a  ;  which  ratio  measures  the 
relative  working  values  of  the  same  mass  of  steam  with  and 
witnout  cylinder-condensation.* 

Integrating  the  expression  for  net  work  done  during  ex- 
pansion, 


*  If  x  is  the  "  dryness-fraction"  of  the  steam  when  worked  to  the  end  of 
stroke,  it  having  been  dry  when  drawn  from  the  boiler,  /,'  =  /,  x  ;  jrt  =  —  . 


73^  A   MANUAL   OF    THE   STEAM-ENGINE. 

we  obtain 


while  the  total  useful  work  per  stroke  is  £FM  —  We  -f-  AX- 
In  this  analysis  the  work-effect  of  re-evaporation  is  neglected 

as  unimportant. 

The  equation  of   these  curves  of  efficiency  for  adiabatic 

expansion  is 


n  — 
The  equation  for  the  present  case  is 

3-«  _  i       arm-"+l  —  a   . 


nea  y< 


The  mean  pressure  is  then 


and  the  mean  effective  pressure  is 


p,r2'"  —  p,r~l       ap.r"1'*  —  ap.r"1    , 

pt  —  -  —    —  —  —  --  —  --  r-1  --  h  A  r~*  —Pi- 
i  —  n  m  —  n-{-  i 

The  mean  effective  pressure  and  the  work  of  the  engine 
are  maxima,  r  varying  and  the  back-pressure,  pb,  being  fixed, 
when 


*  In  fact,  however,  re-evaporation—  the  effect  of  which  is  not  in  such  cases 
usually  found  to  be  important  in  increasing  efficiency  —  usually  prevents  the 
fall  of  terminal  pressure  to  the  value  /3  =/*• 


MAXIMUM  EFFICIENCIES  OF   THE  STEAM-ENGINE.     739 

provided,  as  assumed,  re-evaporation  may  be  neglected.    Then 

r--«r~»  =A 

A 

The  Ratio  of  Expansion  for  Maximum  Efficiency  of  Fluid  is, 

however,  that  which   makes  — a  maximum.     The 

A27. 
"  cut-off,"  or  fraction  of   stroke  completed  at  the  instant  of 

closing  the  steam-valve,  is  —  =  c,  and  its  value  for  maximum 

work  is  that  which  gives  £*  —  ac*~m  =  — . 

The  following  cases,  illustrating  the  results  of  this  method 
of  treatment,  as  applied  to  several  selected  examples,  such  as 
are  met  with  in  ordinary  practice,  are  given  as  exhibiting  a  very 
usual  range  of  values  of  the  quantities  involved  in  the  preced- 
ing equations: 

Character  of  Engine.                            /,  pb  a  m  n  rt 

I.  Non-condensing  engine 100  20  0.2  1.5  1.115  4-5 

II.  Condensing,  un jacketed 40  5  O.2  0.5  1.115  2.5 

III.  compound,  jacketed 60  6  0.1  i.i  1.125  °-° 

IV.  "  "        too      5      o.i      o.o      1.135     10.0 

In  the  first  three  of  the  above  cases,  the  steam  is  taken  from 
the  boiler  nearly  dry ;  in  the  last,  it  is  so  far  superheated  that 
it  expands  as  practically  dry  steam,  cylinder-condensation 
being  negligible. 

Case  2. — The  second  assumed  case  is  probably  that  usually 
met  with  in  practice,  initial  condensation  ceasing  with  the 
closing  of  the  expansion-valve,  and  re-evaporation  occurs 
throughout  substantially  the  whole  period  of  expansion.  Then, 
taking  b  =  I  —  a,  b  thus  measures  the  proportion  of  actual 
work  done  at  full  stroke  to  that  which  the  same  steam,  with- 
out cylinder-condensation,  would  do;  while  r*  is  a  factor  pro- 
portional to  the  wastes  at  other  ratios  of  expansion.  We  may 
write,  for  fhe  net  power  delivered : 


74^  A    MANUAL    OF   THE   STEAM-ENGINE. 

Here  plvl  measures,  as  before,  the  work  obtainable  from  the 
same  weight  of  dry  steam,  up  to  the  given  point  of  cut-off, 
when  working  at  the  same  ratio  of  expansion,  and  when, 
therefore,  bplvl  =/>/z/1  =  (i  —  #)/,?', ,  as  taken  in  the  first  case. 
The  above  expression,  r  varying,  becomes  a  maximum  when 


qn  '    bqn    pl ' 

The  mean  effective  pressure  is 

n  —  rl~ 
A  =  b1*  'A   n—  i       A  ' 

and  the  equation  of  the  curve  of  efficiency  is,  for  this  case  of 
non-adiabatic  expansion, 


y  = 


n  —  i 


For  the  case  of  nearly  hyperbolic  expansion,  which  is  a 
common  one  for  this  class  of  engines, 


Wn  =  bp,v,(\  +  log,r)r  -A^,, 
nearly  ;  which  is  a  maximum  when 


"*// 

The  mean  effective  pressure  is  A  —  bp^i  -\-  log,,  r]rq~l  —  pb. 

The  value  of  q  varies  from  o,  nearly,  to  0.5  ;  being  greatest 
with  most  efficient  engines. 

The  ratios  of  expansion  for  maximum  efficiency  are  those 
which  satisfy  the  above  equations. 

The  following  are  corresponding  values  of  a,  b,  and  n: 

a  o.oo  .10  .20  .30 

b  i. oo  .90  .80  .70 

n  1.135  1.125  1.115  1-105 


MAXIMUM  EFFICIENCIES  OF   THE  STEAM-EXGIXE.     741 

The  consumption  of  steam  and  cost  of  power  in  these  cases 
is  measured  by  the  volume  actually  introduced  at  the  initial 
pressure,  as  with  the  non-conducting  cylinder. 

The  values  of  a  and  b  are  very  widely  variable,  as  has  al- 
ready been  seen  (Chap.  \j,  with  variation  of  working  conditions, 
size  and  construction  of  engine  ;  the  engine  can  easily  obtain 
a  fairly  approximate  figure  for  either,  taking  that  found  by  ex- 
perience to  be  usually  characteristic  of  similar  engines  of  nearly 
the  size  of  that  which  his  judgment  commonly  leads  him  to 
anticipate  will  be  approximately  that  of  the  engine  to  be  de- 
signed. Where  the  commercial  and  other  problems  to  be  here 
discussed  relate  to  an  engine  actually  in  use.  these  quantities 
may  sometimes  be  directly  determined. 

Professor  Marks  has  solved  this  problem,  incorporating  in 
his  expressions  for  efficiency  the  Rankine  function  of  conden- 
sation-waste.* These  expressions  thus  become  somewhat 
complicated,  and  graphical  methods  are  commonly  preferred 
by  the  engineer,  in  solving  all  problems  of  this  class. 

182.  The  Efficiency  of  Capital  is  the  final  and  the  most 
vitally  important  of  the  problems  of  maximum  efficiency.  It 
determines,  when  solved,  the  best  ratio  of  expansion,  all  things 
considered.  But  since  the  quantity  of  work  to  be  performed 
and  the  power  of  the  engine  are  the  magnitudes  usually  given, 
and  since  the  size  of  engine  needed  to  do  a  given  amount  of 
work  varies,  other  conditions  being  the  same,  with  the  extent 
to  which  expansion  is  carried,  the  solution  of  the  problem  giv- 
ing the  ratio  of  expansion  at  maximum  commercial  efficiency, 
or  efficiency  of  capital,  is,  really,  the  determination  of  the 
proper  size  of  engine  for  the  case  taken. 

The  solution  of  this  problem  evidently  involves  a  study  of 
all  the  conditions  affecting  either  first  cost  or  expenses  of 
operation,  immediate  or  remote,  direct  or  indirect,  during  the 
life  of  the  apparatus.  Of  these  items  of  cost,  some  are  constant 
for  the  case  assumed  :  some  vary  with  the  size  of  engine ;  and 

*  Steam-engine ;  3d  ed.,  p.  191. 


742  A   MANUAL    OF   THE   STEAM-ENGINE. 

others  are  variable  with  the  size  of  boiler  and  quantity  of  steam 
demanded.* 

In  Case  8,  §  174,  making  the  sum  of  both  items  of  variable 
annual  expense — those  variable  with  size  of  engine  and  those 
variable  with  quantity  of  steam  demanded — a  minimum,  the 
sum  of  these  items  and  of  all  invariable  expenses,  i.e.,  of  the 
total  running  expense,  becomes  a  minimum,  and  the  problem 
is  solved  when  the  ratio  of  that  sum  to  the  quantity  of  work  is 
thus  made  a  minimum.  A  knowledge  of  these  conditions  and 
of  all  other  expenses,  constant  as  well  as  variable,  is  also  es- 
sential to  the  treatment  of  Case  Q.f 

Since  economy  of  fuel  and  steam  demands  the  use  of  a 
large  engine,  working  steam  with  considerable  expansion,  and 
gives  reduced  size  and  weight  of  boiler,  it  is  evident  that  the 
first  of  the  two  problems,  Case  8,  §  174,  is  to  be  solved  by  de- 
termining what  proportion  of  engine  and  boiler  will  be  cheap- 
est when  summed  up  at  the  end  of  the  life  of  the  plant  ;  this 
is  settled  when  the  ratio  of  expansion  at  maximum  commer- 
cial efficiency  is  known,  since  the  mean  pressure  is  thus  fixed, 
and  the  best  size  of  engine  and  boiler  is  thus  settled.  The 
work  will  then  be  done  less  economically  either  by  a  larger 
engine  and  a  smaller  boiler,  or  by  a  smaller  engine  supplied 
with  more  steam  by  larger  boilers. 

The  last  enunciated  problem,  Case  9,  is  solved  by  determin- 
ing what  degree  of  expansion  and  resulting  mean  pressure  and 
work  will  give  the  power,  from  an  engine  and  boiler  already 
installed,  at  least  total  cost  per  horse-power.  The  first  of  these 
problems  contains,  as  elements,  all  items  of  cost  variable  with 
change  of  proportions  of  engines  and  boilers  capable  of  doing 
the  same  given  quantity  of  work  ;  the  second  considers  every 
item  of  expense,  while  the  amount  of  power  is  the  variable 
quantity.  Both  problems  require  the  study  of  all  the  costs  of 
steam-power,  the  determination  of  the  way  in  which  each  is 


*  The  Several  Efficiencies  of  the  Steam-engine  ;  R.  H.  Thurston. 
f  First  treated,  so  far  as  the  writer  is  aware,  by  Messrs.  Wolff  and  Denton. 
Trans.  Am.  Society  Mech.  Engrs.,  1881  ;  American  Engineer,  1881. 


MAXIMUM  EFFICIENCIES  OF  THE  STEAM-ENGINE.    743 

related  to  total  expense,  and  the  manner  in  which  each  varies 
with  variation  of  the  variable  quantities  in  either  case.  The 
first  of  these  is  the  designer's  problem,  the  second  the  owner's 
or  the  user's,  as  the  Author  has  customarily  designated  them. 
If  we  have  given  a  certain  annual  invariable  expense  of 
operation,  certain  additional  expenses  variable  with  size  of 
engine,  and  therefore  with  the  ratio  of  expansion  adopted,  and 
certain  other  additional  expenses  variable  with  quantity  of 
steam  demanded  and  with  size  of  boiler  needed,  and  thus  also 
dependent  upon  the  ratio  of  expansion  at  which  that  steam  is 
used,  we  may  call  the  two  latter  quantities,  respect  ively./~"(r) 
and/"(f),  while  the  constant  part  maybe  called  C.  Then  the 
total  annual  expense  is  f\r)-\-f"(r)-t-Cr  which  is  a  minimum 
when  the  variable  part,  f\r)-\-f  "(r)=j\r)  is  a  minimum,  and 
this  is  a  minimum  when  its  ratio  to  work  done,  F(r),  is  a  min- 

imum, Le.,  when  ^^  is  a  minimum,  or  d^\  -s-dr  =  o.    The 


value  of  r  which  satisfies  this  condition  determines  the  required 
mean  pressure,  and  gives  Maximum  Commercial  Efficiency. 

The  determination  of  the  value  of  r  which  makes      p 

a  minimum  gives  the  solution  of  Case  9. 

Case  10  is  solved  by  determining  at  what  ratio  of  expansion 
the  cost  of  power  becomes  equal  to  the  market  value  of  the 
power,  less  a  stated  paying  profit. 

The  Annual  Cost  of  Steam  Power  thus  consists  : 

(1)  Of  certain  expenses  which  are  invariable,  whether  the 
work  is  done  by  a  large  engine  with  high  ratio  of  expansion 
and  small  boilers,  or  with  a  smaller  engine  working  at  a  low 
ratio  of  expansion  and  with  necessarily  larger  boilers.     These 
expenses  are,  usually  :    rent  of  building  or  interest  on  cost  ; 
taxes,  repairs,  etc.,  etc.,  on  structure  and  cost  of  location  :  the 
"  engineer's"  salary,  and  sometimes  all,  sometimes  part,  of  the 
fireman's  or  "stoker's"  wages;  also  sundry  minor  expenses, 
or  a  part  of  each  of  other  expenses,  which  as  a  whole  are 
variable. 

(2)  The  interest  on  first  cost  of  engine,  in  place  ;  the  cost 


744  A    MANUAL    OF   THE   STEAM-ENGINE. 

of  maintenance  and  repairs  ;  and  a  sum  which  measures  the 
depreciation  in  value  of  the  machine  due  to  its  natural  wear, 
or  to  its  decreasing  value  in  presence  of  changes  that  finally 
compel  the  substitution  for  it  of  an  improved  engine.  Oil, 
waste,  and  other  engineer's  stores  fall  under  this  head.  All 
these  items  are  variable  with  size  of  engine. 

(3)  The  expenses  of  supplying  the  engine  with  steam. 
These  are  : 

(a)  The  cost,  on  fuel  account,  of  the  steam  supplied  ;  and 
which  includes  also  the  cost  of  steam  condensed  en  route  to 
the  engine,  and  that  wasted  by  "  cylinder-condensation  "  and 
by  leakage,  as  well  as  that  actually  utilized.  This  total  quan- 
tity of  steam  greatly  exceeds  that  actually  used  in  the  produc- 
tion of  power  by  simple  transformation  of  heat  energy. 

This  item  varies  with  the  efficiency  of  engine,  and  deter- 
mines the  size  of  boiler  demanded. 

.  (b)  The  interest  on  cost  of  boilers  in  place,  and  their  appur- 
tenances; rent  of  boiler-room,  or  interest  on  its  cost ;  deprecia- 
tion, taxes,  repairs  and  insurance,  wholly  chargeable  to  boilers. 

This  item  is  variable  with  size  of  boiler. 

(c)  Cost  of  attendance  in  excess  of  the  costs  included  in  the 
constant  quantity  of  item  (i)  and  variable  with  size  of  boiler 
or  quantity  of  steam  demanded. 

The  pay  of  the  engineer  in  charge  is  usually  not  chargeable 
to  either  engine  or  boiler  alone :  his  position  is  one  of  super- 
vision over  the  whole  apparatus,  and  a  good  engineer  usually 
keeps  the  closest  watch  over  the  boilers.  With  small  engines, 
the  engineer  is  also  the  fireman.  With  large  engines,  the  num- 
ber of  additional  firemen  may  be  taken  as  proportional  to  the 
quantity  of  steam  demanded  ;  and,  with  very  large  marine 
engines,  a  similar  remark  may  apply  to  engine-room  attendance. 

In  working  up  this  account,  it  w.ill  be  most  convenient  to 
refer  all  costs  to  volumes  of  cylinder,  and  to  so  express  variable 
quantities  that  they  may  enter  the  equations  in  terms  of  the 
ratio  of  expansion,  which  ratio  is  to  be  taken,  as  hereafter 
shown,  as  an  independent  variable  upon  which  all  other  vari- 
able quantities  are  made  dependent.  We  will  enter  all  con- 


MAXIMUM  EFFICIENCIES  OF   THE  STEAM-ENGINE.     745 

slant  quantities  as  so  many  dollars  of  annual  expense ;  the 
total,  invariable  expense  being  denoted  by  A,  which  includes  all 
such  expenses,  whether  chargeable  to  engines  or  boilers,  or 
both.  The  first  cost  of  an  engine  varies  according  to  no  defi- 
nite rule,  and  differs  greatly  with  type  of  engine,  kind  of  valve- 
gear,  character  of  work,  and  value  of  material  and  labor,  both 
at  the  manufactory  and  at  the  place  of  installatioa  With 
standard  forms  01  engine,  nowever,  it  is  found  that  the  cost 
may  be  reckoned,  for  ordinary  variations  of  size,  as  approxi- 
mately proportional  to  volume  of  steam-cylinder;  and  prices 
may  be  fixed  on  that  basis.  The  cost  of  transportation,  other 
things  being  equal,  may  often  be  similarly  estimated  ;  as  may 
expenditures  for  repairs,  engineer's  supplies,  etc.;  although 
these  items  are  less  exactly  determinable. 

For  present  purposes,  it  may  be  assumed  that  interest  on 
cost  of  engine  in  place,  depreciation,  repairs,  and  all  other  ex- 
penses varying  with  size  of  engine,  may  be  reckoned  per  cubic 
foot  of  cylinder. 

The  cost  of  steam  supplied  to  the  engine,  exclusive  of  the 
constant  quantity  entered  in  (i)  may  be  reckoned  as  a  certain 
number  of  dollars  per  pound,  or  per  cubic  foot  of  steam  worked 
in  the  cylinder. 

The  weight  of  steam  supplied  for  the  performance  of  work 
— when  the  weight  per  cubic  foot  of  steam  at  the  given  pressure, 
/,  is  w ;  and  its  total  volume  is  v^  =  vt  -f-  r,  where  r  is  the  "  real " 

iw 
ratio  of  expansion — is  wv^  = ;  its  cost  per  cubic  foot  of 

CWV          CIV 

steam-cylinder  is    —f —  =  — ,  and   its  total  cost  per  year  is 

2Rcwvl  =  2Rc — -,  where  R  is  the  number  of  revolutions  made 

by  the  engine  per  annum. 

To  this  [weight  is  to  be  added  steam  wasted  by  cylinder, 
condensation,  by  leakage,  and  by  conduction  and  radiation  from 
engine  and  boiler.  This  may  be  allowed  for  by  multiplying 
the  last  item  by  a  factor  greater  than  unity,  determined  as 
elsewhere  shown. 


746  A    MANUAL   OF   THE   STEAM-ENGINE. 

183.  Theory  of  Efficiencies  of  the  Ideal  Engine.—  When 
the  cylinder-condensation  and  other  wastes,  and  their  variation 
with  variation  of  the  ratio  of  expansion,  may  be  neglected,  the 
"  Equation  of  Ideal  Steam-engine  Efficiencies"  may  be  writ- 
ten : 


2RWn 


Where  Fmay  be  called  the  counter-efficiency,  and  E"'  is  the 
ratio  of  work  done  to  variable  costs,  and  therefore,  in  the  sense 
here  adopted,  the  efficiency.  This  quantity  becomes  a  mini- 
mum, and  the  best  ratio  of  expansion  and  the  corresponding 
mean  pressure  are  obtained  when,  r  being  made  the  indepen- 
dent variable, 

n  —  nrl~ 
.-  A)  =  o;  r-._*_ 


Here  r  has  become  r"'.  A  is  the  total  annual  charge  per  cubic 
foot  of  cylinder  on  engine  account,  B  is  the  annual  cost  of 
steam  per  cubic  foot  filled  each  stroke,  and  is  measured  by 
2Rwc,  when  R  is  the  number  of  revolutions  of  engine  per  an- 
num, iv  the  weight  of  a  cubic  foot  of  steam  at  the  pressure/,, 
and  c  its  cost  per  pound,  including  all  running  expenses,  in  the 

boiler-room,  and  M  =  -~ 

More  explicitly  :  since  this  problem  demands  minimum  cost 
of  a  known  power,  and  the  ratio  of  expansion  at  Maximum 
Commercial  Efficiency,  we  have 

ptrv,  =  Constant  =  W. 


i 
n  —  i 

The  variable  cost  will  be,  as  before 
P= 


MAXIMUM  EFFICIENCIES  OF  THE  STEAM-ENGINE.    747 

which  is  to  be  made  a  minimum.     But  from  the  equation  of 
condition,  just  given, 


W 


Thence 


du 
and  the  minimum  is  found,  as  above,  when  —  =  o  ;  Le.,  when 


The  construction  of  this  equation  shows  that,  under  the  as- 
sumed conditions,  this  ratio  for  maximum  commercial  economy 
is  not  dependent  simply  on  the  size  of  engine  or  ratio  of  ex- 
pansion :  but  in  the  real  engine  small  cylinders  have  a  higher 
value  of  /»  than  large  e  ngines,  are  more  subject  to  wastes, 
internally  and  externally,  and  have  greater  friction.  They 
therefore  require  to  be  worked,  under  .similar  external  condi- 
tions, with  less  expansion  than  large  engines. 

Thus  the  solution  of  the  problem  determining  the  ratio  of 
expansion  r/"  and  the  mean  pressure  at  "  Maximum  Commer- 
cial Efficiency,  or  Efficiency  of  Capital,"  Case  8,  fixes  the  size 
of  that  engine  which,  doing  the  required  work,  will  do  it  at 
least  cost.  The  sum  of  all  variable  expenses  being  here  made 
a  minimum,  the  total  running  expense,  which  includes  all  in- 
variable charges,  also  becomes  the  least  possible,  and  the  pre- 
scribed work  is  done  at  least  total  annual  cost. 

To  find  the  ratio  of  expansion  at  which  any  given  engine, 
already  constructed  and  in  place,  Case  9,  will  give  the  largest 
amount  of  work  for  the  unit  of  running  expense,  i.e.,  to  deter- 
mine the  "  Ratio  of  Expansion.  r,l¥,  at  Maximum  Efficiency. 
of  a  Given  Plant,"  we  may  use  the  same  general  equation.  In 


74$  A  MANUAL    OF   THE   STEAM-ENGINE. 

this  case,  the  size  of  the  engine  being  fixed,  the  whole  annual 
"  cost  of  engine"  becomes  constant,  and  we  write  the  equation 
in  precisely  the  same  form  as  before, 

V  -     I        A' 
~ 


2RWn      ' 

but  making  the  symbol  A'  cover  all  annual  expenses  of  the  en- 
gine-room, estimated  per  cubic  foot  of  cylinder,  and  including 
all  constant  charges  of  attendance  in  the  boiler-room  as  well  ; 
while  B  now  only  includes  those  costs  which  are  still  variable 
with  the  steam-supply  ;  V  thus  measures  the  ratio  of  total  an- 
nual expenses  of  operation  to  work  done.  We  now  obtain,  by 
the  same  process  as  before,  such  a  ratio  of  expansion  that 


when  TV  is  a  modification  of  M,  such  that  it  represents  the  ratio 
of  the  total  expenses  classed  with  engine-cost  to  the  "  cost  of 
full  steam,"  as  already  taken,  and  r  has  become  r^. 

Again  :  making  A  and  M  or  N  equal  zero  in  the  general 
equation,  and  making  pb  the  sum  of  useless  resistances  ex- 
pressed as  the  intensity  of  pressure  on  the  piston, 


A 

and  r  —  r"  ,  the  ratio  of  expansion  at  "  Maximum  Efficiency 
of  Engine." 

Similarly,  if  /3  is  the  actual  back-pressure  in  the  steam-cyl- 
inder, 


and  we  have  the  ratio  of  expansion  at  "  maximum  efficiency  of 
fluid,"  r  =  rj. 

To  solve  this  problem,  therefore,  we  are  to  determine  the 
costs  of  steam,  assuming  the  engine  to  work  at  full  stroke,  in- 


MAXIMUM  EFFICIENCIES  OF   THE   STEAM-ENGINE.     74Q 

eluding  all  incidentals  dependent  upon  its  quantity ;  make  this 
the  scale  of  measurement ;  find  the  total  costs  of  engine  in  the 
same  manner  and  on  the  same  scale ;  ascertain  the  total  con- 
stant annual  or  hourly  expenses;  introduce  these  quantities 
into  our  general  equation,  or  our  graphical  construction,  and 
solve  for  the  required  ratio  of  expansion.  This  determined, 
we  are  to  find  what  size  of  engine,  working  at  this  ratio,  will 
give  the  demanded  power,  and  the  problem  is  completely 
solved. 

Should  the  size  so  determined  be  far  different  from  that 
assumed  in  the  estimates  of  costs  and  losses,  a  second  approxi- 
mation, based  upon  the  new  estimates  of  these  quantities,  will 
give  a  satisfactory  solution. 

In  each  of  these  several  cases  the  expression  obtained  is  de- 
rived, it  will  be  noted,  by  making  r  the  independent  variable, 
and  determined  by  the  magnitude  of  the  ratio  of  the  two  cost- 
items,  and  is  the  result,  under  the  given  conditions,  indepen- 
dent of  the  actual  size  of  the  engine.  Thus  we  determine,  in 
each  case,  the  ratio  of  efficiency  which  is  correct,  under  the  as- 
sumed conditions,  for  all  engines  of  the  class  upon  which  our 
estimates  are  based.  We  thus  are  able  now  to  tabulate  the 
proper  size  of  engine  for  assumed  quantities  of  work,  and  the 
powers  at  which  each  engine,  once  set  at  work,  will  operate 
with  maximum  efficiency,  commercial  or  other.  Finally,  com- 
paring costs,  it  can  be  determined  in  any  known  case  just  when 
a  change  of  engine  will  be  financially  advisable. 

But  this  simple  method  of  treatment  cannot  be  applied 
where  cylinder-condensation  becomes  a  serious  item ;  in  fact, 
therefore,  it  is  comparatively  valueless  for  very  many  cases  in 
engineering  practice. 

184.  Rankine's  Diagram  of  Efficiency. — For  the  ideal 
case,  or  any  fair  physical  approximation,  Rankine's  graphical 
treatment  of  the  problem  here  studied  is  conveniently  applica- 
ble, and  by  its  use  the  engineer  may  easily  solve  such  problems 
by  a  simple  construction  on  his  drawing-board. 

In  illustration :  Suppose  an  engine,  of  one  cubic  foot  ca- 
pacity, to  be  in  operation,  expanding  steam  adiabatically,  its 


750 


A    MANUAL    OF    THE    STEAM-ENGINE. 


cylinder  and  piston  being  impervious  to  heat,  and  the  engine 
having  an  adjustable  expansion-gear.  When  following  full- 
stroke  it  uses  one  cubic  foot  of  steam  per  stroke,  at  initial 
pressure;  when  "cutting  off  "at  half-stroke,  one  half  cubic 


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FIG.  166. — RANKINE'S  EFFICIENCY-DIAGRAM. 

foot,  and  at  a  cut-off  of  one  quarter,  one  fourth  of  a  foot,  are 
used,  the  quantity  used  always  being  inversely  as  the  ratio  of 
expansion.  To  determine  the  best  ratio  of  expansion  :  Con- 
struct a  curve,  OA,  Fig.  166,  of  which  the  abscissas  are  pro- 
portional to  the  amount  of  steam  used,  while  the  ordinates  are 


MAXIMUM  EFFICIENCIES  OF   THE  STEAM  ENGINE.     751 

proportional  to  the  mean  absolute  pressure  for  that  degree  of 
expansion,  and  the  "  total  work"  of  the  steam  so  measured  off. 
Drawing  a  line,  BC,  parallel  to  the  base,  and  at  a  height  pro- 
portional to  the  back-pressure  in  the  engine-cylinder,  the  ordi- 
nate  from  any  point  in  the  curve  down  to  this  line  will  measure 
the  corresponding  "  mean-effective  pressure"  shown  by  the  in- 
dicator for  that  degree  of  expansion,  and  will  be  proportional 
to  the  "  indicated  power"  of  the  engine.  Again :  Drawing  a 
line,  DE,  at  the  height  measuring  the  sum  of  all  useless  resist- 
ances, the  "  net"  or  "  dynamometric"  power  of  the  engine,  as 
transmitted  to  the  machinery  of  transmission,  is  measured  by 
ordinates  between  the  curve  and  this  line.  Finally,  extending 
this  second  line  toward  the  left,  and  measuring  off  upon  it  a 
distance  proportional  to  the  cost  of  operation  so  far  as  it  de- 
pends upon  the  plant,  and  measured  on  the  same  scale  as  that 
used  in  laying  off  DG  on  the  base-line  in  terms  of  cost  of 
steam,  the  sum  of  the  two  costs,  as  £/%  measures  the  total 
expense  of  obtaining  the  power ;  while  the  height  of  ordinate 
GH,  measured  from  the  last  drawn  line,  is  proportional  to  the 
net  amount  of  power  obtained.  For  any  one  amount  of  con- 
stant expense,  as  determined  by  the  location  of  the  point,  F, 
the  line  FH,  drawn  tangent  to  the  curve,  touches  the  latter  at 
a  point  marking  the  ratio  of  expansion  at  maximum  commer- 
cial economy,  or  if  drawn  from  the  axis  OY,  as  DK,  it  identi- 
fies the  ratio  for  maximum  "efficiency  of  engine." 

To  solve  this  problem  of  maximum  efficiency :  Draw  the 
mean-pressure  curve  OA,  making  the  base-line,  OX,  a  measure 
of  all  costs,  "  at  full  steam,"  variable  with  quantity  of  steam 
demanded  by  the  engine,  and  the  ordinates  proportional  to 
the  mean  pressure,  corresponding  to  the  cut-off.  Draw  a  line 
parallel  to  the  base,  as  BC  or  DE,  at  a  height  corresponding 
to  the  back-pressure  plus  useless  resistances  of  engine.*  Take 
DF  equal  to  the  unvarying  costs,  independent  of  steam-sup- 
ply, on  the  same  scale  on  which  DE  measures  costs  of  full 

*  I.e.,  back-pressure  plus  mean-effective  pressure  as  found  on  the  "friction- 
diagram." 


752  A  MANUAL    OF   THE   STEAM-ENGINE. 

steam.  Draw  a  tangent,  Fff,  to  the  curve  OH  A  and  let  fall 
a  perpendicular  from  H  to  the  base-line. 

The  point  thus  identified  on  OX  will  indicate  the  proper 
ratio  of  expansion  for  highest  total  commercial  efficiency. 

This  simple  and  beautiful  construction  is  correct  and  ex- 
act, when  cylinder-condensation  and  other  wastes  of  the  real 
engine,  as  leakage,  may  be  neglected.  For  other  cases  this 
construction  may  lead  to  widely  inaccurate  results.  It  is  ob- 
vious that  any  accurate  and  reliable  method  must  take  account 
of  all  losses  of  heat,  and  must  thus  distinguish  between  effi- 
cient and  inefficient  classes  of  heat-engines. 

185.  Theory  of  Efficiencies  of  Real  Engines.—  The  di- 
rect process  of  analytical  treatment  of  this  general  problem  for 
real  engines,  adopted  by  the  Author,  is  the  following  : 

Let  it  be  known  what  style  of  engine  is  to  be  adopted,  for 
any  case,  and  what  kind  of  boilers  and  attachments  are  to  be 
used  in  supplying  steam.  Let  the  costs  of  attendance  and  all 
other  expenses  be  ascertainable.  Then,  to  adopt  Rankine's 
terms,  ascertain  A,  the  annual  variable  "cost  of  engine"  of  the 
selected  type,  per  cubic  foot  of  steam-cylinder,  and  £,  the  an- 
nual variable  "  cost  of  boiler,"  per  cubic  foot  of  steam-cylinder 
supplied  without  expansion  and  without  allowance  for  cylinder- 
condensation  or  leakage  ;  ascertain  all  other  costs,  invariable 
with  change  of  size  of  either  engine  or  boiler  within  the  range 
of  the  problem,  and  call  their  total  C. 

The  "  cost  of  engine"  will  be,  as  before,  Avt  =  Arvl  ;  the 
"cost  of  boiler"  will  be  Bv^  and  the  constant  charges  C. 

Make  4  =  M. 
z> 

The  work  done  per  stroke  may  be  called  WM,  and  work  per 
annum  becomes  2RWn. 

The  ratio  of  the  total  of  annual  variable  costs  of  power  to 
work  done  by  the  engine  is 


2RWn        ' 

r"  . 
which  is  a  minimum  when  -  TJ  -  is  a  minimum. 


MAXIMUM  EFFICIENCIES  OF    THE   STEAM-EXCISE.     753 

The  value  of  Wu  may  here  be  obtained  by  multiplying  the 
value  of  W,  for  adiabatic  expansion,  such  as  would  be  obtained 
in  a  non-conducting  cylinder,  by  a  factor  variable  with  the  ratio 
of  expansion,  as  already  shown,  which  shall  measure  the  ratio 
of  actual  work  done  in  the  metallic  cylinder  to  that  performed 
with  adiabatic  expansion.  Thus : 

Let  b  represent  the  proportion  of  steam  present  in  the 
working  cylinder  when  r  =  i ,  as  reduced  by  the  cylinder-con- 
densation ;  let  r1  represent  the  rate  of  variation  of  losses  with 
increase  of  ratio  of  expansion  ;  and  let  n  be  the  index  for  the 
expansion-line  of  the  mixture. 

/         nr~* r~m  \ 

Then  we  shall  have  :  Wm  =  2R\bp^ r*— pp\. 

\  ft  I  j 

The  "  General  Equation  of  all  Steam-engine  Efficiencies" 
therefore,  now  becomes 


which  becomes  a  minimum  and  makes  the  Commercial  Effi- 
ciency of  an  Engine,  for  the  required  work,  a  maximum  when, 
to  obtain  r/",  we  have  made 


+ 


q-m+i         _       «-T      A  ™ 

~Mn(3-if      -- 


When  the  ratio  of  expansion,  r**9  at  "  Maximum  Efficiency 
of  a  Fixed  Plant"  is  required,  Avt  is  constant,  and  we  may 
make 

' 

*  =  N,  and  the  equation  for  Efficiency  of  Plant  becomes 


"  .    (C) 


754  A   MANUAL   OF   THE   STEAM-ENGINE. 

and  this  gives,  similarly,  for  riv  and  a  maximum, 

^  +  -J^-^~l- 


'(?-!)  •&.— -I)  Nn(q-l) 

n  —  I       A 


To  obtain  r"  for  Maximum  Efficiency  of  Engine,  we  make 
N  =  o,  and  have 

9    ^-:       ^-n+i          _     n-i      p, 
q-l  n(q-l)  ~nb(q-i)p; 

and  to  obtain  Maximum  Efficiency  of  Fluid,  pb  becomes/,,  and 


in  which  r/  satisfies  the  equation. 

When  ^  =  i  and  q  =  o,  we  have  the  «^«/  case  considered 
in  §  5,  and  the  equation  (B)  for  r,'"  becomes,  as  before,  for  the 
perfect  engine, 


for  Maximum  Commercial  Efficiency  ;  and  we  again  obtain  for 
the  ideal  case  of  Maximum  Economy  of  a  Given  Plant,  for  relv, 


(H) 


For  Maximum  Efficiency  of  Engine  we  now  again  obtain  a 
value  of  re",  such  that 


and  finally  for  ideal  Maximum  Efficiency  of  Fluid  we  find  a 
value  of  re'  such  that 

'   .-"-.-  r-.j  -----  ,..    .    .    .    (J) 

precisely  as  already  stated. 


MAXIMUM  EFFICIENCIES  OF   THE   STEAM-ENGINE.     /$$ 

By  making  the  assumption  considered  allowable  by  Mr. 
Buel  and  by  Professor  C.  A.  Smith,  and  apparently  justified 
by  the  experiments  of  Emery  and  the  work  of  the  Author,  as 
already  remarked  (Chapter  V),  the  equations  for  the  ideal 
engine  and  the  Rankine  diagram  may  sometimes  be  made  to 
yield  substantially  accurate  and  satisfactory  results.  In  such 
cases  the  internal  wastes  are  taken  as  sensibly  invariable  for  all 
ratios  of  expansion  and  can  be  reckoned  as  a  part  of  the  con- 
stant charge  in  A  ;  and  thus  the  value  of  FD,  Fig.  166.  or  of  J/, 
is  increased  proportionally.  As  seen  later,  this  value  is  usually 
2  or  3  per  cent  in  the  exact  case.  J/  may  become,  by  the 
addition  of  internal  wastes,  12  or  15  per  cent  for  un jacketed 
mill-engines,  8  or  10  per  cent  for  jacketed  simple  engines,  as 
low  as  5  to  7  per  cent  for  compound  engines,  and  still  less  for 
the  higher  types.  N  will  be  thus  increased  to  a  figure  2  or  3 
per  cent  larger  than  J/,  for  non-condensing  engines,  in  ordinary 
work,  assuming  the  engines  of  at  least  two  or  three  hundred 
horse-power,  and  6  or  8  per  cent  greater  for  condensing 
engines,  as  seen  later,  in  the  tables. 

The  constants  in  the  formulas  should  be  carefully  deter- 
mined, if  possible,  by  experiment  on  the  class  and  the  size  and 
speed  of  engine  to  be  designed  ;  but,  in  the  absence  of  better 
data,  are  taken  by  the  Author  with  moderately  large  engines, 
at  usual  speeds,  as  follows,  for  good  practice : 

*  t 

I.  Cylinders  jacketed,  steam  superheated 

at  boiler 0.90        o.         1.06 

II.  Cylinders  jacketed,  steam   saturated, 

but  dry  at  boiler 0.85    —0.25     1.06 

III.  Cylinders  unjacketed,  steam  saturated, 

but  dry  at  boiler 0.85    —  0.3      0.98 

IV.  Cylinders  unjacketed,  steam    slightly 

moist 0.80    —  0.5      O-95 

Case  I  is  illustrated  by  the  best  work  of  well-known  and 
successful  builders.  The  value  of  b  is  obtained  by  comparing 


75  A  MANUAL    OF   THE   STEAM-ENGINE. 

the  actual  results  of  test  with  the  figures  for  the  perfect  engine 
to  determine  the  waste ;  that  of  n  is  obtained  by  assuming 
these  engines  effectively  jacketed,  the  steam  being  retained 
dry  and  saturated  throughout  the  stroke  ;  and  q  is  taken  to 
be  o,  since  the  rate  of  transfer  of  heat  to  exhaust  seems  to  be 
nearly  constant  for  such  engines,  as  well  as,  for  the  usual  ratios 
of  expansion,  of  minimum  amount.  The  second  case  is 
obtained  by  examining  scattered  records  of  somewhat  less 
efficient  engines.  The  values  of  b  and  q  for  III  are  obtained 
by  studying  the  performance  of  good  unjacketed  engines  \ 
while  the  last,  IV,  came  originally  from  the  results  of  test  of 
the  U.  S.  S.  Michigan,  with  an  allowance  of  10  per  cent  for  the 
unrecorded  waste  concealed  by  re-evaporation.  In  all  cases 
the  variations  in  value,  as  determined  by  conditions  already 
fully  described  (Chapter  V)  should  be  considered  where  the 
experimental  data  are  taken  from  engines  of  a  different  class 
or  size. 

186.  Curves  of  Efficiency  for  Real  Engines. — The 
correct  curve  for  the  diagram,  for  actual  engines,  has  not  yet 
been  expressed  by  any  exact  equation.  It  is  very  variable  in 
location,  in  form,  and  in  dimensions,  and,  as  yet,  can  only  be 
exactly  determined  by  experiment. 

In  the  diagram  above  given,  as  is  evident,  the  quantities  of 
steam  laid  down  in  arithmetical  progression  on  the  base-line 
cannot  now  correspond  with  the  ratios  of  expansion  there 
taken;  since  in  actual  engines  those  values  are  not  in  exact,  or 
in  constant,  inverse  proportion.  The  quantity  of  steam  drawn 
from  the  boiler  is  not  measured  by  the  volume  of  cylinder 
open  to  steam  up  to  the  point  of  cut-off ;  nor  is  the  mean 
pressure  obtained  with  any  given  weight  of  steam  drawn  from 
the  boiler  at  each  stroke,  even  approximately,  equal  to  that 
given  by  expansion  in  a  non-conducting  cylinder.  Both  these 
causes  operate  to  depress  and  flatten  the  curve  of  efficiency, 
and  thus,  often,  to  reduce  the  ratio  of  economical  expansion 
far  below  that  predicted  when  the  former  and  impossible  con- 
ditions were  assumed.  The  vertical  scale  of  pressures  and  the 
horizontal  scale  of  ratios  of  expansion  have  become  altered  in 


MAXIMUM  EFFICIENCIES  OF   THE   STEAM-EXCISE.     757 

relative  magnitude,  and  the  latter  becomes  for  usual  cases  a 
variable  scale. 

To  obtain  a  solution  of  the  actual  problem  as  presented 
daily  to  the  designing  engineer,  a  new  method  of  procedure 
must  be  adopted.  The  Author  has  proposed  the  following  : 

187.  Thurston's  Diagrams  and  Curves  of  Real  Effi- 
ciency.— It  has  become  evident  that  the  best  ratio  of  expan- 
sion or  proper  "  point  of  cut-off,"  and  the  mean  effective 
pressure  to  be  assumed  in  designing  a  proposed  engine,  for  any 
actual  case,  is  determined,  not  by  the  percentage  of  loss  sus- 
tained at  that  point  simply,  or  by  the  cylinder-condensation 
there  taking  place,  but  by  the  method  of  variation  of  such  loss 
all  along  the  curve  of  efficiency  and  at  other  ratios  of  expan- 
sion ;  since,  in  the  metallic  cylinder,  the  proportion  of  the 
water  present  in  the  working  fluid  is  constantly  varying  with 
change  of  volume,  and  the  loss  of  pressure  and  of  work  is  con- 
stantly and  proportionally  varying,  producing  a  curve  of  effi- 
ciency differing  greatly  in  character,  form,  and  location  from 
that  given  by  a  non-conducting  cylinder.  It  is  obtained  thus : 

Assume  for  the  unit  of  measure  so  much  steam  as  is  drawn 
from  the  boiler  at  one  stroke  of  the  piston,  without  expansion. 
Draw,  Fig.  167,  OX,  and  divide  it,  as  unity  of  volume  or  of 
weight,  into  a  scale  of  equal  fractional  parts.  Erect  at  X  a 
perpendicular,  XAB,  and  divide  it  into  any  convenient  number, 
say  100,  of  equal  parts.  Were  there  no  condensation-wastes, 
the  fluid  being  worked  in  a  vessel  of  non-conducting  material, 
instead  of  an  iron  steam-cylinder,  the  mean  pressure  at  full 
stroke  and  the  work  done  per  cubic  foot  or  per  pound  of 
boiler-steam  would  be  measured  by  XB,  and  the  curve  of 
mean  total  pressures,  or  of  steam  used  per  "  total  "  horse-power 
per  hour,  would  be  OWE. 

Condensation  reduces  the  work  at  full  stroke,  and  it  is 
actually  measured  by  XA.  Were  the  condensation  in  con- 
stant proportion  for  all  values  of  the  real  ratio  of  expansion, 
the  ordinates  of  the  true  curve  would  be  proportional  to  those 

of  O  WB,  and  the  values  of  —  would  remain  proportional  to  the 


758 


A  MANUAL   OF   THE   STEAM-ENGINE. 


expenditure  of  steam,  as  in  adiabatic  expansion.  But  the 
amount  of  condensation  usually  increases,  and  often  very 
rapidly,  with  increasing  expansion,  and  at  one  half,  one  quarter, 
or  one  eighth  cut-off  more,  and  sometimes  much  more,  than 


FIG.  167.— THURSTON'S  REAI,  CURVES  OF  EFFICIENCY. 

one  half,  one  quarter,  or  one  eighth  as  much  steam  is  used  as  at 
full  stroke.     The  scale  of  ratios,  — ,  is  thus  not  only  shifted,  but 

is  made  a  scale  of  unequal  parts,  of  which  the  successive  values 
must  be  located  by  determining  the  amount  of  steam  used  at 

each   point  of  cut-off,  and  placing  the  value  -  opposite  the 

value  of  the  corresponding  amount  of  steam  expended,  as  has 
been  done  in  Fig.  166. 


MAXIMUM  EFFICIENCIES  OF   THE   STEAM-ENGINE.     759 

It  may  be  remarked  here  that  if,  as  is  sometimes  under 
special  circumstances  nearly  true,  the  losses  by  condensation 
and  leakage,  or  both,  are  so  great  as  to  annul  the  benefit 
derived  from  expansion,  the  curve  flattens  down  to  a  straight 
line,  OA.  In  every  engine  a  point  is  reached  by  increasing  r, 
at  which  the  amount  of  steam  used  per  hour  per  total  horse- 
power is  as  great  as  at  full  stroke ;  in  every  case,  therefore,  the 
true  curve  crosses  the  line  OA,  as  at  C.  The  line  OCE  is 
thus  representative  of  the  class  of  mean-pressure  or  efficiency 
curves  given  be  actual  engines.  Could  the  variation  of  expen- 
diture of  heat  be  exactly  expressed  by  an  algebraic  equation, 
this  equation  would  be  that  of  the  line  ACE,  and  the  problem 
would  be  capable  of  exact  solution  by  algebraic  methods. 

It  will  be  seen  that  the  employment  of  this  curve  for  the 
real  case  by  the  method  previously  applied  to  the  ideal  case, 
in  the  solution  of  the  actual  problem,  as  practically  meeting 
the  engineer,  results,  primarily,  in  the  determination  of  that 
quantity  of  steam  per  stroke,  as  a  fraction  of  the  conventional 
unit  taken,  which  will  yield  the  demanded  power  at  minimum 
cost.  The  identification  of  the  corresponding,  required,  ratio 
of  expansion  for  maximum  efficiency  is  effected  after  the  solu- 
tion of  this  problem  is  completed.  The  problem  solved  might 
have  been  thus  stated  : 

Required,  the  quantity  of  steam,  taken  as  a  fraction  of  that 
used  at  full  stroke,  without  either  expansion  or  condensation, 
which  should  be  worked  per  stroke  to  insure  minimum  total 
cost  of  the  prescribed  power. 

This  becoming  known,  the  corresponding  point  of  cut-off  is 
at  once  determinable. 

188.  Solution  of  Problems  for  Actual  Engines. — Draw 
HG  at  a  height  above  OX,  Fig.  167,  equal  to  the  back-pressure, 
p3  •  then  the  tangent  line  HK  identifies  a  point  K,  which  gives 
the  ratio  of  expansion  and  the  mean  pressure  at  maximum 
efficiency  of  fluid — since  the  ordinate  GK  measures  the  work 
done  by  the  steam  HG  drawn  from  the  boiler — and  the  ratio 

(*K 

*—=  becomes  a  maximum  at  G.     Drawing  ML  to  represent 
HG 


760  A    MANUAL    OF    THE   STEAM-ENGINE. 

the  pressure  demanded  to  overcome  all  useless  resistance, 
/=/3+//,  a  similar  construction  identifies  D  as  the  point 
corresponding  to  the  ratio  of  expansion  and  the  mean  pressure 
at  maximum  efficiency  of  engine.  Finally,  extending  this  line 
to  Fand  making  VM  proportional  to  cost  of  all  running  ex- 
penses, stated  in  terms  of  costs  of  engine  and  accessories  per 

A 
cubic  foot  of  cylinder,  VM '  =  -%-  —  M  for  the  case  of  engine 

working  at  full  stroke,  the  tangent  line  VZ  meets  the  curve  at 
a  point,  D',  which  gives  the  ratio  of  expansion  and  the  mean 
pressure  at  maximum  commercial  efficiency.  Comparing  these 
values  of  r  with  those  given  by  the  tangents,  HR,  MP,  VW, 
drawn  to  the  curve  OWB,  for  dry  saturated  steam  expanded 
adiabatically,  it  is  seen  that  the  best  ratio  of  expansion,  and 
the  mean  pressure  to  be  chosen,  must  be,  in  each  actual  ex- 
ample, less  than  in  the  hypothetical  case,  and  may  even  become 
unity  for  each  kind  of  efficiency,  with  very  slow  piston-speeds, 
where,  were  no  loss  of  heat  to  occur  in  the  manner  here  con- 
sidered, considerable  expansion  would  be  desirable.  These 
differences  all  become  greater  as  the  back-pressures  and  current 
expenditures  become  less. 

Making  the  value  of  VM  a  measure,  in  the  case  of  an  engine 
in  use,  of  the  total  current  expenses,  including  the  constant 
as  well  as  variable  items  of  cost,  as  of  attendance,  of  rent, 
insurance,  etc.,  which  do  not  depend  on  size  of  engine, 

A' 

VM  =  ~7T  —  N,  and  a  value  of  r  will  be  obtained  which  is  that 
n 

real  ratio  of  expansion  at  which  maximum  work  is  done  for  a 
given  expenditure,  per  hour  or  per  annum,  on  a  plant  actually 
established. 

This  problem  is  less  frequently  presented  to  the  engineer 
than  those  already  given,  and  is  not  the  problem  of  maximum 
commercial  efficiency ;  since,  this  ratio  and  the  corresponding 
power  of  engine  being  determined,  it  will  be  found,  on  solv- 
ing for  maximum  commercial  efficiency,  the  "  designer's  prob- 
lem" as  the  Author  has  called  it,  that  another  proportion  of 
engine  with  higher  ratio  of  expansion  will  supply  the  power 


Ji/AXIJ/UM  EFFICIENCIES  OF   THE  STEAAl-EJCGIXE.     j6l 

now  demanded  at  still  lower  cost.  To  this  new  engine  the  last 
problem  again  applies,  and  the  practical  conclusion  to  be 
drawn  from  the  solution  of  the  interminable  succession  of 
problems  of  this  last  character  which  thus  follow  the  first 
is  that  the  largest  amount  of  power  possible  should  be  en- 
trusted to  a  single  engineer,  or  "  engineer's  crew,"  and  placed 
under  one  roof,  etc.  In  this  last  case,  all  items  become  con- 
stant except  those  dependent  upon  the  quantity  of  fuel  burned. 

Finally,  the  last  of  these  problems  may  be  solved. 

To  ascertain  what  ratio  of  expansion,  what  mean  pressure 
should  be  adopted,  and  what  amount  of  work,  as  a  maximum, 
can  be  profitably  obtained  from  an  established  plant :  Compute 
the  net  power  obtainable  from  the  engine  without  expansion, 
and  the  market  value,  or  otherwise  real  value  to  the  proprietor, 
of  that  power,  and  estimate  the  cost  of  fuel  and  all  items  of 
cost  variable  therewith.  Divide  the  price  of  power  by  this 
cost.  .Then  lay  off,  on  the  base-line  appropriate  to  the  given 
engine,  the  distance  5F,  produced,  equal  to  the  quotient,  tak- 
ing the  distance  MS  as  unity,  and  from  the  extremity  of  this 
prolonged  base-line  draw  a  straight  line,  TAf  to  the  point  A, 
at  the  altitude  AS  equal  to  the  measure  of  the  net  power  just 
calculated.  Finally  draw  a  line,  UA,  parallel  to  this  hypothe- 
nuse  of  the  triangle  so  described,  and  tangent,  as  at  Z\  to  the 
curve  of  efficiency-  The  point  of  tangency  Z'  wfll  identify  the 
minimum  profitable  ratio  of  expansion*  and  thus  determine  the 
maximum  amount  of  work  obtainable  from  this  engine  with 
profit.  For,  at  this  point  of  tangency  the  ratio  of  total  cost  of 
power  to  the  price  obtainable  for  it,  or  to  its  actual  value,  is 
that  already  given  as  the  greatest  permitting  a  fair  profit,  while 
the  ratio  of  expansion  so  determined  is  that  giving  that  power 
at  that  rate  of  cost. 

The  value  of  the  Ratio  of  Expansion  at  Maximum  Profitable 
Power  is  evidently,  in  all  actual  examples,  less,  and  the  work 
done  is  greater,  than  in  either  of  the  preceding  cases,  and  is 
dependent  upon  the  market  value  of  that  power. 

In  all  cases,  the  ratio  of  expansion  computed  or  determined 
is  the  real  ratio ;  the  apparent  ratio  is  the  former,  decreased  by 


762  A    MANUAL   OF   THE   STEAM-ENGINE. 

clearance,  and  increased,  often  considerably,  by  the  wire-draw- 
ing which  occurs  just  before  the  valve  is  seated. 

It  is  evident  that  loss  of  steam  by  leakage  modifies  the 
curve  of  efficiency  in  the  same  general  way  as  does  loss  of  heat 
by  cylinder-condensation. 

For  cases  in  which  it  is  allowable  to  take  the  weight  of 
steam  condensed  as  constant  at  all  ratios  of  expansion,  the 
problem  may  be  greatly  simplified,  and  the  change  of  the  form 
of  the  graphical  construction  from  that  adopted  originally  by 
Rankine  is  then  but  slight. 

Thus,  in  Fig.  166,  §  184,  set  off  DF  equal  to  the  "cost  of 
engine"  plus  that  proportional  cost  which  measures  the  assumed 
or  actual  constant  value  of  steam  wasted  by  internal  condensa- 
tion and  otherwise  ;  giving  a  total  cost,  GF,  which  will  include 
not  only  the  "  cost  of  engine"  and  "  cost  of  steam,"  but  also 
the  wastes  of  the  real  engine.  This  correction  obviously 
throws  the  point  /''farther  toward  the  left,  and  thus,  by  carry- 
ing the  point  of  tangency,  //,  in  the  opposite  direction,  gives 
an  approximately  correct  measure  of  the  best  ratio  of  expan- 
sion for  the  case  taken.  It  is  probable  that,  in  very  many 
cases,  this  simple  modification  of  Rankine's  ideal  curve  and 
original  construction  will  be  found  to  give  perfectly  satisfactory 
results. 

Another  and  equally  .simple,  though  less  correct,  method  of 
approximation  is  to  raise  the  base-line  EDF  such  a  proportion 
of  the  abscissa  of  the  point  A  as  will  measure  the  percentage 
of  wastes  at  a  ratio  r  =  I,  and  make  the  construction  other- 
wise as  before. 

189.  Construction  of  Diagrams  of  Actual  Efficiencies.— 
By  the  application  of  this  method,  as  proposed  by  the  writer, 
we  may  thus  determine,  from  the  results  of  experiment,  a  set 
of  data  and  a  graphical  representation  of  those  results  which 
may  serve  as  a  standard  for  the  class  to  which  the  engine  ex- 
amined belongs.  It  is  further  evident  that,  the  ratio  of  expan- 
sion at  maximum  efficiency  being  determined  by  experiment, 
and  with  precision  by  this  graphical  method,  it  becomes  easy 
to  ascertain  with  exactness  the  value  of  the  ratio  of  expansion 


Tofaccfag,  763. 


Fig. 
sition 
s  the 
maxi- 
y  ex- 
sum 
jiving 
ngine 

ies  of 
>rking 
jnted. 
is  the 
of  no 
msion 
is  the 
steam 
2  line 
.m  in- 
ad  by 
B  is 
<eted, 
:iency 
m;  D 
igine  : 
s  and 
i  prac- 
n  the 
jidby 


or  the 
j  rela- 
of  ex- 


Tofacefage  763. 


MAXIMUM  EFFICIENCIES  OF   THE   STEAM-E\GINE.     763 

at  maximum  commercial  economy.  The  base-line,  FZ,  Fig. 
1 68,  for  maximum  efficiency  of  engine  being  fixed,  the  position 
of  the  point  V  on  that  line  is  readily  obtained,  and  thus  the 
line  VZ  becomes  known,  and  the  ratio  of  expansion  at  maxi- 
mum commercial  economy  is  determined.  Similarly,  by  ex- 
tending the  line  VL  until  it  becomes  proportional  to  the  sum 
of  all  costs,  constant  and  variable,  the  ratio  of  expansion  giving 
maximum  work  per  dollar  expended  with  the  given  engine 
may,  if  desired,  be  found. 

The  accompanying  plate,  Fig.  168,  represents  a  series  of 
real  curves  of  efficiency,  several  of  which  are  given  by  working 
engines.  Such  curves  are  here,  for  the  first  time,  presented. 
The  straight  line  A^Ay  for  the  case  in  which  n  =  —  i,  is  the 
line  of  constant  efficiency  obtained  in  an  assumed  case  of  no 
gain  and  no  variation  of  efficiency  with  increasing  expansion 
from  r  =  o  to  r  =  oc.  The  curve  marked  G,  and  dotted,  is  the 
standard  curve  of  efficiency  for  adiabatic  expansion  of  steam 
containing  initially  ten  per  cent  water  («  =  1.125).  The  line 
F  is  the  curve  of  mean  pressure  or  of  efficiency  for  steam  in- 
itially dry  (if  =  1.135).  The  other  curves  are  all  obtained  by 
reference  to  experiments  on  various  classes  of  engines.  B  is 
the  curve  of  efficiency  for  the  common  marine,  unjacketed, 
single-cylinder,  condensing  engine ;  C  is  the  curve  of  efficiency 
for  the  same  engine  using  moderately  superheated  steam  ;  D 
is  that  of  a  "  compound  "  jacketed,  condensing,  marine  engine  : 
E  applies  almost  exactly  to  both  non-condensing  engines  and 
compound  engines  of  the  best  classes,  and  the  curve  F  is  prac- 
tically correct  for  the  last-named  class  of  engines  when  the 
steam  is  kept  thoroughly  dry  by  effective  superheating,  and  by 
reheating  in  an  intermediate  receiver. 

Curve  B  is  thus  obtained  : 

Collating  Isherwood's  with  other  experiments  made  for  the 
United  States  Navy  Department,*  we  find  the  following  rela- 
tive measures  of  steam-consumption  at  various  ratios  of  ex- 
pansion, and  of  work  done  by  it : 

*  Researches  in  Engineering;  vol.  n.  Table,  p.  xsoriv. 


764  A    MANUAL    OF   THE    STEAM-ENGINE. 

Cut-off  -  (real) I       .3       .5       .7         .9       i.oo 


r 


"        —(apparent) 05     .25     .47     .68       .89     i.oo 

Relative  weights  of  steam 16     .41     .60     .76       .92     i.oo 

"total  work"  done.  ..    .21      .56     .82     .97     i.oo     i.oo 

The  base-line,  B,  for  this  case,  in  which  —  =  — ,  is  drawn  on 

Pi       8 

the  plate,  and  on  this  line  are  a  set  of  values  of  -  correspond- 
ing to  the  relative  weights  of  steam  as  laid  down  on  the 
bottom-scale,  .10  above  .16,  .30  above  .41,  etc.,  etc.,  and  theordi- 
nates  erected  at  these  points  are  made  proportional  to  the  mean 
pressures  and  the  total  work  done  at  those  ratios  of  expan- 
sion ;  and,  thus  carefully  laying  down  these  points,  the  line 
B^B  is  constructed  as  the  curve  of  efficiency  for  the  engine,  of 
which  those  of  the  United  States  steamers  Eutaw,  Michigan, 
and  all  "  American  river  steamboat  engines"  are  representatives. 

In  a  similar  manner,  by  collating  the  data  obtained  by  the 
trial  of  the  Georgiaria's  engine,  using  superheated  steam,  with 
the  experiments  of  Hirn  showing  a  reduction  of  exhaust  waste 
by  superheating,  we  obtain  the  curve  of  efficiency  C^C  and  the 
base-scale  accompanying  it.  A  set  of  experiments  on  the 
Bache  gives  the  line  Dfi,  and  the  curve  E,E  is  found,  by  trial, 
to  meet  cases  of  good  work  with  non-condensing  engines,  un- 
jacketed,  but  worked  at  high  piston-speed,  and  of  some  of  the 
very  best  results  obtained  with  compound  engines  of  the  most 
successful  types.  Curve  F  seems  to  meet  those  cases  in  which 
superheating  has  been  so  efficient  as  nearly  to  prevent  all  con- 
densation, and  the  line  corresponds  closely  with  the  adiabatic 
for  steam,  dry  initially,  and  only  condensing  so  much  as  is  due 
to  the  performance  of  work. 

In  the  last  figure,  the  straight  line.  A,  may  be  taken  as 
measuring  the  work  done  in  the  engine  up  to  the  point  of 
cut-off,  to  which  work  its  ordinates  are  proportional ;  while 
the  line  of  adiabatic  mean  pressures  gives,  similarly,  the  total 


MAXIMUM  EFFICIENCIES  OF   THE  STEAM-EXG1XE.     76$ 

work,  and  their  difference  the  gain  by  expansion.  The  several 
curves  exhibit  the  extent  to  which  this  gain  is  affected  by 
wasteful  conditions  in  the  ideal  and  the  various  forms  of  real 
engine  represented. 

To  obtain  an  exact  solution  of  these  problems,  the  quantity 
of  steam  present  in  the  cylinder  at  the  point  of  cut-off  must  be 
precisely  measured  and  compared  with  the  quantity  sent  to  the 
engine  from  the  boiler. 

100.  Method  of  Use  of  the  Diagram. — Comparing  curves 
F  and  G,  Fig.  168,  representing  the  case  of  steam  expanding 
in  a  non-conducting  cylinder,  i.e..  adiabatically,  with  the  other 
curves,  obtained  for  expansion  in  real  engines,  it  is  seen,  at  a 
glance,  that  the  more  perfectly  exhaust-waste  by  cylinder-con- 
densation is  guarded  against,  the  more  closely  does  the  actual 
engine  approach  to  the  perfect  engine  in  its  utilization  of 
steam,  and  the  less  effective  the  provision  against  such  loss,  the 
more  widely  does  the  curve  of  efficiency  depart  both  in  loca- 
tion and  form  from  the  ideal  curve,  finally  approximating  to 
the  straight  line  of  constant  efficiency-  A^A.  While  the  best 
engines  approach  comparatively  near  the  curve  of  maximum 
possible  efficiency,  the  great  majority  of  condensing  engines  in 
use  are  of  the  class  represented  by  that  giving  curve  B ;  which 
latter  is,  however,  by  no  means  a  case  of  remarkably  low 
efficiency.  In  many  cases  the  curve  will  be  found  to  fall  within 
the  line  B. 

Selecting  one  of  these  curves,  as  B  or  C,  we  may  solve 
either  or  all  of  the  problems  already  defined  by  merely  apply- 
ing a  straight-edge  to  the  diagram.  For  B  we  have  /,  =  40 : 

pt  =  5  ;  —  =  —  =  0.125.  To  determine  the  best  mean  pres- 
sure and  ratio  of  expansion  at  maximum  efficiency,  draw  the 
base-line  at  the  altitude  0.125,  and  from  its  junction  with  the 
ordinate  at  the  zero  point  draw  the  line  HI  tangent  to  the 
curve  ;  it  touches  the  curve  at  /  and  the  corresponding  mean 
pressure  and  ratio  of  expansion  on  the  base-line  beneath  is  a 

trifle  less  than  -  =  0.4;  r  —  2.5  nearly — a  result  confirmed  by 
reference  to  the  original  data. 


766     .  A   MANUAL    OF   THE    STEAM-ENGINE. 

Next  ascertain  the  hourly  or  annual  cost  of  supplying  the 
engine  with  steam  when  worked  without  expansion,  including 
all  items  of  expense  variable  with  the  quantity  of  steam  used, 
and  determine  the  variable  part  of  all  running  expenses  in  the 
engine-room,  including  interest,  insurance,  rent,  cost  of  oil,  and 
so  much  of  the  wages  of  the  attendants  as  is  properly  taken  as 
variable  with  the  size  of  engine.  Suppose,  as  in  a  case  taken 
by  the  Author,  that  the  latter  is  found  to  be  two  per  cent  of 
the  former,  M '=  .02. 

From  the  point  T,  at  the  ordinate  .02,  on  the  left  of  the  H, 
draw  the  tangent  to  the  curve,  as  TL  on  the  curve  B ;  its  point 
of  tangency  identifies  the  best  mean  pressure  and  ratio  of  ex- 
pansion for  commercial  efficiency. 

Similarly  compare  the  "  cost  of  full  steam"  with  the  sum  of 
all  other  running  expenses  chargeable  to  the  plant ;  if  the  ratio 
is  N  =  .04,  draw  the  tangent  line  WL  from  the  ordinate  .04, 
and  thus  find  that  ratio  of  expansion  which  will  give  most 
work  for  the  money  expended  on  a  plant  already  installed. 
The  lines  PQ,  RV,  and  SU  thus  determine  these  three  ratios 
for  the  curve  F,  of  a  well-constructed  non-condensing  engine, 

using  perfectly  dry  steam  and  with  a  ratio  —  =  0.20.    The  line 

NM  determines  the  best  mean  pressure  and  ratio  of  expansion 
at  maximum  efficiency  for  the  case  D,  a  compound  engine 

Pb 
doing  good  work  with  —  -  =  .05. 

191.  Estimation  of  Expenses. — The  following  example 
illustrates,  in  detail,  the  calculation  of  values  of  M  and  of  N: 

Rated  power  of  given  engine  and  boiler 500  H.  P. 

Working  time,  per  annum 3,ooo  hrs. 

(A)  Costs  of  engine  (variable  with  size  of  engine). 

Cost  of  engine  (approximate) $10,000 

Annual  interest  at  6  per  cent $600 

cost  of  repairs  and  depreciation,  4  p.  c 400 

"  "     "  materials  used 50 


Total  annual  cost $1,050 


MAXIMUM  EFFICIENCIES  OF  THE    STEAM-ENGINE.     /6/ 

(B)  Costs  of  boiler  (variable  with  demanded  boiler -power). 

Cost  of  boiler :  actual  (approximate) $12,000 

for  "  full  steam" 24,000 

Interest  on  cost,  using  steam  without  expansion,  at  6  p.  c.$i,44O 

Repairs  and  depreciation  at  15  per  cent 3,600 

Minor  expenses  per  annum,  say 200 


Total  annual  maximum  cost  .....................  $5,240 

(C)  Fuel  Account  (variable  with  size  of  boiler). 
Coal,  per  year  at  the  rated  power  ................     2,000  tons 

"       "       "     with  no  expansion  ...............     4,000     " 

Cost  of  fuel  at  "  full  steam,"  at  $5  per  ton  .......  $20,000 

"     "     "     transportation  and  storage  at  500  ....     2,000 

Total  maximum  per  year  ..................  $22,000 

(D)  Attendance  (wholly  or  partly  constant,  or  variable). 

(a)  "  Engine-driver's"  (engineer's)  pay,  per  year  .........  $Ti,ooo 

(b)  "  Firemen's"  (stokers')  pay,  per  year  ("  full  steam")  ____    i  ,200 

$2,200 

(E)  Incidentals  (constant  as  a  rule). 
Rent,  taxes,  insurance,  etc.,  per  annum  .................  $1,000 

Studying  the  statement  of  costs,  the  designing  engineer 
decides  in  each  case,  and  for  each  problem  presented,  how  the 
items  should  be  grouped.  For  the  case  of  a  stationary  steam- 
engine,  such  as  is  here  presented,  he  would  find 

M—  =  0.035,  nearly, 


if  the  costs  /?.,  Db  are  not  variable  within  the  probable  range  of 
variation  of  expansion  ;  and 


768  A    MANUAL    OF   THE   STEAM-ENGINE. 

Assuming  cost  of  fire-room   labor  variable  with  quantity  of 
steam  demanded, 

A  +  D+E 
N=  —       _          =0.15,  nearly, 


for  the  first  case,  and 

=  °.i°,  nearly, 


for  the  second  case.  In  marine  engineering,  storage  becomes 
an  important  matter,  in  items  A  and  D,  and  in  B,  as  well  as 
very  important  in  C  and  £,  since  every  cubic  foot  occupied  by 
machinery,  fuel,  or  attendants  displaces  a  cubic  foot  of  paying 
load.  With  very  large  powers,  the  items  D  both  become  to  a 
certain  extent  variable,  the  one,  Da,  with  magnitude  of  the 
whole  plant,  the  other,  Db,  with  quantity  of  fuel  burned.  Cor- 
rectness in  making  up  the  bill  of  costs  will  be  found  to  be 
absolutely  essential.* 

192.  Statement  of  Results.  —  Laying  out  these  curves  on 
a  conveniently  large  scale  and  proceeding  as  just  indicated,  the 
Author  obtained  the  results  exhibited  in  Table  I,  here  given. 
Cases  I  to  VI,  inclusive,  are  obtained  from  curved;  VII  to 
XII  from  curve  B;  XIII  to  XVIII  from  E\  and  XIX  to  XXIV 
from  the  best  curve  of  efficiency,  on  the  plate,  F. 

The  ratio  of  expansion  at  Maximum  Efficiency  of  Fluid 
will  be  found  in  column  r/t  that  at  Maximum  Efficiency  of 
Engine  under  re",  and  the  Best  Ratio  of  Expansion  for  Com- 
mercial Efficiency,  or  for  Maximum  Efficiency  of  Capital,  is 
given  under  re'"\  M,  N,  are  the  ratios  of  cost.  Comparing  the 
first,  and  especially  the  second,  set  with  the  last,  the  enormous 
variation  due  to  cylinder-condensation  is  readily  appreciated. 
Even  the  last  case  is  far  from  the  efficiency  of  the  perfect  en- 
gine. 

*  For  a  considerable  amount  of  data  in  this  field,  see  the  concluding  chapter 
of  Part  II. 


MAXIMUM  EFFICIENCIES  OF   THE   STEAM-EXG1XE.     769 

The  mean  pressures  and  ratios  of  expansion  for  superheated 
steam  in  the  un  jacketed  (Fig.  1  68  )  cylinder  are  obtainable  from 
curve  C.  Here 

Pi  =  initial  pressures  measured  from  perfect  vacuum  ; 

pt  =  back-pressure  in  cylinder  : 

pb  =  same  plus  friction  ; 

J/  =  ratio  of  variable  part  of  cost  of  engine  to  variable 
part  of  cost  of  steam,  when  r  —  i. 

The  values  here  presented  for  these  several  cases  are  not  to 
be  taken  as  exact  for  other  examples,  but  must  always  be  cor- 
rected, in  the  simple  ways  already  described  (Chap.  V)  for 
variations  of  size,  speed  and  temperature  variations.  They  are 
given  as  representative  illustrations,  and  the  engineer  design- 
ing new  engines  should,  whenever  possible,  construct  his  own 
more  exact  diagram  and  make  his  own  solution  of  the  problem 
before  him. 

The  determination  of  the  last  of  the  several  ratios  in  the 
table  constitutes  the  solution  of  the  "  Designer's  Problem." 
To  finally  settle  the  size  of  the  engine  to  be  designed,  on  this 
commercial  basis,  it  is  only  necessary  to  ascertain  what  size  of 
engine,  working  at  the  determined  ratio  of  expansion  for  maxi- 
mum commercial  efficiency,  will  perform  the  specified  required 
work. 

We  have  the  power  required, 


in  which  the  power  is  prescribed,  and  the  value  of/,,  taken  as 
the  mean  effective  pressure  corresponding  to  this  power,  is 
known  from  the  stated  conditions  of  the  problem  and  the  value 
of  the  now  determined  ratio  of  expansion  ;  while  the  velocity, 
V,  of  piston  is  exactly  or  approximately  known,  or  may  be  as- 
sumed ;  then  the  area  of  piston  is 

33,000  H.P. 
P.V       ' 


770  A    MANUAL    OF   THE   STEAM-ENGINE. 

TABLE  I. 

RATIOS   OF   EXPANSION  AT   MAXIMUM    EFFICIENCY  OF  FLUID, 
OF  ENGINE  AND  OF  CAPITAL. 

SINGLE  CYLINDERS. 


Class  I. 

Class  II. 

Absolute 

Initial 
Pressures. 

Non-condensing, 
High  Speed. 

Condensing, 
Moderate  Speed. 

Case 

Case 

I                       , 

No. 

No. 

P 

An 

Atmos- 
pheres. 

A 

A 

M 

/7 

< 

'<" 

'e 

I 

A 

M 

A 

tf 

r.» 

'-,'" 

40 

2.8 

2* 

I 

iS 

20 

.02 

2 

2 

2 

2 

VII 

3 

S 

.04 

S 

2| 

y 

3 

60 

4-2 

4 

II 

18 

20 

.02 

3 

3 

3 

2f 

VIII 

3  15 

.04 

12 

34    3± 

« 

80 

100 

5-6 
7.0 

II 

III 
IV 

18 

iS 

20 
20 

.02 
.02 

4 

5 

4 

5 

3! 
44 

3i 

IX 
X 

3 
3 

5 

5 

.04 
.04 

16 

20 

4i,  4 
4*  !  44 

3i 

4 

120 

8.4 

8 

V 

18 

20 

.02 

6 

6 

5i 

4 

XI 

3  IS 

.04 

24 

Si 

1 

4i 

ISO 

10.5 

IO 

VI 

18 

20 

.02 

7i 

7 

6 

44 

XII 

3|5 

.04 

30 

o 

51 

5 

COMPOUND,  CONDENSING,  JACKETED. 


Absolute 

Class  III. 

Class  IV. 

Initial 

Pressures. 

Saturated  Steam. 

Superheated  Steam. 

Case 

Case 

\ 

/m 

Atmos- 
pheres. 

No. 

1 

A 

" 

A 
/b 

*•' 

'e" 

<" 

No. 

P* 

/b 

M 

A 

< 

r/ 

r,'" 

40 

2.8 

2* 

XIII 

si 

.04 

7 

6 

^ 

1 

XIX 

24 

S 

>oa 

8 

8 

6 

S 

60 

4.2 

4 

XIV 

3 

5  1 

•04 

II 

8 

7 

4i 

XX 

»i 

*> 

•  OS 

IO 

II 

8 

6 

So 

5-6 

5* 

XV 

3 

5i 

.04 

14 

g 

8 

6 

XXI 

•05 

13 

14 

10 

7 

100 

7-0 

6* 

XVI 

3    6 

.04 

17 

10 

9 

7 

XXII 

£ 

$\ 

.05(18 

16 

12 

8 

120 

8.4 

8 

XVII 

3    6 

•04 

20 

II 

IO 

8 

XXIII 

| 

5i 

•  05 

33 

20 

ij 

Q 

150 

10.5 

IO 

XVIII 

3    6 

.04 

25 

13 

10 

9 

XXIV 

3 

6 

•05 

•7 

rsl 

10 

The  value  of  ^4  being  thus  obtained,  in  terms  of  power, 
mean  pressure,  and  velocity  of  piston,  the  diameter  of  piston 
and  length  of  stroke  are  readily  settled. 

Further  investigation  will,  undoubtedly,  sooner  or  later, 
establish  the  curves  of  efficiency  for  all  standard  types  of  en 
gine  and  for  those  special  cases  for  which  the  engineer  can 


MAXIMUM  EFFICIENCIES  OF   THE   STEAM-EXGIXE.     77 1 

day  only  obtain  them  approximately.  Meantime,  the  plate 
exhibits  a  range  of  variation  of  curve  which  extends  completely 
across  the  field  of  every-day  practice;  and  an  experienced 
engineer  can  trust  his  judgment  in  the  interpolation  of  the  curve 
of  efficiency  for  any  special  case  arising  in  his  own  practice. 
For  example :  Cases  of  best  practice  in  which  the  engine  is 
worked  at  higher  speed,  and  with  a  warmer  condenser,  and 
having  less  friction,  will,  when  corrected  for  any  differences  of 
size,  speed,  and  range  of  expansion  or  temperature,  give  a  curve 
for  the  class  from  which  B  was  obtained  which  will  fall  be- 
tAveen  B  and  C. 

The   values  given  of—    are  interesting  in  comparison  with 

Pt 

the  values  of  rt ,  as  exhibiting  the  enormous  difference  between 
the  best  ratio  of  expansion  in  actual  work  and  the  ratio  giving 
maximum  efficiency  in  the  ideal  case,  and  also  as  strikingly 
presenting  to  the  mind  how  far  we  are  still,  in  actual  practice, 
from  even  an  approximation  to  the  conditions  exhibited  in  the 
perfect,  ideal,  engine. 

TABLE  II. 

RATIOS    OF    EXPANSION    GIVING    MAXIMUM    WORK  AT  MINI- 
MUM  COST  FOR  A  GIVEN  PLANT  OF   KNOWN  PROPORTIONS. 

CLASS  I.  CLASS  II. 


Cases. i        ii       m       IT       v       TI     TH    vm       ix       x       xi      xii 

N 04    .04    .04    .04    .04    .04    .IO    -IO    .IO    .IO    .IO    .IO 

r* I*    2*    2f     3*    3^      4     if    2*       3     3*     3£      4 

CLASS  IIL  CLASS  IV. 

Cases xm    xiv     xv     xn    xvn  xnii    xix    xx     xxi    xxiixxjnxxiv 

*V-.... .IO    .IO    .IO    .IO    .IO    .IO    .12     .12     .12     .12     .12    .12 

r,*V    .   ....  2i    3i    4}    4*    4i    4f      4    4*    4|       5       5     5i 

Table  II  gives  values,  similarly  obtained  for  the  cases 
taken,  of  that  ratio  of  expansion  which  gives  a  maximum 
quantity  of  work  for  the  unit  of  value  with  a  fixed  arrange- 
ment  of  plant.  These  values  are  seen  to  be  very  much 


772  A   MANUAL   OF   THE  STEAM-ENGINE. 

smaller  than  the  ratios  for  maximum  commercial  efficiency  ; 
and,  although  they  may  give  more  work  for  such  unit  than  the 
higher  ratios  just  determined,  they  do  not  give  maximum 
efficiency  of  capital.  For : 

Assume  the  engine  working  at  this  closely  adjusted  ratio  for 
the  now  given  power,  still  more  work  will  be  given  for  the  unit 
of  cost  if  the  value  of  r  be  increased  by  replacing  the  given 
engine  by  a  larger  one,  in  many  cases,  or  in  any  case  by  speed- 
ing up  the  engine,  or  otherwise  doing  the  larger  amount  of 
work  with  a  new  and  higher  ratio  of  expansion.  The  Author 
has  sometimes  accomplished  this  latter  result  by  both  speeding 
up  the  engine  and  carrying  higher  steam,  with  an  automatic 
adjustment  of  expansion.  The  real  limit  to  this  increase  of 
work  done  by  the  given  engine  is  determined  by  quite  other 
considerations  than  those  abo've  noted.  It  is  determined  by 
the  money  value  of  the  power  obtained,  and  this  increase  of 
power  finds  a  limit,  as  has  been  seen,  only  when  either  the 
limit  of  safety  in  working  engine  or  boiler  is  reached,  or  when 
the  money  made  by  the  use  of  additional  power  is  insufficient 
to  pay  a  fair  profit  on  the  additional  expense  incurred  ;  which 
latter  limit  may  be  obtained  at  a  value  of  riv  either  equal  to 
or  less  than  re. 

The  radical  distinction  between  the  problem  of  maximum 
efficiency  of  capital  (8)  and  maximum  commercial  efficiency  of 
a  given  plant  (9),  §  174,  is  here  well  brought  out  by  this  differ- 
ence of  results.  Comparing  Nos.  7,  12,  13,  and  18  of  Table  I 
with  the  same  in  Table  II,  it  is  seen  that,  instead  of  ratios  of 
2,  5,  3,  and  9,  we  have  1.75,  4,  2.5,  and  4!  ;  results  which,  while 
absurd  as  solving  the  "  designer's  problem"  (8),  are  perfectly 
satisfactory  as  a  solution  of  the  "  owner's  problem"  (9). 

193.  Relation  of  Costs  and  Profits.— Table  III  exhibits 
the  effect  of  variation  of  actual  value  of  the  power  in  deter- 
mining the  maximum  amount  profitably  obtainable  from  any 
engine. 

For  example  :  Suppose  the  cost  of  a  horse-power  to  be,  as 
is  frequently  the  case,  about  equal  to  the  cost  of  fuel  (in  the 
furnace)  producing  that  power  without  expansion  ;  then  calling 


MAXIMUM  EFFICIENCIES  OF  THE  STEAM  ENGINE.  773 
this  value  pm  and  this  cost  pc ,  the  base-line  of  the  diagram  will 
be  extended  until  it  measures  fc  =  i  =  N\  twice  the  length 

of  OX,  and  the  angle  made  by  the  line  from  its  extremity  to 
A,  Fig.  1 68,  makes  an  angle  0  =  45°  with  OX.  On  the  large- 
scale  drawing,  set  the  triangle  against  the  edge  of  the  T-square, 
and  adjust  it  to  the  line  here  given ;  find  by  shifting  it  along 
the  blade  that  point  on  the  selected  curve  of  efficiency  at 
which  a  parallel  tangent  can  be  drawn,  and  then  the  ratio  of 
expansion,  rv,  answering  to  this  case,  is  found 

If  an  engine,  IV  of  Class  I,  is  selected,  it  is  found  to  be 
rv  =  2±  :  if  No.  VII  of  Class  II,  rv  =  2,  etc,  etc.,  as  in  Table 
III. 

It  is  particularly  interesting  and  instructive  to  observe  how 
the  importance  of  waste,  as  of  cylinder-condensation,  in  its  in- 
fluence on  the  best  ratio  of  expansion,  here  diminishes  with 
decreasing  expansion,  and  that,  finally,  the  most  economical 
and  the  least  efficient  give  nearly  identical  figures  when  the 
point  of  cut-off  approaches  half-stroke. 

TABLE  III. 

Effect  of  Variation  of  Ratio  of  Market  Value  to  Cost  of  Power, 
Maximum  Limiting  Values  of  rv. 

N1      0.40      0.50      0.60      0.70      0.80     i.  oo 

2* 

2 
2 

2* 
2* 

2* 
2* 

0  22°       27°      31°        35°       39°      45° 

Taking  the  cost  of  fuel,  in  the  furnace,  for  the  engine  work- 
ing without  expansion,  at  $50  per  annum  per  horse-power,  the 
above  table  gives  the  ratio  of  expansion  below  which  a  loss 


II 

VII     

j 

"      II 

"           X 

"    III 

«  •  xv    .... 

7 

5 

4 

3 

"   III 

"     XVII     .... 

7 

5 

4 

3 

«     IV 

"      XXI        9 

7 

6 

4 

3 

"     IV 

"   XXIV       10 

7 

6 

4 

3 

774 


A   MANUAL   OF   THE   STEAM-ENGINE. 


will  accrue  when  the  cash  value  of  the  horse-power  is  20,  25, 
3°>  35>  4°>  and  50  dollars.  At  these  ratios  of  expansion,  all 
that  is  received  for  power  above  these  sums  is  profit. 

For  other  costs,  the  prices  obtained  must  be  correspond- 
ingly varied  to  secure  a  profit. 

194.  Profits  at  any  Fixed  Expansion. — Other  problems, 
the  converse  of  the  last,  may  be  solved  by  this  construction  : 
"  What  is  the  maximum  price  which  can  be  paid  for  power 
without  loss  at  any  given  mean  pressure  or  ratio  of  expansion  ?" 
"  What  profit  is  obtainable  at  a  given  cost  ?"  "  What  total 
cost  makes  any  given  ratio  of  expansion  the  most  economical  ?" 

To  solve  these  problems,  draw  an  ordinate  to  the  line  of 
mean  pressures,  or  the  curve  of  efficiency,  at  the  assumed 
ratio  of  expansion  ;  then  the  abscissa  measures  the  cost,  in 
terms  of  full  steam,  of  the  power  measured  by  the  ordinate, 
above  which  loss  will  accrue,  when  M  =  o.  The  difference  be- 
tween the  total  cost  and  the  higher  price  measures  the  profit 
obtained  if  the  power  is  sold  at  the  larger  figure. 

Table  IV  exhibits  the  variation  of  the  relative  maximum 
allowable  cost  of  power,  with  variation  of  the  ratio  of  expan- 
sion ;  actual  cost  of  expenses  variable  with  fuel,  with  ratio 
unity  being  taken  as  the  unit. 

TABLE  IV. 

Maximum  Limit  of  Relative  Allowable  Cost.  Most  Economical 
Ratio  of  Expansion  assumed  as  r.  Cost  of  Frill  Steam  = 
Unity.  M  or  N  =  o.  I . 


Class      I 

No.       IV      . 

"       II 

"        VII       . 

"       II 

X       .1 

«     III 

XV      . 

"     III 

"    XVII      . 

"     IV 

"      XXI       . 

"     IV 

"  XXIV      . 

•80  .75  -75  -85     .85    

.80  .85  i.i ... 

•75  -80  .95  

.75  .70  .70  .75     .80    .90     i.i 

.75  .70  .70  .70     .70    .75       .90 

.75  .70  .90  .65     .70    .75       .90 

.75  .70  .65  .65     .55    .55       .65 


MAXIMUM  EFFICIEXCIES  OF   THE  STEAM-EXGINE.     77$ 

195.  Cost  of  Engine  as  affecting  the  Best  Ratio  of  Ex- 
pansion.— The  effect  of  variation  in  cost  of  engine  now  be- 
comes of  interest,  and  indeed  a  matter  of  real  importance  to 
the  designer.  Studying  cases  arising  in  practice,  he  will  prob- 
ably find  the  value  of  J/or  J\"to  fall  between  .02  and  .15,  as  in 
those  selected  above,  but  it  will  probably  rarely,  if  ever,  exceed 
0.20. 

The  curve  being  established  correctly  for  any  given  engine, 
it  becomes  the  easiest  possible  matter  to  determine  the  effect 
of  variation  of  this  ratio.  Table  V  gives  such  results  as  seem 
most  instructive,  from  the  cases  here  studied. 

TABLE  V. 

Effect  of  Variation  of  "Exgimt-cost  Ratio"     Best  Values  of 

rf'"  orr?. 
J/ar&  .02      .04     .06     .08      ao     .15      .20 

Class      I  Example         IV  3i  3l  3  2f  2f  2*  2± 

"II  -  VII  ..  2  2  if  if  if  i  \ 

"II  -  X  ..  4  3f  3*  31  2f  2i 

"    HI  -  XV  ..  6  5  4i  4  3*  3 

-  Ill  -  XVII  ..8  6  4|  44  3l  34 

-  IV  -  XXI  ..  6J  6  5i  4l  3f  3i 

-  IV  -  XXIV  -  9  7  6  5  4  3i 

These  differences  in  the  value  of  the  mean  pressure  and 
ratio  of  expansion  at  maximum  commercial  efficiency  are  least 
where  the  exhaust  wastes  are  greatest,  and  as  their  absolute 
values  become  smaller.  Cases  IV,  X,  XVII,  and  XXIV  have 
the  same  initial  steam-pressure  and  are  seen  to  approximate 
toward  the  same  value  of  rt  as  the  value  of  M  or  JV  becomes 
greater,  becoming,  for  the  first  two,  and  for  the  last  two,  nearly 
equal  to  the  maximum  value  here  taken. 

It  is  obvious  that  the  value  rt  becomes  a  good  gauge  of  the 
economical  value  of  the  engine  and  of  its  type,  and  that  the 
greater  these  values,  other  things  equal,  and  the  nearer  r/', 
rt""t  r,'T  approach  each  other,  in  any  given  engine,  the  better 
the  design. 


77$  A   MANUAL   OF   THE    STEAM-ENGINE. 

It  is  now  seen  that  we  have  here  a  method  of  determining 
the  effect  of  variations  of  single  variable  quantities,  while  re- 
taining all  others  constant — a  method  very  greatly  needed,  but 
hitherto  unknown. 

The  case  just  taken  is  an  illustration  of  its  application. 
The  following  is  another  instance  of  no  less  importance : 

196.  Back-pressure  as  Modifying  Economy. — The  Effect 
of  Variation  in   Back-pressure  may  be  studied,  by   means   of 
this  method  of  investigation,  with  the  same  facility. 

Table  VI  exhibits  this  effect  for  a  wide  range  of  cases. 

TABLE  V. 

Effect  of  Variation  of  Initial  Pressure  and  of  Back-pressure. 
Best  Values  of  re'. 

^             *       i       t        t        i       A      A      A 
Class      I     No.    '    IV     2f     3i      si      3i       

«          II          «  VII       I*        If         If    •     If        2i        2i         ..          .. 

"       II      "  X if      2i      2i        3        4 

"     III       "       XVI 4i      6        7          9      ii 

"     IV       "     XXII 6        6        8        12       15 

These  differences  in  value  of  re  are  obtained  on  the  assump- 
tion that  cylinder-condensation  and  all  other  conditions  re- 
main unchanged  while  variation  occurs  in  the  back-pressure. 
In  all  actual  cases,  the  differences  would  be  reduced  by  the 
fact  that  increased  condenser-pressure  and  the  reduction  of 
chilling  effect  which  comes  with  increase  of  back-pressure  so 
check  exhaust  waste  that  the  ratio  for  maximum  efficiency  be- 
comes somewhat  increased  and  these  differences  of  ratio  are 
thus  lessened.  The  gain  from  this  and  other  causes  becomes 
sufficient  at  high  pressures  to  justify  the  use  of  the  simpler  and 
less  expensive  non-condensing  engine  ;  it  will  be  best  appreci- 
ated after  comparison  of  Class  I  with  Class  II.  An  indepen- 
dent solution  of  every  actual  problem  is  always  desirable. 

197.  Deductions. — In  illustration  of  the  use  of  this  method 
and  of  the  application  of  the  results,  we  may  observe  as   in 


MAXIMUM  EFFICIENCIES  OF   THE  STEAM-ENGINE.     7/7 

Table  I  values  of  the  ratio  of  expansion  for  maximum  effi-( 
ciency  for  any  standard  type  of  engine.  Thus .  Case  III  is 
that  of  an  ordinary,  standard,  non-condensing,  drop  cut-off  en- 
gine, steam  65  pounds  (5^  atmospheres)  by  gauge,  and  the  cut- 
off occurs,  properly,  at  a  little  inside  \  stroke ,  Case  V  is  the 
same  with  steam  at  105  by  gauge  (8  atmospheres),  and  its  valve 
should  close  a  little  inside  \  stroke.  For  maximum  commercial 
efficiency  those  engines  should  "  cut  off  "  at  about  £  and  i  re- 
spectively. In  the  second  class,  Case  VII  is  that  of  the  old 
naval  or  modern  very  low-pressure  river-boat  engine  carrying 
25  pounds  of  steam  by  gauge  (2$  atmospheres).  The  valve 
should  drop  so  as  to  completely  shut  off  steam  at  about  half- 
stroke  to  give  minimum  expenditure  for  coal,  and  a  little  later 
to  give  minimum  cost  on  total  account,*  a  result  already 
reached  by  the  builders  of  such  engines.  Case  VIII  is  that  of 
some  of  our  old  Hudson  River  steamboats  (steam  45  by  gauge), 
and  these  two  ratios  are  found  to  be  a  little  greater  and  a  little 
less  than  3.  The  irregularity  of  wheel  which  a  short  cut-off 
produces,  however,  makes  it  inadvisable  to  expand  as  much  as 
this,  even.  Case  IX  is  often  seen  in  mill-engines ;  its  valve 
closes  at  £  and  £  for  the  cases  taken.  Above  this  pressure,  a 
comparison  of  Class  I  with  Class  II  shows  that  in  the  cases 
taken  the  non-condensing  engine  is  about  as  economical  as  the 
other — a  conclusion  justified  by  Isherwood's  comparison  of 
Corliss  engines  f — but  comparing  values  of  rt'"  it  is  seen  that 
the  condenser  may  probably  be  exchanged  for  the  heater  with 
Classes  III  and  IV  only  at  some  very  high  pressure  not  yet  at- 
tained  with  jacketed  engines  of  good  design,  while  the  ten  per 
cent  gain  obtained  at  the  boiler  by  the  higher  temperature  of 
feed  given  by  the  heater  of  the  non-condensing  engine,  to- 
gether  with  the  differences  in  size  of  cylinder,  brings  down  the 
pressure  at  which  total  efficiency  becomes  a  minimum  to  some 

*  Engines  of  this  class  by  good  builders,  having  the  "  Stevens  valve-gear," 
close  the  valve  at  6  feet  on  a  10  feet  stroke,  which,  allowing  for  a  little  throt- 
tling, gives  exactly  this  figure.  Those  fitted  with  the  "Sickles  cut-off  "drop 
the  valve  as  near  half-stroke  as  possible;  they  cannot  "  follow"  further. 

f  journal  Franklin  Institute;  Sept.  1881. 


7/8  A   MANUAL   OF   THE  STEAM-ENGINE 

lower  figure  which  may  be  determined,  by  the  method  here 
given,  for  any  given  case. 

Cases  XV  and  XVI  are  often  illustrated  on  transatlantic 
steamers  and  by  good  compound  pumping-engines.  The  cut- 
off takes  effect  at  •§•  or  \  for  maximum  efficiency  of  engine  and 
fuel,  and  at  \  or  \  for  most  economical  expenditure  of  money,* 
figures  already  settled  upon  by  the  most  successful  builders. 
Cases  XXII  and  XXIII  represent  the  most  advanced  practice 
in  the  use  of  high  steam  pressure,  superheated  steam,  and  re- 
heating at  the  intermediate  receiver,  as  is  done  in  the  pumping- 
engines  of  Cowper,  Corliss,  and  Leavitt.  The  best  ratios  of 
expansion  are  12  and  15,  if  measured  by  duty  attained  and  fuel 
saved,  simply,  and  two  thirds  those  values  give  maximum 
efficiency  of  capital.  Case  XXIV  represents  most  nearly  that 
of  Corliss*  best  pumping-engine,  which  lies  between  XXIII 
and  XXIV ;  its  best  ratio  of  expansion  lies  between  9  and  10, 
if  the  curve  of  efficiency  here  taken  for  Class  IV  suits  that 
case.  If  nine  is  the  real  ratio,  the  apparent  cut-off  will  be 
nearly  at  one  tenth,  while  for  maximum  efficiency  of  engine 
and  maximum  "  duty"  the  valve  should  drop  at  about  one- 
sixteenth  stroke. 

It  should  be  kept  in  mind  that  the  measure  of  cost,  in  all 
problems  relating  to  expense,  as  here  treated,  is  the  total  cost 
per  annum,  without  expansion,  of  all  items  of  Class  3,  i.e., 
variable  with  variation  of  steam-supply. 

The  problem  illustrated  by  the  cases  taken  up  in  Table  III 
is  of  rare  occurrence.  The  following  are  two  such  cases : 

(i)  Where  the  proprietor  of  an  engine  can  rent  power  from 
an  engine  already  set  up,  having  boiler-power  sufficient  to  sup- 
ply an  ample  amount  of  steam,  he  will  obtain  the  best  return 
from  his  invested  capital  by  delivering  so  much  power  at 
remunerative  prices  as  will  give  the  values  re'v,  found  in 
Table  II.  Cases  IV,  V,  and  VI  are  among  the  most  usual, 
the  best  point  of  cut-off  averaging  about  -J  stroke. 

Had  this  quantity  of  power  to  be  demanded  been  originally 

*  Vide  Clark's  Manual  for  Mechanical  Engineers,  pp.  888,  890. 


MAXIMUM  EFFICIENCIES  OF   THE   STEAM-ENGINE.     77$ 

known,  however,  the  proprietor  would  have  done  better  to  have 
ordered,  at  the  first,  a  larger  or  a  faster  running  engine  with  a 
higher  ratio  of  expansion,  and  would  usually  find  it  economical 
to  alter  the  engine  here  assumed  to  be  used — in  the  manner 
already  described — if  possible,  so  as  to  deliver  the  maximum 
power,  working  at  the  shorter  cut-off. 

(2)  The  second  is  that  of  a  naval  engine  intended  to  work 
with  maximum  efficiency  at  low  power,  or  on  long  runs,  and 
only  requiring  high  power  for  short  periods  of  time.  It  has 
sometimes  been  customary  to  design  such  engines  to  .work  with 
high  ratios  of  expansion  while  cruising,  and  to  develop  full 
power  with  less  expansion  when  in  action,  supplying  a  fan- 
blast  for  the  latter  occasion.  For  such  cases  the  best  ratio  at 
low  power  would  be  re",  and  it  might  be  well  to  make  the  ex- 
pansion variable  through  as  wide  a  range  as  from  r"  to  rj*, 
taken  with  extreme  values  of  M  and  N.  As  already  stated,  in 
all  ordinary  work,  the  ratio  of  expansion  at  maximum  com- 
mercial efficiency  is  the  ratio  of  expansion  to  be  adopted  for 
any  engine. 

The  values  here  given  for  M  and  N  are  based  on  cost  of 
fuel  taken  at  $5  per  ton.  The  value  of  the  ratios  of  expansion 
at  maximum  efficiency  will  be  less  at  lower  prices  and  greater 
at  higher  costs,  the  expenses  of  maintenance  of  plant  being 
constant,  since  the  values  of  cost  of  steam  will  be  directly,  and 
of  M  inversely,  as  the  price  of  fuel.  With  coal  at  ten  dollars 
per  ton,  M  will  be  practically  one  half  the  figures  given  above, 
and  the  least  ratio  of  expansion  correspondingly  increased  as 
per  Table  VI. 

Table  III  may  be  consulted  by  the  owner  of  steam-power 
for  cases  which,  as  is  usual,  fall  within  the  given  limits.  For 
exceptional  cases  he,  or  his  consulting  engineer,  can,  when  data 
are  obtainable,  always  make  his  own  curve  of  efficiency  and 
obtain  a  practically  exact  solution  of  the  case  presented. 

The  curve,  B,  in  the  last  group  of  efficiency-curves,  may  be 
taken  as  fairly  approximate  for  simple  locomotives ;  which  fall 
into  the  class  of  simple,  unjacketed  engines.  This  deduction 
is  confirmed  by  comparing  independently  produced  curves. 


780  A    MANUAL    OF   THE   STRAM-ENGINE. 

Mr.  H.  J.  Hotchkiss  has  collated  for  the  Author  a  consider- 
able amount  of  data  from  reports  on  the  practice  of  railways  in 
the  United  States,  for  the  purpose  of  solving  these  problems.* 
Taking  the  value  of  engine  as  $8000,  of  which  45  per  cent, 
$3600,  is  charged  to  boiler  and  tender,  yearly  mileage  33,000, 
life  locomotive,  25  years,  evaporation  7  to  i,  the  engine  costs 
per  mile  $4.50,  boiler  charges  at  "full  steam"  $4.00,  coal  per 
mile  10.5  cents,  labor  7.4  cents,  M  —  0.32,  and  the  problem  of 
the  designer  being  solved,  the  ratio  of  expansion  at  maximum 
commercial  efficiency  should  be  re  =  0.2,  nearly,  and  the  engine 
should  be  given  such  size  and  proportions  that  it  may  do  its 
ordinary  and  average  work  at  that  point  of  cut-off.  Once 
constructed,  however,  it  may  be  employed,  with  gradually  in- 
creasing loads,  under  similar  conditions  as  to  costs  until  its 
steam  is  "  following"  as  far  as  0.7  stroke  and  continuously  pay 
better  and  better,  but  yet  never  as  well  as  an  engine  precisely 
adopted  by  the  designer  for  the  heavier  work. 
A  very  similar  case  gives : 

Cut-off  for  maximum  efficiency  of  fluid , 0.40 

"        "  "  "  "   engine 0.48 

"        "  "          commercial  efficiency 0.63 

"        "  "          work  and  "         0.75 

the  values  of  the  coefficients  being  M  =  0.27 ;  N  =  0.89. 

The  assumed  conditions  may  be  taken  as  representing  a 
common  set  for  their  data,  in  the  United  States  and  Canada. 

The  following  are  figures  obtained  in  1891  in  securing  the 
required  data  for  the  solution  of  the  "designer's  problem"  of 
Chap.  VII,  Part  I. 

Three  types  of  engine  were  proposed  for  driving  the  electric 
machinery  of  a  street  railway :  (I)  simple  non-condensing ; 
(II)  simple  condensing;  (III)  compound  condensing.  Their 
power,  market  value,  etc.,  were,  respectively,  as  in  the  table : 


*  For  much  of  most  valuable  data,  Wellington's  Railway  Location  has  been 
referred  to. 


MAXIMUM  EFFICIENCIES  OF   THE   STEAM-ENGINE.     781 

COSTS  AND  POWER  OF  ENGINES. 

Type I            II  HI 

I.  H.  P.,  rated. 105         105  112 

D-H.P,    "    95          95  96 

Cost  per  I.  H.  P.,  in  place $24        $28  $39 

"      "         "        transmission 2             2  2 

Total  cost $26        $30  $41 

Cost  of  boilers,  set,  per  H.  P $14.00   $12.00  $9.00 

"     "  chimney,  etc 7.00       6.50  6.00 


Total  cost $21.00   $18.50   $15.00 

Total  cost  of  engine $2560    $3040    $3990 

"        "     "boilers ,       1995       1710       1425 


"  outfit $4555     $4750    $5415 

Coal  per  I.  H.  P.  per  hour 3.5         2.75         2.1 

The  annual  costs,  allowing  1.5  per  cent  tax  on  a  two-thirds 
valuation,  interest  5  per  cent,  repairs  2  per  cent,  depreciation 
of  engine  4  per  cent,  boilers  10  per  cent,  oil,  waste,  etc.,  at 
0.0002  per  I.  H.  P.  per  hour,  fuel  at  $3.00  per  ton,  amount  to 
about  as  below : 

I  II  III 

Annual  costs 1 $4500        $57/o        $3168 

and  about  $500  per  annum  could  be  saved  by  adopting  the 
compound  condensing  engine,  or  the  interest  on  $10,000. 

Taking  curve  EE  on  the  last  figure,  Chap.  VII,  Part  I,  as 
satisfactorily  approximate  for  this  case,  making/,  =  100,  pb  =  3, 

—  =  0.033,  M  =  0.07,  the  designer  finds  that  he  should  plan 

A 

his  engine,  for  its  average  power,  at  r  =  7.5,  nearly.    Maximum 

efficiency,  as   determined  by  the   solution   of   the  "owner's 
problem,"  is  obtained  when  r  —  5,  nearly. 


782  A    MANUAL   OF   THE   STEAM-ENGINE. 

We  may  compare  the  preceding  with  the  case  of  a  simple 
"  automatic"  non-condensing  engine  of  about  75  I.  H.  P.,  of 
such  good  construction  and  such  high  speed  as  will  make  its 
curve  substantially  the  same  as  the  last,  the  curve  E  on  the 
plate.  This  engine  gives  the  following  data : 

FIRST  COSTS. 

Power,  I.  H.  P 75 

D.  H.  P 67.5 

Cost,  per  I.  H.  P.,  engine $25 

"         "         shafting 5 


"       "        "  total $30 

"       "         "          boilers,  set $12 

"       "        "          chimney,  etc „ 8 

"       "        "  total $20 

"     total,  engine $2250 

"         "      boilers 1500 


"      plant $3750 

Weight,  water  per  I.  H.  P.,  per  hour,  Ibs 25 

coal      "         "  "       "       " 4 

The  engine  is  to  work  12  hours  a  day,  313  days  in  the  year. 
Water  costs  nothing. 

ANNUAL  COSTS. 

(i)  Invariable  : 

Building  and  land $7000 

Assessment  on 4000 

Annual  taxes  @  1.5  % $60 

Interest  @  5.4  % 378 

Engine-driver's  pay 1000 

Fireman's  "    700 


Total '. $2138 


MAXIMUM  EFFICIENCIES  OF   THE  STEAM  ENGINE.     783 

(2)  Variable  with  engine  : 

Interest  on  cost  @  5.63  % $126.55 

Repairs  @  2  % 45.00 

Depreciation  @  4  £ 90.00 

Taxes  @  1.5  £,  on  f  valuation 24.75 

Oil,  waste,  etc.,  @  94  cents  per  I.  H.  P 70.50 

Total $356.80 

(3)  Variable  with  boiler  : 

Fuel  @  $2  per  ton,  563^ $1126.80 

Interest  @  5.63  % 84.38 

Depreciation  and  repairs  @  155* 225.00 

Insurance  @  0.5  £  on  \  cost 20.00 

Taxes  @  i.i  %  on  cost 16.50 

Total $1472.68 

Total  of  all  annual  variable  costs  (2)  and  (3). .  $1829^48 

Making  use  of  curve  £,  we  find,  for  pb  =  18,  /,  =  95, 
—  =  0.19,  and  M  =  0.85. 

The  results,  obtained  as  before,  are : 

Ratio  of  expansion  for  maximum  efficiency  of  fluid 4.35 

Ditto  for  efficiency  of  engine 3.64 

"  capital 2.94 

And  the  engine  should  be  designed  to  do  its  work  at  cut-off  of 
about  0.3,  but  will  give  highest  duty  when  r  =  3.6,  nearly. 

198.  Variation  of  Cylinder-condensation. — One  other 
among  the  numerous  problems  capable  of  solution  by  this 
method  promises  to  prove  both  interesting  and  important : 

"  Given  the  method  of  variation  of  efficiency  with  varying 
ratios  of  expansion  or  proportions  of  steam  used,  to  determine 

the  method  of  cylinder-condensation  with  varying  values  of  — ." 
To  solve  this  problem,  construct  the  curve  of  efficiency,  as 


784  A   MANUAL   OF   THE   STEAM-ENGINE. 

A,  D,  £,  Fig.  167,  and  draw  the  curves  of  adiabatic  mean 
pressures  for  various  values  of  x,  as  in  dotted  lines  in  that 
figure. 

The  points  of  intersection  of  these  curves  with  the  curve 
of  efficiency  identify  the  ratios  of  expansion  at  which  the 
total  condensation  amounts  to  the  proportion  due  to  the  adia- 
batic line  so  cut. 

In  all  problems  of  maxima  or  minima  solved  by  the  con- 
struction here  given  it  will  be  observed  that  the  item  of  quan- 
tity of  expenditure  made  the  independent  variable  is  that  de- 
pendent upon  the  quantity  of  steam  or  of  fuel  demanded  by 
the  engine. 

199.  Problems  Solved  by  Inspection  of  the  Diagrams. 
— An  important  class  of  problems  of  simple  character  may  be 
solved  with  ease  and  rapidity  by  the  use  of  the  curve  of  effi- 
ciency for  the  class  of  engine  studied  in  any  case,  e.g. : 

(1)  To  determine  the  gain  or  decrease  of  power  obtainable 
by  change  of  ratio  of  expansion  or  point  of  cut-off,  measure 
the  ordinates  of  the  curve  at  the  present  and  at  the  proposed 
ratio  of  expansion.     Their  relative  magnitude  will  be  a  meas- 
ure of  the  relative  power  of  the  engine  at  the  two  points  of 
cut-off,  using  the  quantity  of  steam  measured  by  the  abscissas. 

(2)  To  determine  the  quantity  of  fuel  or  of  steam,  per  hour 
per  horse-power,  to  be  gained  or  lost  by  change  of  the  ratio  of 
expansion,  compare  the  value  of  ratios  of  abscissa  to  ordinate 
at  the  existing  and  proposed  points  of  cut-off ;  their  relation 
will  be  that  of  cost  of  power  in  steam  or  in  fuel. 

(3)  To  determine  the  absolute  amount  of  fuel  or  of  steam, 
consumed  per  horse-power  per  hour,  at  any  assumed  rates  of 
expansion,  first  compute  the  consumption  for  the  given  engine 
as  a  thermodynamic  problem  simply,  and  multiply  by  the  ratio, 

V 
— ,  of  the  mean  pressure  in  the  perfect  engine  at  the  given 

expansion  to  that  shown  by  the  true  curve  of  efficiency  for  the 
engine  studied.  Or,  compute  the  consumption  for  the  engine 
working  without  expansion  and  without  waste,  and  multiply 


MAXIMUM  EFFICIEXCIES  OF    THE   STEAM-EXG1XE.     785 

p 
by  the  ratio,  —L-  ,  obtaining  y  and  pm  from  the  diagram  A", 

the  given  cut-off,  and  remembering  that  /,  measures  the  mean 
pressure  at  full  stroke  of  the  given  steam  used  dry. 

2OO.  Conclusions.— In  view  of  what  has  preceded,  it  be- 
comes obvious  that  the  engineer  purposing  to  write  a  speci- 
fication for  steam  machinery  on  which  bids  are  to  be  made 
with  guarantee  of  performance  should  first  determine  the 
probable  curve  of  efficiency  for  the  type  and  design  of  engine 
called  for,  and  should  solve  all  the  several  problems  relating 
to  its  economy.  He  should  prescribe  the  size  of  engine,  then 
the  mean  pressure,  or  the  ratio  of  expansion  at  which  maxi- 
mum "duty"  is  to  be  obtained,  as  well  as  fix  the  duty  expected 
in  regular  work ;  at  which  ratio  the  work  done  will  be  less  than 
the  regular  working  power  of  the  machine.  He  must  also 
indicate  at  what  mean  pressure,  or  what  degree  of  expansion, 
the  engine  will  be  required  to  do  its  ordinary  work  at  maxi- 
mum commercial  efficiency,  and  should  state  what  limit  of 
economy  at  that  rate  of  work  will  be  accepted.  Finally,  it 
should  be  prescribed  that  the  engine  should  be  capable,  if  its 
work  should  be  increased,  of  attaining  at  least  its  maximum 
4*  efficiency  of  plant"  with  safety,  and  with  a  specified  economy 
which  should  be  reasonably  high. 

Thus :  fixing  the  mean  pressure  and  the  ratio  of  expansion 
for  the  duty-trial,  the  builder  is  able  to  give  an  intelligently 
estimated  guarantee  of  performance  at  highest  efficiency; 
fixing  it  for  maximum  commercial  efficiency  in  regular  work 
fixes  at  the  same  time  the  proper  size  of  engine;  and  the  last 
specification  secures  ample  strength  of  parts. 

The  cases  which  have  been  here  investigated  must  be  taken 
simply  as  illustrative  and  not  as  affording  results  to  be  accepted 
in  any  specified  case  coming  up  in  the  practice  of  the  engineer. 
Every  such  case  should  be  independently  and  thoroughly  in- 
vestigated. A  considerable  amount  of  data  and  some  further 
illustrations  of  the  principles  which  have  been  here  enunciated 
will  be  found  in  the  concluding  chapter  of  the  second  part  of 
this  work. 


786  A    MANUAL    OF   THE   STEAM-ENGINE, 

201.  Absolute  Limits  to  Expansion. — It  has  been  gener- 
ally assumed,  hitherto,  that  the  best  ratio  of  expansion,  whether 
for  maximum  efficiency  of  fluid,  of  engine,  of  capital,  or  of 
plant,  increases  with  increase  of  steam-pressure  without  limit, 
and  that  such  ratio  may  be  indefinitely  increased  with  decrease 
of  the  ratio  of  back-pressure  for  any  one  kind  of  engine,  not- 
withstanding the  fact  that  the  value  of  the  ratio  of  expansion 
is  modified  by  variation  of  the  conditions  of  working,  even 

where  the  ratio  ~  is  the  same.     But  it  may  be  seen  that,  in 

every  engine  operated  under  the  conditions  of  real  work  and  of 
usual  practice,  there  exists  a  limiting  value,  for  any  one  of  these 
"  ratios  of  maximum  efficiency,"  beyond  which  it  cannot  be 
economically  raised,  even  with  a  greatly,  perhaps  infinitely,  ele- 
vated boiler-pressure.  It  will  be  further  seen  that  this  "  abso- 
lute limit "  may  be  readily,  and  probably  often  is,  passed  in 
every-day  practice;  that,  in  the  usual  forms  of  steam-engine,  an 
absolute  limit  exists,  within,  or  not  far  beyond,  the  customary 
working  range  of  expansion,  beyond  which  expansion  cannot 
be  carried  with  economy,  however  high  the  steam-pressure 
adopted;  in  other  words,  with  infinite  pressure,  the  economical 
value  of  the  ratio  of  expansion  will  be  found  often  not  merely 
finite,  but  sometimes  probably  even  within  the  limits  of  familiar 
practice.  The  designing  engineer  keeps  these  facts  and  all  the 
pseviously  described  conditions  in  mind  and  bases  his  deter- 
minations of  the  character  and  the  principal  dimensions  of  the 
engine,  upon  them.  These  investigations  all  have  for  their  pur- 
pose the  solutions  of  the  main  problem  in  finance.  Studying 
the  equations,  it  will  be  found  that,  in  all  except  those  relating 
to  efficiency  of  engine  or  of  fluid,  it  is  possible  to  find  finite 
values  of  r  such  that  their  left-hand  members  shall  reduce  to 
zero  ;  since  n  nearly  always  approximates  unity;  q  varies  from 
q  —  O  to  q  =  0.3  in  good  practice,  and  b  usually  ranges  between 
b  —  0.8  and  b  —  0.9  ;  M  or  N  usually  has  a  value  between  0.02 
and  0.15. 

Thus  the  form  of  the  function  is  such  that  the  first  member 
may  always  be  made  to  disappear  for  some  finite  value  of  r,  and 


MAXIMUM  EFFICIENCIES  OF   THE  STEAU-EXGINE.     7*7 

the  value  of  r,  at  which  this  condition  is  obtained,  constitutes 
an  "  absolute  limit,"  for  the  case  taken,  beyond  which  expan- 
sion cannot  be  carried  economically,  even  with  steam  increased 

to  infinite  tension  :  beyond  this  point  —  becomes  negative,  in- 
dicating the  assumption  of  impossible  conditions. 

Examining  equations  relating  to  the  purely  thermodynamic 
problem,  we  find  no  such  limit ;  the  sign  of  the  first  member 
remains  positive  for  all  values  of  ry  and  can  never  become  zero 
for  a  finite  value  of  that  quantity.  Thus  an  important  differ- 
ence here  evidently  exists  between  the  idtal  engine,  with  its 
non-conducting  cylinder,  and  the  real  engine  working  steam  in 
a  metallic  cylinder,  as  well  as  between  the  case  of  maximum 
efficiency'  of  engine  and  that  of  maximum  efficiency  of  capital. 
In  the  case  of  maximum  efficiency  of  fluid  for  the  ideal  perfect 
engine  only,  is  it  true  that  indefinite  increase  of  steam-pressure 
permits  indefinitely  increased  expansion.  In  all  other  cases  an 
absolute  limit  exists,  fixed  for  each  case,  beyond  which  expan- 
sion cannot  be  economically  carried. 

For  the  U.  S.  steamers  Michigan,  Georgiana,  and  Bache.  for 
which  three  cases  the  real  curves  have  been  obtained,  these 
curves  remaining  unchanged  by  increase  of  pressure,  it  is  im- 
possible economically  to  increase  the  ratio  of  expansion  in  such 
engines  beyond  three,  five,  and  ten,  respectively,  even  with  un- 
limited steam-pressure :  Le.,  even  when  ~f  =  O- 

P\ 

We  conclude : 

(1)  That  in  all  real  engines  there  exists  an  "absolute  limit 
to  the  economical  expansion  of  steam,"  whether  considered 
with  reference  to  efficiency  of  fluid,  of  engine,  or  of  capital : 
which  limit  cannot  be  passed,  whatever  pressure  of  steam  may- 
be carried  up  to  the  point  of  cut-off. 

(2)  That  this  limit  is  found  at  higher  ratios  of  expansion  as 
the  type  of  engine  is  more  efficient,  but  that  the  limit  is  indefi- 
nitely removed  only  in  the  ideal  engine,  and  then  only  as  af- 
fecting the  ratios  of  expansion  at  maximum  efficiency  of  fluid 
and  engine. 


788  A    MANUAL   OF   THE   STEAM-ENGINE. 

(3)  That  this  limit  is  found  at  a  small  value  of  the  ratio  of 
expansion  in  ordinary  and  inefficient  engines,  and  maybe  read- 
ily passed  in  every-day  practice. 

(4)  It  is  evident  that  these  general  propositions  are  true  of 
all   heat-engines    having    fluid    working    substances,    whether 
vapors  or  gases,  worked  in  metallic  cylinders. 


APPENDIX. 


TABLES. 

PACK 

I.  NUMERICAL  CONSTANTS:  CIRCLES;  AREAS;  ETC 790 

II.  LOGARITHMS,  COMMON  AND  NATURAL..  803 

III.  MEAN  PRESSURE  RATIOS 806 

IV.  TERMINAL  PRESSURES 809 

V.  HEAT  TRANSFER  AND  TRANSFORMATION 810 

VI.  COMPARISON  OF  THERMOMETERS 812 

VII.  VOLUMES  OF  WATER;  DENSITIES. 814 

VIII.  METRIC  STEAM  TABLE 815 

IX.  METRIC  STEAM  AND  WORK  TABLE. 818 

X.  STEAM  TABLE;  BRITISH  UNITS 820 

XI.  STORED  ENERGY  ix  STEAM  AND  WATER 827 

XII.  FORMULAS  FOR  PROPERTIES  OF  STEAM 829 

XIII.  FACTORS  OF  EVAPORATION 831 

XIV.  COMPOSITION  OF  FUELS. 832 

XV.  HORSE-POWER  CONSTANTS 834 

XVI.  REAL  RATIOS  OF  EXPANSION 835 

XVII.  LOGS  AND  FORMS  FOR  BLANKS 836 

XVIII.  ELECTRICAL  HORSE-POWER 840 

XIX.  WATER  COMPUTATION  TABLE. 841 

XX.  HIRN'S  ANALYSIS  BLANKS. 843 

XXI.  HEAT  AND  POWER  UTILIZATION;  NON-CONDENSING  ENGINE 845 

XXII.  NOTE  TO  §  112 856 

-        789 


790 


A   MANUAL   OF   THE   STEAM-ENGINE. 


I. 

NUMERICAL  CONSTANTS. 


JZ 

n-n 

«»" 

4 

«* 

«3 

Vi 

fc 

I.O 

3.142 

0.7854 

.000 

I.OOO 

.0000 

.0000 

I.I 

3-456 

0.9503 

.210 

1.331 

.0488 

.0323 

1.2 

3-770 

I.I3IO 

.440 

1.728 

•  0955 

.0627 

1-3 

4.084 

I  3273 

.690 

2.197 

.1402 

.0914 

1.4 

4.398 

1-5394 

.960 

2.744 

.1832 

.1:87 

1.5 

4.712 

1.7672 

2.250 

3-375 

.2247 

.1447 

1.6 

5-027 

2.0106 

2.560 

4.096 

•2649 

.1696 

1-7 

5-341 

2.2698 

2.890 

4-9I3 

•3038 

•J935 

1.8 

5-655 

2-5447 

3.240 

5-832 

.3416 

.2164 

1.9 

5-969 

2-8353 

3.610 

6.859 

.3784 

.2386 

2.0 

6.283 

3-1416 

4.000 

8.000 

.4142 

•2599 

2.1 

6-597 

3-4636 

4.410 

9.261 

.4491 

.2806 

2.2 

6.912 

3-8013 

4.840 

10.648 

.4832 

.3006 

2-3 

7.226 

4.1543 

5-290 

12.  167 

.5166 

.3200 

2.4 

7.540 

4-5239 

5.760 

I3-824 

5492 

.3389 

2.=: 

7-854 

4.9087 

6.2SO 

15.625 

-5811 

•3572 

26 

8.168 

5-3093 

6.760 

17.576 

.6125 

•3751 

2.7 

8.482 

5-7256 

7.290 

19.683 

.6432 

•3925 

2.8 

8.797 

6.1575 

7.840 

21.952 

•  6733 

•4095 

2.9 

Q.III 

6.6052 

8.410 

24.389 

.7029 

.4260 

3.0 

9.425 

7.0686 

9.00 

27.000 

•7321 

.4422 

3-i 

9-739 

7-5477 

9.61 

29.7QI 

•  7607 

.4581 

3-2 

10.053 

8.0425 

10.24 

32.768 

.7889 

.4736 

3-3 

10.367 

8.5530- 

10.89 

35-937 

.8166 

.4888 

3-4 

10.681 

9.0792 

11.56 

39-304 

•  8439 

•5037 

3-5 

10.996 

9.6211 

12.25 

42-875 

.8708 

0183 

3-6 

11.310 

10.179 

12.96 

46.656 

-8974 

.5326 

3-7 

11.624 

10.752 

13.69 

50.653 

•9235 

•5467 

3-8 

11-938 

11.341 

14  44 

54-872 

•9494 

•5605 

3-9 

12.252 

11.946 

15-21 

59-3I9 

.9748 

•5741 

4.0 

12.566 

12.566 

16.00 

64.000 

.0000 

•5874 

4.1 

12.881 

*3-203 

16.81 

68.921 

.0249 

.6005 

4.2 

I3-I95 

13-854 

17.64 

74.088 

.0494 

•6134 

4-3 

13  5<>9 

14-522 

18.49 

79-507 

.0736 

.6261 

4-4 

13-823 

15.205 

19.36 

85.184 

.0976 

.6386 

4-5 

14.137 

15.904 

20.25 

91.125 

-1213 

.6510 

4.6 

14.451 

16.619 

21.  l6 

97.336 

.1448 

.6631 

4-7 

M.765 

17-349 

22.09 

103-823 

.1680 

675f 

APPENDIX. 
CONSTANTS — Continued. 


791 


- 

- 

,»? 

m* 

m* 

<rm 

h 

-.'- 

15.080 

18.096 

23.04 

110.592 

2.1909 

1.6869 

4-9 

15-394 

::    -" 

24.OI 

117.649 

2.2136 

1.6985 

5-o 

•-.---. 

19-635              25-00 

125.000           2.2361 

1.7100 

5-J 

16.022 

20.428              26.01 

132.651            2.2583 

1.7213 

5-2 

16.336 

21.237 

27.04 

140.608           2.2804 

1-7325 

5-3 
5-4 

16.650 

22.062 
22.902 

28.09 
29.16 

148.877           2.3022 
157.464       i     2.3238 

1-7435 
1-7344 

:-: 

17-279         23.758 

30.25 

166.375            2.3452 

1.7652 

5-6 

17-593         24.630 

31.36                 175.616               2.3664 

1.7753 

5-7 

17.907         25.513             32.49             185.193            2.3875 

i.7S63 

5-8 

lS.221            26.421                 33-64                 I95.II2               2.4053 

1-7967 

5-9 

18-535            27.340 

34.81                 205.379               2.4290 

1.8070 

6.0 

18.850     1      28.274                 36.00                 216.000               2.4495 

1.8171 

6.1 

19.164            29.225                 37.21                 226.g8X.              2.4693 

:    -:-; 

6.2          I9-47S         30.191             38-44             238.328           2-4900 

1.8371 

6.3         19-792     s     31-173             39-6* 

250.047           2.5100 

1.8409 

6.4          20.106         32.170             40.96 

262.144           2.5298 

1.2566 

6-5 

20.420            33-IS3                 42.25 

274-625            2.5495 

:    -       : 

6.6 

20-735          34-212             43.56             287.496            2.5691 

1.  57*3 

6.7 
6.8 

21.049     !     35-«57              44-$9              300.  7t_-             =    :"- 
21.363          36-317             46.24             3M-432            2.6077 

i.S5« 

:    -  -r 

6.9 

21.677 

37-393 

47-61 

3*8.509 

2.6268 

1.9038 

7-o 

21.991 

*    --: 

49-00 

343-000 

2.6458 

1.9129 

7-i 

22.305 

39-592 

50.41 

357-9" 

2.6646 

-  : 

22.619 

40.715 

51-84 

373-248 

=  »a 

I.93!O 

7-3 

22.934 

41.854 

53-29 

389-017 

2.7019 

1-9399 

7.4         23.243 

43.008 

54-76 

405-224 

2.7203 

1.9487 

7.5          23.562 
7.6         23.876 
7.7         24.190 

44-179 

':':.: 

56.25 
57-76 
59-29 

421.87$ 

458-976 
456.533 

2-7336 
1.756! 

2-7749 

1-9574 
1.9661 
1-9747 

7.8  t       24.504 

47.784            60.84 

474-552 

2-7929 

1.9332 

7.9         24-819 

49-017 

62.41 

493.039 

2.8107 

1.9916 

8.0  i      25.133 

50.266 

64.00 

512.000 

:   '-.-. 

2.OOOO 

8.1         25.447         51-530            65.61 

531-441 

2.8461 

2.0083 

8.2         25.761         52.810             67-24             551-463 

2.0165 

£ 

26.075        *4-i°6            68.8g 
26.389        55-4i8           70-56 

57L787 
592-704 

2.8810 
2.8983 

2.0247 
2.0328 

8-5 

26.704 

56.745              -:  ."- 

614.125            2.9155 

2.0408 

8.6         27.018 

-     '-             73-96 

636.056            2.9326 

2.04S8 

8.7         27-332 
8.5         27-646 

59-447              75-69 
60.821              77-44 

655.503            2.9496 
681.473            2.9665 

2.0567 
2.0646 

8.9         27-060 

62.211              79-21 

704.969            2.9833 

2.0724 

792 


A  MANUAL   OF   THE   STEAM-ENGINE. 
CONSTANTS — Continu  ?d. 


p 

nit 

n-" 
4 

«» 

«3 

v« 

s 

v« 

9  o 

28.274 

63-617 

81.00 

729.00O 

3.0000 

2.0801 

9.1 

28.588 

65.039 

82.81 

753-571 

3.0166 

2.0878 

9.2 

28.903 

66.476 

84.64 

778.688 

3  0332 

2.0954 

9'3 

29.217 

67.929 

86.49 

804.357 

3-0496 

2.1029 

9-4 

29-53I 

69.398 

88.36 

830.584 

3.0659 

2.1105 

9-5 

29.845 

70.882 

90.25 

857-375 

3-o8i2 

2.1179 

9.6 

30.159 

72.382 

92.16 

884.736 

3-0984 

2.1253 

9-7 

30-473 

73.898 

94.09 

912.673 

3-II45 

2.1327 

9.8 

30.788 

75-430 

96.04 

941.192 

3  1305 

2.1400 

9-9 

31.102 

76.977 

98.01 

970.299 

3-1464 

2.1472 

IO.O 

3i-4r6 

78.540 

IOO.OO 

1000.000 

3.1623 

2.1544 

10.  I 

3I-730 

80.119 

102.01 

1030.301 

3.1780 

2.1616 

IO.2 

32.044 

81.713 

104.04 

1061.208 

3-1937 

2.  1687 

10.3 

32.358 

83.323 

I06.O9 

1092.727 

3-2094 

2-1/57 

10.4 

32.673 

84.949 

108.16 

1124.863 

3.2249 

2.1828 

10.5 

32.987 

86.590 

110.25 

1157.625 

3.2404 

2.1897 

10.6 

33-301 

88.247 

112.36 

1191.016 

3-2558 

2.1967 

10.7 

33-615 

89.920 

114.49 

1225.043 

3.2711 

2  .  2036 

10.8 

33-929 

91.609 

116.64 

1259.712 

3-2863 

2.2104 

10.9 

34-243 

93.313 

118.81 

1295.029 

3.30I5 

2.2172 

II.  0 

34-558 

95-033 

121.00 

1331.000 

3-3166 

2.2239 

ii.  i 

34-872 

96.769 

123.21 

1367.631 

3-33I7 

2.2307 

II.  2 

35-136 

98.520 

125.44 

1404.928  • 

3-3466 

2-2374 

"•3 

35-500 

100.29 

127.69 

1442.897 

3-3615 

2.2441 

11.4 

35.814 

102.07 

129.96 

1481.544 

3-3764 

2.25O6 

"•5 

36.128 

103.87 

132.25 

1520.875 

3-3912 

2.2572 

ii.  6 

36.442 

105.68 

I34-56 

1560.896 

3.4059 

2.2637 

11.7 

36.757 

107.51 

136.89 

1601.613 

3-4205 

2.2702 

II.  8 

37-071 

109.36 

139.24 

1643.032 

3-4351 

2.2766 

11.9 

37-385 

I  I  I.  22 

141.61 

1685.  159 

3.4496 

2.2831 

12.  0 

37-699 

II3.IO 

144.00 

1728.000 

3-4641 

2.2894 

12.  1 

38.013 

114.99 

146.41 

1771.561 

3-4785 

2.2957 

12.2 

38.327 

II6.90 

148.84 

1815.848 

3.4928 

2.3021 

12.3 

38.642 

II8.82 

151.29 

1860.867 

3  5071 

2  .  3084 

12.4 

38.956 

120.76 

153-76 

1906.624 

3-5214 

2.3146 

12.5 

39.270 

122.72 

156.25 

1953.125 

3-5355 

2  .  32O8 

12.6 

39-584 

124.69 

158.76 

2000.376 

3-5496 

2.3270 

12.7 

39-898 

126.68 

161.29 

2048.383 

3-5637 

2-3331 

12.8 

40  .  2  1  2 

128.68 

163.84 

2097.152 

3-5777 

2.3392 

12.9 

40.527 

130.70 

166.41 

2146.689 

3.59I7 

2-3453 

13-0 

40.841 

132.73 

169.00 

2197.000 

3-6056 

2.3513 

13-1 

41-155 

134.78 

171.61 

2248.091 

3-6i94 

2-3573 

13.2 

41.469 

136-85 

174.24 

2299.968 

3.6332 

2.3633 

APPENDIX, 

rrrrrmrinf    Cimdmm,*' 


793 


•             TT 

•»* 

4 

- 

•* 

."- 

.-. 

13-3 

S    -  ': 

13-4 

.:  .-.'- 

141-03       179-56      2406.104 

3-6606 

2-3752 

I3-S 

42.412 

I43-M       182.25      2460.375 

3-6742 

2.3511 

15.6 

42.726 

145-27 

134.96      2515-456 

-- 

13-7 

43  040 

147-41       187.69 

2571-353   3-7013 

I  :.;i 

13-  S 

43  -.-=- 

.    :-        19044 

96x8.072  1  3.7148 

;  •;:;-: 

13-9 

151.75     193-21 

2685.619  I  3.7283  2.4044 

14-0 
14-1 

45-oS2     153  94     196.00 
44.996     156-15  [   :--.-: 

2744.000 
2803.221 

3-7417   2.4IOS 
3-7550   2.4159 

14-2 

44-611              201.64 

2863.988 

3-7653   2.4216 

14-3 

44925 

:    : 

204-49 

99x4.207 

3-7*»5  |  2^272 

14-4 

45-239 

162.36 

207-36 

•985-984 

3-7947  j  »-4329 

14-5 
14-6 

45-553 

-:  -  - 

165-13 
167-42 

210.25 
213-16 

3048.625 

3112.136 

3-8079  j  2.4385 

-  -  -  :    -  -—  : 

_  :-: 

169.72 

216-09      3176.523 

:•  -••-: 

:  —  .- 

I4-S 

172-03 

219-04  .    3241.792 

-  -----z 

14-9 

46.810 

174  37 

222.01   |    3307.949 

3.8600 

2.4607 

15-0 
I5-I 
15-2 

47-124 
47-438 
47 

176.72 

:-.  -,* 
:::  -' 

225-00 
228.01 
231.04 

3375.000 
344X.95I 
35H.80B 

'•  :- 

2.4662 
2-4717 
:  .--: 

15-3 

--   rr       :::  -: 

234-09 

3581-577 

3-9115 

2-4525 

15  *•!• 

4S-3SI     :   :: 

237-16 

3652.264 

3-9243 

2.4*79 

15-5 

:-;  -:•; 

24025 

_--:-  -: 

3.9370 

2-4935 

15-6 

49.009     191-13 

243-36      3796-416 

.-  ----- 

15-7 

49-523     193-59 

•46-49 

:v, 

:•  -'--I- 

2-5059 

I5-S 

49-637 

196.07 

24964 

3944-312 

3-9749 

2.5092 

15-9 

49-951 

198.56 

;::  ,: 

4019.679 

3  9875 

2.5146 

•6.0 

:  .   I  \  :          -'  -  -   -'- 

256.00 

4090.000  1  4  -Oooo 

2.5193 

I6.I 
16.2 

50.894  1   206.19 

259-21 
:  :  „ 

4173-281      2.5251 

4251.528    4  0249   2.5303 

16.3 
16.4 

•-'-..'     ::?:- 
51.522     211.24 

S.96 

4330-747    4-0373 
4410.944    4-0497 

2-5406 

16.5 
16.6 
16.7 

51.836 
52.150 
52.465 

"••  -3 
216.42 
219.04 

:-:  :  = 

:.:  : 

•78-89 

££296 
4657-463 

4.0620  ;|  2.5458 
4.0743  '  2.5509 

_  •-••-.   :  ;  ;  : 

16.8 

52-779 

221.67 

--:  :.     .-.:  -  •-:    -  ..- 

;  -   ; 

,6.9 

53-093 

-:-  :- 

985-61     4826.809 

4.1110 

2.5663 

17.0 
17-1 

17-2 

153-407 
53-721 
54-035 

22698 

:;:  -V 
132-35 

289-00 
292-41 

=  •-:  :- 

4013-000 
5000.211 
5088.448 

4-1231 
4.135* 
4-M73 

2-5713 
2  5763 

17-3 

54-350     235-06 

5177-717 

4-1593 

^5563 

17-4 

54.664     237-79 

302.76 

5266.024 

4-I7I3 

2-5913 

794 


MANUAL   OF  THE  S7EAM-ENGINE. 
CONSTANTS  —  Continued. 


n 

nir 

•*! 

«» 

«* 

Vn 

3 

V~t 

17-5 

54-978 

240.53 

306.25 

5359-375 

4-I833 

2.5963 

I7.6 

55-292 

243.29 

309-76 

545L776 

4.1952 

2.6012 

17.7 

55.606 

246.06 

313.29 

5545-233 

4.2071 

2.  6o6l 

I7.8 

55.920 

248.85 

316.84 

5639-752 

4.2190 

2.6IOC) 

17-9 

56.235 

251.65 

320.41 

5735-339 

4-2308 

2.6158 

18.0 

56.549 

254-47 

324-00 

5832.000 

4.2426 

2.6207 

18.1 

56.863 

257.30 

327-61 

5929.741 

4-2544 

2.6256 

18.2 

57-177 

260.16 

33L24 

6028.568 

4.2661 

2-6304 

18.3 

57-491 

263.02 

334.89 

6128.487 

4.2778 

2-6352 

18.4 

57-805 

265.90 

338.56 

6229.504 

4-2895 

2.6401 

18.5 

58.119 

268.80 

342-25 

6331-625 

4-3012 

2.6448 

18.6 

58.434 

271.72 

345  •  96 

6434-856 

4-3I2S 

2.6495 

18.7 

58.748 

274.65 

349-69 

6539-203 

4.3243 

2.6543 

18.8 

59-062 

277-59 

353-44 

6644.672 

4-3359   2.6590 

18.9 

59-376 

280.55 

357-21 

6751-269 

4-3474 

2.6637 

19.0 

59-690 

283.53 

361.00 

6859.000 

4-3589 

2.6684 

19.1 

60.004 

286.52 

364.81 

6967.871 

4.3703   2.6731 

19.2 

60.319 

289.53 

368.64 

7077.888 

4.3818  1  2.6777 

19-3 

60,633 

292.55 

372-49 

7189.057 

4.3932  j  2.6824 

19-4 

60.947 

295-59 

376.36 

7301.384 

4-4045 

2.6869 

19-5 

6l.26l 

298.65 

380.25 

7414.875 

4-4159 

2.6916 

19.6 

61.575 

301.72 

384-16 

7529-536 

4.42/2 

2.6962 

19-7 

61.889 

304.31 

388.09 

7645-373 

4.4385 

2.7008 

19.8 

62  .  204 

307-9! 

392.04 

7762.392 

4-4497 

2-7053 

19.9 

62.518 

311.03 

396-01 

7880.599 

4-4609 

2  .  7098 

20.  0 

62.832 

314-16 

400.00 

8000.000 

4-4721 

2.7144 

20.1 

63-146 

3I7-3I 

404.01 

8120.601 

4-4833 

2.7189 

20.2 

63.460 

320.47 

408.04 

8242.408 

4-4944 

2-7234 

20.3 

63-774 

323-66 

412.09 

8365.427 

4.5055 

2./279 

20.4 

64.088 

326  85 

416.16 

8489.664 

4-5166 

2.7324 

20.5 

64.403 

330.06 

420.25 

8615.  125 

4.5277 

2.7368 

20.  6 

64.717 

333-29 

424.36 

8741.816 

4.5337 

2.7413 

20.7 

65.031 

336.54 

428.49 

8869.743 

4-5497 

2-7457 

20.8 

65-345 

339-8o 

432.64 

8989.912 

4.5607 

2.7502 

20.9 

05.659 

343-07 

436-81 

9129.329 

4-5716 

2-7545 

21.0 

65-973 

346  •  36 

441.00 

9261.000 

4-5826 

2-7589 

21.  1 

66.288 

349.67 

445-21 

9393-931 

4-5935 

2.7633 

21.2 

66.602 

352-99 

449-44 

9528.128 

4.6043 

2.7676 

21.3 

66.916 

356.33 

453-69 

9663.597 

4-6152 

2.7720 

21.4 

67.230 

359-68 

457.96 

9800.344 

4.6260 

2.7763 

21-5 

67.544 

363-05 

462.25 

9938.375 

4.6368 

2.7806 

21.6 

67.858 

366.44  |   466.56 

10077.696  |  4-6476 

2-7849 

21.7 

68.173 

369.84  :   470.89 

10218.313    4-6583   2.7893 

APPENDIX. 
CONSTANTS — Omtinmed. 


795 


•         -          "*4 

«»                    «* 

*^ 

h 

21.  8 

21.9 

;;•::; 

373-25 
376.69 

475-24         10360.232 
479.61         10503.459 

4.6690 
4  6797 

2-7935 
*-7!9* 

22.0 

69.115 

380.13 

484.00        10648.000 

'     4-6904 

:    :"-i 

22-1 

69-429 

383.60 

488.41         10793-861 

\    4-Ton 

:   lofa 

22.2             69.743 

387-08           402.84         10941.048 

'     4-7»i7 

- 
2.8103 

22-3    ;         70-058 

390-57            497  29     .     11089.567 

4-7223 

2.8147 

22.4    ,         70-372 

394-08 

501.76    ;    11239.424 

4-7329 

:   -:-, 

22.5  i      70.686 

39761 

506.25        11390.625 

4-7434 

-.   -;-: 

22.6    ;         7I.OOO 

401.15 

510.76        11543.176 

4-7539 

2.  £273 

»-7            71-314 
22.8   j        71.268 

404-71 

515-29 

5;  -  -- 

11697.083 
IIS52.352 

4-7644 
4-7749 

2.5314 
2.8356 

22.9          7»-942 

411.87 

524-41 

12008.989 

-    --:- 

-  -.--: 

23.0  '       72-«57 

4I5-48 

529.00 

12167.000 

4.7958 

2.8438 

23.1  j       72-571 

419  10 

533.61        12326.391 

-    -   ft 

2  |fH 

23-2          72-885 

422-73 

:.--.  24          12487.  :-  i 

4-8166 

2.8:21 

23.3 

73-199 

4^6  39 

542.89       12649.337 

4-S270 

•.•961 

23-4 

73-513 

430-05 

547  56 

12312.904 

4  8373 

2.3603 

23-5 

73-827 

433-74 

552.25 

i2977.tJS 

4  3477 

2-8643 

23.6 

74-142 

437-44 

556.96          13144.256 

4-SfSo 

!.86fc| 

-:-  - 

74-456 

441-15 

561.69          13312.053 

4-8683 

2.8724 

23-8 

74-770 

144.88 

566.44 

13481.272 

4    —: 

:.:-: 

23.9 

75-084 

448-63 

571-21 

13651.919 

.    :--r 

=  .::  ;| 

24-0 

75.398 

452  39 

576.00 

13824.000 

4-S990 

•.MM 

24-1 
24-2 

75-712 
76.027 

456-17 
459-96 

-      -: 
585-64 

13997-521 
14172.481 

4-9092 
4-9»93 

:   Ma 

:   -  .:  = 

24-3 

76.341 

463-77 

500-49 

14345.907 

4.9295 

24-4 

76.655 

467-60 

595-36 

14526.784 

4-9396 

2.9004 

24-5 

76-969 

471-44 

600.25 

14706.125 

4  9497 

2.9044 

24.6 

n  --:• 

475-29 

605.16 

14886.936 

4-9598 

2.9063 

24-7 

77-597 

479.16 

610.09 

15069.223 

4-0699 

2.9123 

24-8 

77.911 

483-05 

615.04 

15252.992 

4  9799 

2.9162 

24.9 

78.226 

486.96 

620.01 

15438-249, 

4-9899 

2.9201 

25-0 

:--  -r 

490-87 

625.00          15625.000 

5.0300 

:     :.: 

25-1 

494-81 

630.01       !       I58I3.25I 

5-0099  i 

2.9279 

25.2 

-     :'•- 

498-76 

635-04 

16003.008 

5.0199 

2.9318 

25-3 

79.482 

502.73 

640.09              16194-277 

5-0299 

2.9356 

25-4 

79-796 

506-71 

645.16             16987.064 

5      ?-: 

2-9395 

25-5 

So.m 

510.71 

650.25 

16581.375 

5-0497 

2-9434 

25-6 

80.425 

5U.72 

655-36 

16777.216 

5.0596 

2-9472 

25-7 

i     •":• 

|i»-73 

660-49 

16974-593 

5.0605 

2.9510 

2--     - 

81.053 

522.-; 

665-64 

17173.512 

5-0793 

2-9549 

25.  9         81.367 

526.85 

670.81 

17373-979 

:•--.: 

2.9536 

A  MANUAL  OF  THE  STEAM-ENGINE. 

CONS  TA  NTS  —  Continued. 


" 

wir 

«jir 

4 

«* 

«> 

»? 

$3 

26.0 

81.681 

530.93 

676.00 

17576.000 

5.0990 

2.9624 

26.1 

81.996 

535-02 

681.21 

I7779-58I 

5.1088 

2.9662 

26.2 

82.310 

539-13 

686.44 

17984.728  i  5.1185 

2.9701 

26.3 

82.624 

543-25 

691.69 

18191.447    5.1283 

2-9738 

26.4 

82.938 

547-39 

696.96 

18399.744    5.1380 

2.9776 

26.5 

83.252 

551-55 

702.25 

18609.625  1  5.1478 

2.9814 

26.6 

83.566 

555-72 

707-56 

18821.096  !  5.1575  ,  2.9851 

26.7 

83.881 

559.90 

712.89 

19034.163    5.1672   2.9888 

26.8 

84.195 

564-10 

718.24 

19248.832    5.1768   2.9926 

26.9 

84.509 

568.32 

723-61 

19465.109    5-1865   2.9963 

27.0 

84-823 

572.56 

729.00 

19683.000    5.1962   3.0000 

27.1 

35.137 

576.80 

734-41 

19902.511    5-2057   3.0037 

27.2 

85-45r 

581.07 

739-84 

20123.648  :  5-2153  3-0074 

27-3 

85-765 

585.35 

745-29 

20346.417 

5.2249  !  3-OIII 

27.4 

86.080 

589.65 

750.76 

20570.824 

5.2345    3.0147 

27-5 

86.394 

593-96 

756.25 

20796.875    5.2440  3-0184 

27.6 

86.708 

598.29 

761.76 

21024.576   i   5.2555    3-0221 

27.7 

87.022 

602.63 

767.29 

21253.933      5-2630   3.0257 

27.8 

87-336 

606.99 

772.84 

21484.952      5-2/25    3.0293 

27.9 

87.650 

611.36 

778.41 

21717.639      5.2820 

3-0330 

28.0 

87.965 

6I5-75 

784.00 

21952.000 

5.29I5 

3.0366 

28.1 

88.279 

620.  16 

789.61 

22188.041 

5.3009 

3.0402 

28.2 

88.593 

624.58 

795-24 

22425  .  768 

5-3103 

3-0438 

28.3 

88.907 

629.02 

800.89 

22665.  187 

5-3197 

3-0474 

28.4 

89.221 

633.47 

806.56 

22906.304 

5-329I 

3-0510 

28.5 

89.535 

637-94 

812.25 

23149.125 

5.3385 

3-0546 

28.6 

89.850 

642.42 

817.96 

23393-656 

5-3478 

3-0581 

28.7 

go  164 

646.93 

823.69 

23639.903   1   5-3572 

3-0617 

28.8 

90.478 

651.44 

829.44 

23887-872 

5.3665 

3-0652 

28.9 

90.792 

655-97 

835-21 

24137.569 

5-3758 

3.0688 

29.0 

91.106" 

660.52 

841.00 

24389.000 

5.3852 

3.0723 

29.1 

91.420 

.665.08 

846.81 

24642.171 

5  •  3944 

3-0758 

29.2 

91-735 

669.66 

852.64 

24897.088 

5-4037 

3-0794 

29-3 

92.049 

674.26 

858.49 

25153.757 

5-4129 

3.0829 

29.4 

92.363 

678.87 

864.36 

25412.184 

5-4221 

3.0864 

29.5 

92.677 

683.49 

870.25 

25672.375 

5-4313 

3-0899 

29.6    92.991 

688.13 

876.16 

25934.336 

5-4405 

3-0934 

29.7    93.305 

692.79 

882.09 

26198.073 

5-4497 

3.0968 

29.8    93-619 

697.47 

888.04 

26463.592 

5.4589 

3-1003 

29.9 

93-934 

702.15 

894.01 

26730.899 

5.4680 

3.1038 

30.0 

94.248 

706.86 

900.00 

27000.000 

5-4772 

3.1072 

30.1    94-562 

711.58 

906.01 

2727O.9OI 

5.4863   3-1107 

30.2  1   94-876 

716.32 

912.04 

27543.608 

5.4954   3-1141 

APPEXDIX. 
CONSTANTS — Continued. 


'97 


m 

trm 

«»-        «* 

4 

"•      *; 

fc 

30.3 

95.190 

721.07       918.09 

27818.127   5-5045 

3-1176 

30-4 

95  505 

725.83       924.16 

28094.464   5-5136 

3.1210 

30-5 

95.819 

730.62       930.25 

28372.625   5.5220 

3.1244 

30.6 

96.133 

735-42       936.36 

28652.616 

5-5317 

3.1278 

30-7 

96-447 

740.23       942.49 

28934.443 

5-5407 

3-1312 

30.8 

96.761 

745.06       948.64 

29218.112 

5-5497 

3.1346 

30.9 

97-075     749-91     954-81 

29503.629 

5-:!=7 

3-13*0 

31  o 

97-3S9     754-77     961-00 

29701.000 

5-5678 

3.1414 

3i-i 

97.704  :   759.65     967.21 

30080.231 

5o767 

3-I448 

31.2 

98.018 

764.54     973-44 

30371.328 

5-5S57 

3.1481 

3i-3 

93.332 

769.45     979-69 

30664.297 

5-5946 

3-I5I5 

31-4 

98.646 

774-37     985-96 

30959.144 

5.6035 

3.1548 

31-5 
31.6 

98.960     779-31     992-25 
99.274     784-27     998.56 

31255.875 
31554.496 

5-6124 
5-6213 

3.1582 
3.1615 

3i-7 

99.588     789-24    1004-89 

31855.013 

5-6302 

3.1648 

31-  3 

99-903  ,   794-23    1011.24 

32157.432 

5-639I 

3-i65i 

31-9 

100.22      799  23 

1017.61 

32461.759 

5-6480 

3.I7I5 

32-0 

100.53     804.25 

1024.00 

32768.000 

5.6569 

3-1748 

32.1 

100.85 

809.28 

1030.41 

33076.161 

5-6656 

3.1781 

32.2 

101.16 

814.33 

1036.84 

33386.248  !  5.6745 

3.1814 

32-3 
32.4 

101.47 
101.79 

819.40 
824.48 

1043.29 
1049.76 

33698.267 
34012.224 

5.6833 
5.6921 

3.1847 
3.1880 

32-5 

IO2.IO 

829.58 

1056.25 

34328.125  . 

5-7008 

3-19*3 

32.6 

102.42 

834-69 

1062.76 

34645.976 

5.7096 

3-^945 

32-7 

102.73 

839.82 

1069.29 

34965-783 

5-7183 

3-1978 

32.8 

103.04 

844-96 

1075.84 

35287.552 

5.7271 

3.2010 

32.9 

103.36 

850.12 

1082.41 

35611.289 

5-7358 

3.2043 

33-0 

103.67 

855.30 

1089.00 

35937.000 

5.7446 

3-2075 

33-1 

103-99 

860.49 

1095.61 

36264.691 

5-7532 

3.2108 

33-2 

104.30 

865.70 

1102.24 

36594  368 

5.7619 

3.2140 

33-3 

IO4.62 

870.92    1108.89 

36926.037 

5-7706 

3-2172 

33-4 

104.93 

876.16    1115.56 

37259.704 

5-7792 

3.2204 

33-5 

105.24 

881.41    1122.25 

37595-375 

5-7879 

3.2237 

33-6 

105.56 

886.68 

1128.96 

37933-056 

5-7965 

3.2269 

33-7 

105.87 

891.97 

1135.69 

38272.753 

5-8051 

3-2301 

33  -8 

IO6.I9 

897-27 

1142.44 

38614.472 

5-8I37 

3-2-532 

33-9 

106.50 

902.59 

1149.21 

38958.219 

5.8223 

3-2364 

34-o 

106.81 

907.92 

1156.00 

39304.000 

5-8310 

3.2396 

34-1 

107.13 

913.27 

1162.81 

39651.821 

5-8395 

3.2428 

34-2 

107.44 

918.63 

1169.64 

40001.688 

5.8480 

3-2460 

34-3 
34-4 

107.76 
108.07 

924.01 
929.41 

1176.49 
1183.36 

40353.607 
40707.584 

5-8566 
5.8651 

3-2491 
3-2522 

798 


A   MANUAL   OF   THE   STEAM-ENGINE. 

CONSTANTS — Continued. 


n 

„ 

«»- 
4 

n" 

«» 

^n 

h 

34-5 

108.38 

934-82 

1190.25 

41063.625  ;  5.8736 

3.2554 

34-6 

108.70 

940.25 

1197.16 

41421.736   5.8821 

3.2586 

34-7 

109.01 

945.69 

1204.09 

41781.923   5.8906  !  3.2617 

34-8 

109.33 

95I-I5 

1  2  1  1  .  04 

42144.192   5-8991  3.2648 

34-9 

109.64 

956.62 

I2I8.OI 

42508.549   5-90/6  3-2679 

35-o 

109.96 

962.11 

1225.00 

42875.000 

5.9I6I 

3.2710 

35-i 

110.27 

967.62 

I232.OI 

43243.551 

5-9245 

3-2742 

35-2 

110.58 

973-14 

1239.04 

43614.208 

5.9329 

3-2773 

35-3 

110.90 

Q78.68 

1246.09 

43986.977 

5  9413 

3-2804 

35-4 

III.  21 

984.23 

1253.16 

44361.864 

5-9497 

3-2835 

35-5 

"I-  53 

989.80 

1260.25 

44738-875 

5-958r 

3.2866 

35-6 

111.84 

995.38 

1267.36 

45118.016 

5.9665 

3-2897 

35-7 

112.15 

lOOO.gS 

1274.49 

45499.293 

5-9749 

3-2927 

35-8 

112.47 

I006.6O 

1281.64 

45882.712 

5.9833 

3-2958 

35-9 

112.78 

1012.23 

I28S.8I 

46268.279 

5.9916 

3.2989 

36.0 

113.10 

1017.88 

I296.0O 

46656.000 

6.0000 

3.3019 

36.1 

113.41 

1023.54 

1303.21 

47045.881 

6.0083 

3-3050 

36.2 

"3-73 

IO29.22 

1310.44 

47437-928 

6.0166 

3-3080 

36-3 

114.04 

1034.91 

1317.69 

47832.147   6.0249 

3-3III 

36.4 

"4-35 

IO4O.62 

I324-96 

48228.544  |  6.0332 

3.3I4I 

39-5 

114.67 

1046.35 

1332.25 

48627.125   6.0415 

3.3I7I 

36.6 

114.98 

1052.09 

I339-56 

49027.896   6.0497 

3.3202 

36  7 

"5-30 

1057.84 

1346.89 

49430.863   !   6.0580 

3-3232 

36.8 

115.61 

1063.62 

1354.24 

49836.032     6.0663 

3-3262 

36.9 

115.92 

1069.41 

I36l.6l 

50243.409     6.0745 

3.3292 

37-o 

116.24 

1075-21 

1369.00      5O653.00O 

6.0827 

3-3322 

37-1 

"6-55 

108  i  .  03 

1376.41 

51064.811 

6.0909 

3-33=2 

37-2 

116.87 

1086.87 

I383.84 

51478.848     6.0991 

3.3382 

37-3 

117.18 

1092.72 

1391.29 

5I895.II7 

6.1073 

3-3412 

37-4 

117.50 

1098.58 

1398.76 

52313.624 

6.1155 

3-3442 

37-5 

117.81 

1104.47 

1406.25 

52734-375 

6.1237 

3-3472 

37-6 

118.12 

1110.36 

1413.76 

53I57-376 

6.1318 

3-3501 

37-7 

118.44 

1116.28 

1421.29 

53582.633 

6.1400 

3-3531 

37-8 

118.75 

1122.21 

1428.84 

54010.152 

6.1481 

3.3561 

37-9 

119.07 

1128.15 

1436.41 

54439-939 

6.1563 

3-3590 

38.0 

119-38 

II34-" 

1444.00 

54872.000 

6.1644 

3-3620 

38.1 

119.69 

1140.09 

I45I.6I 

55306.341 

6.1725 

3-3649 

38.2 

I2O.OI 

1146.08 

1459.24 

55742.968 

6.1806 

3-3b79 

38.3 

120.32 

1152.09 

1466.89 

56181.887 

6.1887 

3-3708 

38-4 

I2O.64 

1158.12 

1474.56 

56623.104 

6.1967 

3-3737 

38-5 

120.95 

1164.16 

1482.25 

57066.625 

6.2048 

3-3/67 

38.6 

121.27 

1170.21 

1489.96 

57512.456 

6.2129 

3.3796 

38.7 

121.  *S 

1176.28 

1497.69 

57960.603 

6.2209 

3-3825 

APPENDIX. 

CONSTANTS— Continued. 


799 


• 

- 

-; 

ft* 

- 

t^ 

h 

38.8 

121.89 

1182.37   1505.44   58411.072 

6.2289 

3-3854 

38.9 

122.21 

1188.47 

1513-21 

58863.809 

6.2370 

3-3883 

39-0 

122.52 

1194.59 

1521.00 

59319.000 

6.2450 

3.3912 

39-i 

122.84 

1200.72 

1528.81 

59776.471 

6.2530 

3-3941 

39-2 

123.15 

1206.87 

1536.64   60236.288 

6.2610 

3-3970 

39-3 

123.46 

1213.04 

1544.49   60698.457 

6.2689 

3-3999 

39-4 

123.78    !    1219.22 

1552.36   61162.984 

6.2769 

3-4028 

39-5 

124.09       1225.42 

1560.25    61629.875 

6.2849 

3.4056 

39-6 

124.41       1231.63       I568.I6       62O99.I36 

6.2928 

3.4085 

39-7 

124.72       1237.86       1576.09       62570.773 

6.3008 

3-4"4 

39-8 

125.04       1244-10       1584.04       63044.792 

6.3087 

3-4I42 

39-9 

125.35       1250.36       1592.01       63521.199 

6.3166 

3.4I7I 

40.0 

125.66       1256.04 

1600.00   64000.000 

6-3245 

3-4200 

40.1 

125.98    1262.93    1608.  01    64481.201  1  6.3325 

3-4228 

40.2 

126.29    1269.23    1616.04    64964.808    6.3404 

3-4256 

40-3 

126.61 

1275.56    1624.09    65450.827 

6.3482 

3-4285 

40.4 

126.92 

1281.90 

1632.16   65939.264 

6.3561 

3.43I3 

40.5 

127.23 

1288.25 

1640.25    66430.125 

6.3639 

3-4341 

40.6 

127.55   1294.62   1648.36   66923.416 

6.3718 

3-4370 

40.7 

127.86    1301.00    1656.49  i  67419.143 

6.3796 

3-4398 

40.  S 

128.18   1307.41   1664.64   67911.312 

6.3875 

3-4426 

40.9 

128.49   1313-82 

1672.81 

68417.929 

6-3953 

3-4454 

41-0 

128.81    1320.25 

1681.00    68921.000 

6.4031 

3.4482 

41.1 

129.12   1326.70   1689.21   69426.531 

6.4109 

3-45io 

41-2 

.129.43   1333.17   1697.44   69934.528 

6.4187 

3-4538 

41-3 

129.75 

1339.65   1705.69   70444.997 

6.4265 

3.4566 

41-4 

130.06 

1346.14   1713-96 

70957.944 

6-4343 

3-4594 

41-5 

130.38 

1352.65 

1722.25 

7I473.375 

6.4421 

3-4622 

41.6 

130.69   1359-18 

1730.56    71991.296 

6.4498 

3-4650 

41-7 

131.00  1  1365.72 

1738.89    72511.713    6.4575 

3-4677 

41.8 

131.32 

1372.28 

1747-24 

73034.632    6.4653 

3-4705 

41.9 

131.63 

1378.85 

1755-61 

73560.059    6.4730 

3-4733 

42.0 

131-95 

1385.44 

1764.00 

74088.000    6.4807 

3.4760 

42.1 

132.26   1392.05 

1772.41 

74618.461 

6.4884 

3-4788 

42.2 

132.58   1398.67 

1780  84 

75151.448    6.4961 

3-4815 

42.3 

132.89 

1405.31 

1789.29 

75686.967 

6.5038 

3-4843 

42.4 

133.20 

1411.96 

1797.76 

76225.024 

6.5115 

3.4870 

42.5 

133-52 

1418.63 

1806.25 

76765.625 

6.5192 

3-4898 

Ja.6 

133-83 

1425.31 

1814-76 

77308.776 

6.5268 

3-4925 

42.7 
42.8 

134.15 
134.46 

1432.01 
1438.72 

1823.29 
1831.84 

77854.483 
78102.752 

6-5345 
6.5422 

3-4952 
3-4080 

42.9 

134-77 

1445-45 

1840.41 

78953.589 

6.5498 

3-5007 

800 


A  MANUAL   OF   THE  STEAM-ENGINE. 

CONSTANTS — Continued. 


43-o 

«JT 

-i 

•„ 

«V 

«   h 

I35-09 

1452.20 

1849.00 

79507.000 

6-5574 

3  •  5034 

43-1 

135-40 

1458.96 

1857.61 

80062.991 

6.5651 

3-5o6i 

43-2 

135-72 

1465.74 

1866.24 

80621.568 

6-5727 

3-5088 

43-3 

136.03 

1472.54 

1874.89 

81  182.737 

6.5803 

3.5II5 

43-4 

136.35 

1479-34 

1883.56 

81746.504 

6-5879 

3-5I42 

43-5 

136.66 

1486.17 

1892.25 

82312.875 

6-5954 

3-5169 

43-6 

136.97 

1493-01 

1900.96 

82881.856 

6  .  6030 

3-5196 

43-7 

137.29 

1499.87 

1909.69 

83453-453 

6.6ic6 

3-5223 

43-8 

137.60 

1506.74 

1918.44 

84027.672 

6.6182 

3-5250 

43-9 

137.92 

1513-63 

1927.21 

84604.519 

6.6257 

3-5277 

44-0 

138.23 

1520.53 

1936.00 

85184.000 

6.6333 

3-5303 

44-i 

138.54 

I527-45 

1944.81 

85766.121 

6.6408 

3-5330 

44-2 

138.86 

1534-39 

1953  64 

86350.888 

6.6483 

3-5357 

44-3 

139-17 

I54L34 

1962.49 

86938.307 

6.6558 

3-5384 

44-4 

139-49 

1548-30 

1971.36 

87528.384 

6.6633 

3  •  54-^c. 

44-5 

I39-80 

I555-28 

1980.25 

88121.125 

6.6708 

3-5437 

44-6 

I4O.  12 

1562.28 

1989.16 

88716.536 

6.6783 

3-5463 

44-7 

140.43 

1569-30 

1998.09 

89314.623 

6.6858 

3.5490 

44.8 

140.74 

1576.33 

2007.04 

899I5-392 

6.6933 

3-55i6 

44-9 

I4I.O6 

I583-37 

2016.01 

90518.849 

6.7007 

3-5543 

45-0 

I4L37 

I590-43 

2025.00 

91125.000 

6.7082 

3-5569 

45-1 

141.69 

I597-5I 

2034.01 

9I733-85I 

6.7156 

3-5595 

45-2 

142.00 

1604.60 

2043.04    92345.408 

6.7231 

3-5621 

45-3 

142.31 

1611.71 

2052.09  i  92959.677 

6./305 

3-5648 

45-4 

142.63 

1618.83 

2061.16  '  93576.664 

6-7379 

3-5674 

45-5 

142.94 

1625.97 

2070.25 

94196.375 

6-7454 

3-5700 

45-6 

143.26 

1633.13 

2079.36 

94818.816 

6.7528 

3-5726 

45-7 

143-57 

1640.30 

2088.49 

95443-993 

6.7602 

3-5752 

45-8 

143.88 

1647.48 

2097.64 

96071.912 

6.7676 

3-5778 

45-9 

144.20 

1654.68 

2106.81 

96702.579 

6-7749 

3-5805 

46.0 

I44.5I 

1661.90 

2116.00 

97336.000 

6.7823 

3-5830 

46.1 

144.83 

1669.14 

2125.21 

97972.181 

6.7897 

3-5856 

46.2 

145-14 

1676.39 

2134-44 

98611.128 

6.7971 

3-5882 

46-3 

145.46 

1683.65 

2143.69 

99252.847 

6.8044 

3  •  5908 

46.4 

145-77 

1690.93 

2152.96 

99897.344 

6.8117 

3  •  5934 

46.5 

146.08 

1698.23 

2162.25 

100544.625 

6.  8191 

3-5960 

46.6 

146.40 

1  7°5  -54 

2171.56 

101194.696 

6.8264 

46-7 

146.71 

1712.87 

2180.89 

101847.563 

6-8337 

3.6011 

46.8 

M7.03 

1720.21 

2190.24 

102503.232 

6.8410 

3-6037 

46.9 

147-34 

I727-57 

2199.61 

103161.709 

6.8484 

3-6063 

47-o 

I47.65 

1734-94 

2209.00 

103823.000 

6.8556 

3.6088 

47-1 

147-97 

1742.34 

2218.41 

104487.111  ,  6.8629 

3-6114 

47-2 

148.28 

1749.74 

2227.84 

105154.048    6.8702 

3.6i39 

APPENDIX. 

fn — ri~T-     Cimfimmtf 


801 


. 

4 

IT. 

h 

47  3 

148.60 

1757.16             2237.29              105823.817 

",        -   "  "  - 

3-6165 

47-4  i 

:  _  :  .  :  : 

1764.60             2246.76              106496.424 

--    "-:       36190 

47-5 

149-23 

1772.05              2256.25              I07I7I.875 

6.8920      3.6216 

47-6 

149-54 

1779.52              2265.76              107850.176 

6-8993      3  .6241 

47-7  j 

:-      -: 

1787.01              2275.29             108531.333 

6.9065 

: 

47-8  ; 

150.17 

1794    51 

2284.84       109215.352 

6.9137 

:  -:- 

47-9 

1802.03              2294.41              109902.239 

6.9209     3.6317 

48-0' 

I:      - 

1809.56             2304.00              110592.000 

6.9282      3.6342 

i     : 

151.11 

lSl7.II          !        23I3.6I                  111284.641 

6-9354     3-6368 

48.2 

151.42 
151-74 

1824.67         '        2323.24                 111980.168 

:-:;  ::          2332.89          112678   587 

6.9426     3.6393 
6.9498     3.6418 

48.4 

152.05 

1839.84    j     2342.56         113379.904 

6-9570  •  3-6443 

48.5 

152.37 

1847-45         2352-25          114064-125 

6.9642 

.-  --'- 

48.6 

:=:  :r 

1855.08         2361.96 

114791.256 

6-97M     3-6493 

--.- 

153.00 

1802.72         2371.69 

115501.303 

6-97S5     3-6518 

153-31 

1870.38         2381.44 

116214.272 

3.6*43 

153.62 

1878.05         2391.21          116930.169 

6.9928 

3.6568 

49-0 

153-94 

18*5.74          2401.00          117649.000 

.7.0000 

3-6593 

49  I 
49-2 
49-3 

154-25 
154-57 

:-_   -- 

1803.45          2410.81 
1901.17          2420.64 
1908.90          2430-49 

118370.771 

119095-488 
119823-157 

7-0071 
7-0143 
7.0214 

m 

49-4 

155.19 

1916.65          2440.36          120553.784 

7-0285  |  3-669* 

49-5 
49-6 

:::     -.: 

•:•    '- 

1924.42          2450-25 
1932.21          2460.16 

:;::--    --: 
122023.936 

7-0356 

3-6717 
3-6742 

49-7 

156.14 

1940.00 

:_-.    :•. 

122763.473 

7.0498 

3-6767 

156.45 

1947-82 

2480.04 

123505.992 

7.0569 

,  .... 

49-9 

156.77 

1955.65     i     2490.01 

124251.409 

7.0640 

3.6816 

50.0 
51.0 

157.08 
160.22 

1963.50 
:  _:    -: 

2500.00 
2601.00 

125000.000 
132651.000 

7.0711 
7-I4I4 

:  •'.-''- 

52.0 

163-36 

2123.72 

2704-00 

140605.000 

7-2IH      3.7325 

53-0 

166.50 

2206.19 

2809.00 

148877.000 

7.2801 

54-0 

169.64 

2290.22 

2916.00          157464.000 

.;    gj 

55-0 

172.78 

-  -.  -  :     -  •: 

3025.00         166375.000 

f.iloi 

56.0 
57-0 

175-93 
179.07 

M63.01 

3136-00 
3249-00 

175616.000 
185193-000 

7-4*33     3-8259 
7.5498     3-8485 

:T    : 

182.21 

:;  _:.:•- 

5364    x 

195112.000       7-6158     3-8709 

59-O 

185.35 

2733-97 

IfBl     • 

205379.000 

7.6811     3-8930 

60.0 

188.49 

:-:-  ^ 

3600.00 

216000.000 

7.7460     3.9149 

61.0 

191.63 

2022-47 

3721-00 

226981.000  :  7.8102    3-9365 

62.0 

194-77 

3019.07 

.-•--•    : 

238328.000  1    7-8740     3-9579 

63.0 
64.0 

197.92 
201.06 

3117.25 
3216.99 

3969.00 
4096.00 

250047-000  i     7-9373     3-9791 
262144-000  ;     8.0000     4.0000 

65.0 
66.0 

204.20 

33I8.3I 

3421.20 

4225.00 
4356-00 

274625.000 
287496  ooo 

8.0623     4.0207 
8.1240     40412 

802 


A  MANUAL  OF  THE  STEAM-ENGINE. 
CONSTANTS — Continued. 


n 

nit 

"'I 

„• 

3 

v* 

*'« 

67.0 

210.48 

3525-66 

4489.00 

300763.000 

8.1854 

4.0615 

68.0 

213-63 

363I-69 

4624.OO 

314432.000 

8.2462 

4.0817 

69.0 

216.77 

3739-29 

476I.OO 

328509.000 

8.3066 

4.1016 

70.0 

219.91 

3848-46 

4QOO.OO 

343000.000 

8.3666 

4.1213 

71.0 

223.05 

3959.20 

5041.00 

357911.000 

8.4261 

4.1408 

72.0 

226.19 

4071.51 

5184.00 

373248.000 

8.4853 

4.1602 

73-0 

229.33 

4185.39 

5329.00 

389017.000 

8.5440 

4-J793 

74-o 

232.47 

4300.85 

5476.00 

405224.000 

8.6023 

4.1983 

75-o 

235-62 

4417.87 

5625.00 

421875.000 

8.6603 

4.2172 

76.0 

238.76 

4536-47 

5776.00 

438976.000 

8.7178 

4.2358 

77.0 

241.90 

4656.63 

5929  oo 

456533.000 

8.7750 

4-2543 

78.0 

245.04 

4778.37 

6084  .  oo 

474552.000 

8.8318 

4.2727 

79.0 

248.18 

4901.68 

6241.00 

493039.000 

8.8882 

4.2908 

80.0 

25L32 

5026.56 

6400.00 

512000.000 

8.9443 

4-3089 

81.0 

254-47 

5153.01 

6561.00 

531441.000 

9.0000 

4.3267 

82.0 

257.61 

5281.03 

6724.00 

551368.000 

9-0554 

4-3445 

83.0 

260.75 

54IO.62 

6889.00 

571787.000 

9.1104 

4-3621 

84.0 

263.89 

554L78 

7056.00 

592704.000 

9.1652 

4-3795 

85.0 

267.03 

5674.50 

7225.00 

614125.000 

9.2195 

4-3968 

86.0 

270.17 

5808.81 

7396.00 

636056  .  ooo 

9.2736 

4.4140 

87.0 

273-32 

5944-69 

7569.00 

658503.000 

9.3274 

4.4310 

88.0 

276.46. 

6082.13 

7744.00 

681472.000 

9.3808 

4.4480 

89.0 

279.60 

6221.13 

7921.00 

704969.000 

9.4340 

4.4647 

90.0 

282.74 

.  6361.74 

8100.00 

729000.000 

9.4868 

4.4814 

91.0 

285.88 

6503-89 

8281.00 

753571.000 

9-5394 

4-4979 

92.0 

289.02 

6647.62 

8464.00 

778688.000 

9-59I7 

4-5144 

93-0 

292.17 

6792.92 

8649.00 

804357.000 

9-6437 

4-5307 

94.0 

295-3I 

6939.78 

8836.00 

830584.000 

9.6954 

4-5468 

95-0 

298.45 

7088.23 

9025.00 

857375-000 

9.7468 

4.5629 

96.0 

301-59 

7238.24 

9216.00 

884736.000 

9.7980 

4-5789 

97.0 

304-73 

7389.83 

9409.00 

912673.000 

9.8489 

4-5947 

98.0 

307.87 

7542.98 

9604  .  oo 

941192.000 

9-8905 

4.6104 

99.0 

311.02 

-697.68 

9801.00 

970299.000 

9.9499 

4.6261 

IOO.O 

3I4-I6 

7854-00 

lOOOO.OO 

lOOOOOO.OOO 

IO.OOOO 

4.6416 

APPENDIX. 


803 


II. 

LOGARITHMS. 
HYPERBOLIC  LOGARITHMS. 


Log. 


Log. 


N. 


Log. 


N. 


Log. 


Log. 


*a 

•: 
:r 
- 

-r 
'-  - 

:g 

.65 1 
•70 

:E| 
.85 


.05 


•3365 
.3716 
•4055 
•4383 
.4700 
.5008 
.5306 


•35 
40 

•45 


3.60 
3-65 
3-70 
3-75 
3.80 
3-85 
3-90 
3-95 

10 


5 

•30 
•35 
40 

-: 


" 

io 
•85 


5892 


6.40 


6.70 
6.80 
6.90 
7-00 

7-20 

7-40 
7.60 

8'ot 

I'25 
8.50 

8-75 
9.00 
9.25 
9-50 
9-75 
10.00 
it. oo 

13.00 

13.00 

I4.OO 


.8871 
.902. 
.9169 
-93'5 
-9459 
•974* 
.0015 
.0281 
.0541 
•0794 

.1102 

:£ 

:Z5 
.2513 

33 


.77*6 


COMMON  LOGARITHMS:  10-1200. 


S 


804 


A  MANUAL   OF  THE  STEAM-ENGINE. 
COMMON  LOGARITHMS — Continued. 


8     9 

Oiff 

N. 

0 

1 

2 

30 

47712 

47857 

4800, 

48144 

48287 

48430 

48572 

48714 

48855  48996 

40 

31 

49136 

49276 

49415 

49554 

49693 

49831 

49969 

50,06 

50243  50379 

36 

32 

50515 

50651 

50786 

50920 

51055 

5"88 

5,322 

51455 

5,587   51720 

32 

33 

51851 

51983 

52244 

52375 

52504 

52634 

52763 

52892  53020 

8 

34 

53275 

53403 

53529 

53656 

53782 

53908 

54033 

54158  54283 

4 

35 

54407 
55630 

54531 
55751 

54654 
55871 

54777 
5599' 

54900 
56,10 

55023 
56229 

55*45 
56348 

55267 
56467 

55388  55509 
56585  56703 

7 

1 

57978 

56937 
58092 

57054 
58206 

57I7I 
58320 

57287 
58433 

57403 

S75I9 
58659 

57634 
58771 

57749   57864 
58883   58995 

4 

i 

39 

59106 

592,8 

59329 

59439 

59550 

59660 

59770 

59879 

59988   60097 

09 

40 

60206 

60314 

60423 

6053, 

60638 

60746 

60853 

60959 

61066   6,172 

06 

41 

61278 

61384 

6,490 

6,595 

61700 

61805 

61909 

62014 

62118   6222, 

04 

42 

62325 

62428 

6253, 

62634 

62737 

62839 

62941 

63043 

63,44   63246 

43 
44 

63347 
64345 

63448 
64444 

63548 
64542 

63649 
64640 

63749 
64738 

63849 
64836 

63949 
64933 

64048 
65031 

64147   64246 
65128  1  65225 

99 

97 

45 

65321 

65418 

655M 

656,0 

65706 

65801 

65896 

65992 

66087  i  66,8, 

95 

46 

66276 

66370 

66464 

66558 

66652 

66745 

66839 

66932 

67025  67117 

93 

47 

672,0 

67302 

67394 

67486 

67578 

67669 

67761 

67852 

67943  68034 

90 

48 
49 

68*24 

69O2O 

682,5 
69,08 

68305 
69,97 

68395 
69285 

68485 
69373 

68574 
69461 

68664 
69548 

68753 
69636 

68842   68931 

69723  ;  69810 

89 
87 

5° 

69897 

69984 

70070 

70157 

70243 

70329 

70415 

70501 

70586   70672 

86 

5' 
52 

70757 
71600 

70842 
7,684 

70927 
7,767 

71012 
71850 

7,096 
7'933 

71181 

72016 

7,265 
72099 

71349 
72181 

7M33  1  7I5I7 
72263   72346 

84 
83 

53 

72428 

72509 

72591 

72673 

72754 

72835 

72916 

72997 

73078   73159 

81 

54 

73239 

73320 

73400 

73480 

7356o 

7364° 

73719 

73799 

73878   73957 

80 

55 

74036 

74"5 

74194 

74273 

74351 

74429 

74507 

74586 

74663   74741 

78 

56 
57 

74819 
75587 

74896 
75664 

74974 
75740 

75051 
758,5 

75,28 
75891 

75205 

75282 
76042 

76^8 

75435   755" 
76193   76268 

76 

58 

76343 

764,8 

76492 

76567 

76641 

767,6 

76790 

76864 

76938   770,2 

74 

59 

77085 

77159 

77232 

77305 

77379 

77452 

77525 

77597 

77670   77743 

73 

60 

77815 

77887 

77960 

78032 

78,04 

78,76 

78247 

78319 

78390   78462 

72 

61 

78533 

78604 

78675 

78746 

788,7 

78888 

79029 

79099   79169 

7» 

62 

79239 

79309 

79379 

79449 

79518 

79588 

79657 

79727 

79796   79865 

69 

63 

79934 

80003 

80072 

80140 

80209 

80277 

80346 

804,4 

80482   80550 

68 

64 

80618 

80686 

80754 

80821 

80889 

80956 

81023 

8,090 

81158   81224 

67 

65 

8,291 

8,358 

8,425 

81491 

81558 

8,624 

81690 

8,757 

8,823   8,889 

66 

66 

81954 

82020 

82086 

82,5, 

822,7 

82282 

82347 

824,3 

82478   82543 

65 

67 

82607 

82672 

82737 

82802 

82930 

83059 

83-23   83,87 

64 

68 

83251 

833,5 

83378 

83442 

83506 

83569 

83632 

83696 

83759   83822 

63 

69 

83885 

83948 

840,1 

84073 

84.36 

84,98 

8426, 

84323 

84386   84448 

63 

7° 

845,0 
85126 

86 

84634 
85248 

84696 
85309 

84757 
85370 

848,9 
85431 

84880 

84942 

85552 

85003   85065 
856,2   85673 

62 
61 

72 

85733 

85794 

85854 

859,4 

85974 

86034 

86094 

86,53 

862,3   86273 

60 

73 

86332 

86392 

8645, 

865,0 

86570 

86629 

86688 

86747 

86806   86864 

59 

74 

86923 

86982 

87040 

87099 

87157 

872,6 

87274 

87332 

87390   87448 

58 

75 

87506 

87564 

87622 

87679 

87737 

87795 

87852 

879,0 

87967   88024 

58 

70 

88,38 

88,95 

88252 

88309 

88366 

88423 

88480 

88536   88593 

57 

77 

88649 

88705 

88762 

88818 

88874 

88930 

88986 

89042 

89098   89154 

56 

78 

89209 

89265 

89321 

89376 

89432 

89487 

89542 

89597 

89653   89708 

55 

79 

89763 

89818 

89873 

89927 

89982 

90037 

90091 

90146 

90200   90255 

55 

80 

90309 

90363 

904,7 

96472 

90526 

90580 

90634 

90687- 

90741   90795 

54 

8, 

90849 

90902 

90956 

9,009 

9,062 

91,16 

91,69 

91222 

91275   91328 

53 

82 

91381 

91434 

9,487 

91540 

91593 

91645 

9,698 

91803   91855 

52 

83 

9,908 

9,960 

920,2 

92065 

921,7 

92,69 

92221 

92273 

92324   92376 

52 

84 

92428 

92480 

9253' 

92583 

92634 

92686 

92737 

92788 

92840   92891 

85 

92942 

92993 

93044 

93095 

93*46 

93IQ7 

93247 

93298 

93349   93399 

51 

Be 

93450 

93500 

9355  i 

9360, 

93651 

93702 

93752 

93802 

93852   93902 

50 

87 

93952 

94002 

94052 

94101 

94I51 

94201 

94250 

94300 

94349   94399 

50 

APPENDIX. 

COMMON  LOGARITHMS — Centimud. 


80S 


;;.' 
;;; 


s 

;;; 


| 

..:-- 


01384        01326 
0*703       OI745 


o 

033432  05383 

03743  osTifa 

04139  !  04179 

04532  .  0457. 

0493*  04961 

05308  05346 


95569 


97405  t  97451 


99051 


::-:- 


3 
06145 


zs 

sg  sS 

03060  03100 

58  32 

oSS  o^ 

°9°3fc  **3^7/ 

^  ss 
.a-ss 

°693g  ^6^67 

OTaoB  07335 

07664  07700 


97543 


:.:^ 
04717 
05115 

I;:;1; 


95*3* 

1 


33 


•n: 


DM. 


35 


:-::: 

::;;;    3 


of  Xapemn  Ioe»riUi«s. 


11  = 


.    -    •:•:• 

0-434*945    9-6377*43 -*»• 


806 


A   MANUAL   OF   THE   STEAM-ENGINE. 


III. 

MEAN   PRESSURES   FOR  VARIOUS   METHODS  OF   EXPANSION. 
Values  of  —  .     Adiabatic  Expansion  of  Steam. 


Ratio  of 
Expansion. 

Hi  k 

$ 

u 

PERCENTAGE  OF  STEAM  AND  VALUB  OF  n. 

100 

I-I35 

90 
1.125 

80 
1.115 

76 

I.  Ill 

70 
1.105 

60 
1.095 

5° 
1.085 

100 

1-333 

2 

i 

.829 

.831 

•833 

.834 

•  835 

.836 

•837 

.810 

2* 

1 

.785 

.787 

.788 

.789 

.790 

.791 

•793 

•  754 

2* 

t 

•  744 

.746 

•  747 

.748 

•749 

•750 

•  751 

.714 

at 

T4T 

.707 

.708 

.710 

.711 

.712 

•713 

.714 

•  675 

3 

i 

•675 

.676 

•677 

.678 

.679 

.681 

.683 

•  639 

3i 

A 

.644 

.645 

.647 

.648 

.649 

.650 

.652 

.606 

9i 

A 

•  633 

.635 

•  636 

.637 

•639 

.641 

•643 

.600 

31 

1 

.616 

.618 

.619 

.620 

.622 

.624 

.626 

•  576 

3* 

TV 

•591 

•  592 

•  593 

•594 

•59b 

.596 

•598 

•552 

4 

i 

.567 

.568 

•570 

•572 

•573 

•574 

•576 

•523 

4 

1 

.525 

•527 

•  528 

•  530 

•531 

•533 

•534 

.486 

5 

i 

.488 

.491 

•493 

•494 

.496 

.498 

.500 

•447 

51 

A 

•458 

.460 

.462 

•463 

•  465 

.467 

.470 

.417 

6 

i 

•432 

•434 

•435 

•437 

•439 

.441 

•  443 

•390 

6| 

A 

.409 

.410 

.411 

•  413 

.415 

.417 

.420 

•369 

7 

1 

.387 

•39° 

•  392 

•  394 

.400 

•403 

•405 

•345 

8 

i 

•  355 

•356 

•  357 

•  358 

•  360 

•  361 

•  363 

.312 

10 

iV 

.298 

•  300 

.302 

•  303 

•  304 

•305 

.308 

.263 

20 

A 

.170 

•173 

•175 

•  177 

.178 

.180 

.182 

.144 

50 

A 

.080 

.082 

.083 

.084 

.084 

.085 

.086 

.063 

100 

riff 

.044 

•045 

•  045 

.046 

.046 

•047 

048 

•034 

APPENDIX. 


.807 


III.— (Continual.) 
MEAN   PRESSURES   FOR  VARIOUS   METHODS  OF  EXPANSION. 


Values  of  &L  for  Steam,  Air.  Gas,  and  Mixtures. 


Rutio  of 

l'.»|uir  i.  '. 

Point  of  cut-off, 
r 

Slruin  I'.M'.»>'I>»K, 

Dry  nnd  Siiluruted, 

M,  l.04<. 

Mol«  Air  In  Com- 
preiHorn,  N,  i.sio. 

Steam  and  Leak- 
age, Aetna!  En- 
gines. 

GM  and  Vapor  In 
Own  engine,  *,  1.60. 

Gases. 

Isother- 
mal,-, 

1  .00. 

Adiabat- 
*.«, 

l-4». 

«,<xso. 

•,0.75. 

2 

i 

.841 

-825 

.914 

-875 

.783 

.846 

.801 

2* 

f 

-793 

-787 

.888 

.844 

-733 

.804 

-753 

2* 

1 

.760 

-745 

.866 

.800 

.683 

.765 

.707 

2i 

A 

•717 

.700 

.846 

-785 

.638 

.731 

.668 

3 

i 

.695 

.665 

.824 

•752 

.598 

.699 

.638 

3* 

A 

.665 

.635 

.802 

-732 

-578 

.670 

.596 

3i 

i 

.652 

.625 

•796 

.716 

.50 

.661 

.$88 

3i 

1 

.632 

.605 

.782 

-704 

.Stf 

.642 

.serf 

3t 

A 

.608 

.580 

•775 

.684 

•5i5 

.616 

.:- 

4 

i 

.587 

.550 

-750 

w 

.486 

.566 

.518 

4i 

i 

.540 

.510 

.720 

.624 

.441 

-555 

•473 

5 

i 

.510 

.482 

-695 

.600 

.406 

.522 

.428 

5+ 

ft 

4* 

•455 

.674 

.560 

-371 

-492 

.406 

6 

i 

•454 

.420 

.650 

.530 

•349 

-465 

--  = 

4 

A 

-430 

.390 

.632 

.515 

.326 

441 

.358 

7 

+ 

.409 

-375 

.612 

.500 

•3«3 

.421 

-337 

8 

i 

-372 

.340 

.697 

.468 

.276 

.385 

.302 

10 

A 

.326 

.284 

•532 

.412 

•  225 

.330 

-253 

20 

A 

.192 

-165 

-396 

.272 

.103 

.200 

.138 

50 

A 

.091 

.074 

•245 

.193 

.050 

.098 

.060 

IOO 

tfc 

.053 

.040 

.180 

.134 

.025 

.056 

.032 

8o8 


A  MANUAL   OF  THE   STEAM-ENGINE. 


III.— (Continued.) 
MEAN   PRESSURE   RATIOS. 


r 

A 

B 

C 

r 

A 

B 

C 

r 

A 

B 

C 

r 

.1 

B 

C 

I.O 

I  000 

I  000 

1.  000 

5-3 

•  473 

•5°3 

.488 

9.6 

.312 

-340 

•  324 

17.8 

.194 

.218 

.204 

i.i 

oigge 

o:996 

0.996 

5-4 

•472 

•  497 

.482 

9-7 

.310 

.338 

.32* 

8.0 

.192 

.216 

.202 

1.2 

0.983 

0.983 

0.983 

5-5 

•  467 

.492 

•  477 

9.8 

•  3°7 

•335 

•  3'9 

8.2 

.190 

•215 

.200 

1.3 

.966 

.968 

.967 

5-6 

.46. 

.486 

•47' 

9-9 

•  3°5 

•333 

•  3'7 

8.4 

.189 

.214 

•'99 

1-4 

•  947 

•952 

•95° 

5-7 

•456 

.481 

.466 

10.  0 

•3°3 

•33° 

•3'4 

8.6 

.I87 

.212 

.197 

1-5 

.928 

•934 

.931 

5-8 

•45° 

•475 

.460 

IO.2 

•  299 

•325 

.310 

8.8 

.185 

.210 

.195 

1.6 

.910 

•9'9 

.914 

5-9 

•445 

.470 

•455 

10.4 

•295 

.321 

.306 

9.0 

•  '83 

.208 

•'93 

1-7 

•  890 

.900 

•895 

.440 

•  465 

•45° 

10.6 

.291 

•3'7 

.302 

9.2 

.182 

.207 

.192 

1.8 

.880 

•875 

6.1 

•434 

.460 

•445 

10.8 

.287 

•3'3 

.298 

9-4 

.180 

.205 

.190 

1.9 

'III 

.862 

.856 

6.2 

•429 

•455 

•44° 

ii  .0 

.283 

•3°9 

•294 

9.6 

.179 

.204 

.189 

3.0 

'I?, 

.846 

.840 

824 

6-3 

•  424 

•  45° 

•435 

II.  2 

•279 

.305 

.290 
.286 

19.8 

.178 

.202 

.187 
1  36 

2.2 

:98 

!8i° 

fcs 

.419 
.414 

•44' 

.426 

ii.  6 

.272 

.2gS 

^283 

20.2 

•I75 

198 

!i84 

2-3 

.780 

•795 

'•7&7 

6.6 

.409 

.436 

.421 

ii.  8 

.268 

.294 

•279 

20.4 

•'74 

:,96 

.'83 

2.4 

•763 

.780 

•771 

6-7 

•4°5 

.432 

•4'7 

12.0 

.264 

.290 

•275 

20.6 

•'73 

•'94 

.182 

2.5 

.748 

.766 

.756 

6.8 

.401 

.428 

•4'3 

12.2 

.26. 

.287 

.272 

20.8 

•'93 

.180 

3.6 

•732 

•75° 

.740 

6.9 

•  396 

•424 

.408 

12.4 

•257 

.268 

21.  0 

.  169 

.192 

.178 

3.7 

.718 

.736 

.726 

•393 

.421 

.405 

12.6 

•254 

^280 

•  265 

21  .2 

.168 

.191 

•'77 

2.8 

.705 

•723 

•7'3 

7-1 

.389 

•417 

.401 

12.8 

.277 

.262 

j  21.4 

.167 

.190 

.176 

3.9 

.692 
.680 

.710 
.699 

.700 
.688 

7*2 
7-3 

•385 
•  381 

•4': 
.410 

•397 
•393 

13-2 

•245 

.271 

.256 

21.8 

.164 

.187 

•'74 
•173 

3.1 

.668 

.687 

.676 

7-4 

•377 

.406 

•39° 

13-4 

.242 

.268 

•253 

•  163 

.186 

.172 

3-2 

.656 

•675 

.664 

7-5 

•373 

.402 

•  386 

13.6 

•239 

.265 

•  250 

j  22.2 

.162 

.185 

.171 

3-3 

•645 

.664 

•653 

7-6 

•  370 

•399 

•383 

3-8 

•  236 

.262 

•  247 

22.4 

.161 

.i84 

.170 

3-4 

.634 

•653 

.642 

7-7 

.367 

•396 

.3*0 

4.0 

•234 

.260 

•245 

22.6 

.160 

.183 

.169 

3-5 

.622 

.642 

.631 

7.8 

•392 

i-376 

4-2 

•  231 

.257 

.242 

22.8 

•'59 

182 

.168 

3-6 

.612 

•  632 

.621 

7-9 

36C 

•389 

•373 

4-4 

23.0 

.158 

.180 

.167 

.602 

•593 

.622 
.613 

.611 
.602 

S.i 

•356 
•353 

is 

4.6 
4-8 

.22; 

•  5' 

•234 

23-2 

23-4 

.156 

•155 

'.\77l 

.I65 

.164 

3-9 

.584 

.604 

•593 

8.2 

•350 

-379 

.364 

5-0 

.221 

•  47 

-232 

23-6 

•154 

.177 

.163 

4.0 

•572 

.596 

.583 

8-3 

•347 

.376 

.361 

13.2 

.219 

•  45 

.230 

23.8 

•J53 

.176 

.162 

•565 

•587 

•575 

8.4 

•344 

•373 

.358 

'5^ 

.21; 

•  42 

.227 

24.0 

•IS' 

•i74 

.160 

4-2 

.556 

•578 

.566 

8-5 

•34' 

•37' 

•355 

.215 

.  40 

.225 

24.2 

.150 

•'73 

•'59 

4-3 

•  548 

.570 

•558 

8.6 

•338 

•  368 

•352 

i  j 

.21; 

•  38 

.223 

24.4 

.149 

.172 

•  158 

4-4 

.540 
•53Z 

•563 

•  550 
•542 

8-7 
8.8 

•335 
•332 

:S 

•349 
•346 

\  '2 

20< 

•  36 

•  34 

.221 
.219 

24.6 
24.8 

.148 
.147 

•17' 
.170 

:\% 

4.6 

•  525 

•548 

•535 

8.9 

•33° 

•  358 

•34 

i  .. 

.20; 

•  32 

.217 

25.0 

.146 

.169 

•155 

4-7 

•  5'8 

•542 

•  528 

9.0 

•327 

•355 

•34° 

i  .1 

.20' 

•  3° 

•2'5 

4-8 

•5" 

•535 

.521 

9.1 

•324 

•353 

•337 

i  .1 

.20; 

.  28 

•213- 

4-9 

.504 

.528 

•5M 

9.2 

•  322 

•351 

•335 

17.0 

.201 

.  26 

.211 

S-o 

.496 

.522 

.506 

9-3 

.320 

•348 

•332 

17.2 

•199 

.224 

.209 

5-2 

'ft 

•5'5 
•  5°9 

.500 
•494 

9-4 
9-5 

•3'7 
•3'5 

•345 
•343 

.329 
•327 

17.. 
17.6 

.197 
•195 

.22: 

.207 
•205 

Column  r,  the  ratio  of  expansion  =  — 

"     A ,  ratio  of  mean  to  initial  pressure,  —  =  — 
P\ 


For  dry  steam,  expand- 
ed without  gain  or  loss 
of  heat,  in  a  non-con- 
ducting cylinder. 

A,       '  +  hyp.  log.   r  (  For     damp     steam, 

— -  =  — • — — - <    expanded      receiv- 

f\  (   ing  heat. 

For  dry  steam,  ex- 
panded receiving 
heat  sufficient  to  pre- 
vent liquefaction. 


RULE. — To  find  the  mean  pressure  exerted  throughout  the  stroke,  multiply  the  initial  pres- 
1       '  mber  opposite   the  ratio  of  e> 

jpansion.    (From  Northcott.) 


sure  by  the  number  opposite  the  ratio  of  expansion,  in  the  column  corresponding  with  the 
conditions  of  ext 


APPENDIX. 


809 


IV. 

TERMINAL  PRESSURE  RATIOS 


r 

A 

B 

C 

r 

A 

B 

c 

- 

A 

-1- 

r 

A 

S 

C 

I.O 

0.00 

.11 

°'° 

0.00 

5:2 

5-58 
5-70 

; 

5-29 

J-3 

i    4 

10.  s 
10.6 

8.3      9-47 
8-4      9-59 

13-8 

31 

13.8 
14.0 

1  6.  2 

16.5 

1.2 

.22 

I  .  2 

I.  21 

4-- 

5-84 

•:- 

5-4' 

B-a 

10.7 

8.5      9-64 

14.2 

19.1 

14.2 

,6.3 

*-3 

1-4 

•34 

•  45 

*-3 

1.32 

i-43 

5-0 

5-1 

5-98 

!:|; 

s.e 

10.9 

8.6 
8-7 

^88 

»4-4 
14.6 

19.4 
19-7 

M-4 

14.6 

17.0 
17.2 

1-5 

;.? 

6.24 

.9 

s!a 

1.2 

8.8    10.0 

14.8 

20.0 

14.8 

1.6 

•69 

i  65 

5-3 

6.38 

5-3 

5.88 

i  , 

8.9     10.2 

15-0 

20.3 

17  8 

1-7 
1.8 
1.9 

.92 

1.7 

i.S 

11 

5-4 

a; 

8 

6.00 

6.12 

«.,3 

Q.O 
9-1 

9.2 

i!s 

9.0 
>•» 

10.3 
10.4 
10.6 

15-2 

20.6 
20  9 
21.2 

15.2 

si 

(8.0 
18.2 
i8.S 

9.0 

.16 
.28 

2.0 

2.08 

5-7    6-9' 
5-8    7  °5 

M  !:g 

9-3 

0.4 

I.O 
2.0 

0.3 
0-4 

10.7 
10.8 

IS-8 
16.0 

21-5 
21.8 

3:1 

18.7 
19.0 

9.2 
3-3 

2.4 

•4° 

:ll 

2.2 

••3 

2.4 

2.31 
2.42 

2-53 

ONOM/i 

M  b  i 

7.18 
7.32 

7-45 

K 

6.1 

sl 

>-|j 

2-3 

2-5 

H 

10.9 

16.2 
16.4 
16.6 

22.1 
22-4 
22    7 

16.2 

16.4 

16.6 

19.3 

31 

2-5         -76 

2.64 

6.1 

7-59 

6.  2 

6.95 

G.8 

2.6 

j.  '* 

•3 

16.8 

23.0 

14.8 

20.0 

9.6 

1:1 

.89 

.01 

I'l 

2.1; 

11 

12 

£4 

7:3 

9.0 

2.8 

29 

..0 

•4 
-5 

17.0 
17.2 

23-3 
23-6 

17.0 
17.2 

20.3 

9.9 

•M 

.26 

2.C 

2-99 

8.14 

e:§ 

7.30 
7-42 

10.4 

3-5 

10.4 

177'.6 

23.9 
24.2 

'7-4 
17.6 

21  .0 

3.0 

•39 

3-" 
j.i 

3.21 
3-32 

:•• 

S3 

a 

7-54 

TO    ' 

3.8 

!o^S 

;3 

17.8 
18.0 

24-5 

24-8 

17-8 
18.0 

21.  0 

3-2 

•64 

3   ? 

3-43 

M 

8.55 

8.9 

7-78 

II.  0 

4-3 

II.C 

.8 

18.2 

25.* 

18.2 

21.8 

3-3 

•77 

3-3 

7.0 

8.69 

7.0 

7.90 

II.  2 

14.6 

II  .  2 

.0 

f!-i 

25.4 

'H 

22.0 

3-4 

.89 

3-4 

3.67 

7-  * 

8.83 

8.02 

II.  4 

4-9 

II  -4 

•  3 

18.6 

25.7 

18.6 

22.3 

3-5 

.02 

3-5 

3-79 

8.06 

7-2 

8.14 

Il.t 

5-2 

Il.t 

•  5 

18.8 

26.  • 

18.8 

22.  S 

3-6 

H 

3-9 

•  15 
.28 

•41 
•54 

1:1 

5-9 

3.90 
4.01 
4-13 
4-25 

7-3 
7-4 

5:1 

9.10 
9.24 
9-38 
9.52 

7-3 

7-4 
7*3 
y.e 

8.27 
8.38 
8.49 
8.62 

ii.  S 

12.0 
12.2 
12.4 

6.1 

II.  S 
12.0 
12.2 

•7 

•5 

19.0 
19.2 
19.4 
19.6 

26:9 

27.2 

19.0 
19.3 
19-4 

22.8 
23.1 

Si 

4.0 
4-1 

.66 

•79 

4.0 

4.1 

4-36 
4-47 

5:1  $:S 

a 

8.74 
8.87 

12.6 
12.? 

6.7 
7.0 

12.  f 
-.2.S 

.8 

.0 

19-8 

20.0 

27.5 
37-9 

10.8 

20.0 

23.9 
24.1 

4-3 

.91 

4.60 

7.9     Q.Q4 

8-99 

13.0 

7-3 

13.0 

5-2 

21.0 

29.5 

21.0 

25.4 

4-3 
4-4 

4-5 

3 
•32 

4-3 

4-4 
4-5 

W 
4-95 

S  .0 

S.  i 

S.2 

10.2 
10.3 

s'.i 

S.2 

9.11 
9-23 
9-35 

iB 

1:2 

13.9 

SJ 

5-5 
5-7 

22.0 
23-0 
24.0 

Hi! 

22.0 
23-0 

2S!o 

29.3 

4.6 

5-45 

4-C 

5-o6 

Column  r,  ratio  of  expansion  =  — 
v\ 

A,  ratio  of  initial  to  final  pressure,  /, 


rtf 


i  For  dry  steam,  expanded  with- 
out gain  or  loss  of  heat  in  a 
non-conducting  cylinder. 

For  damp  steam,  expanded 
receiving  heat. 

For  dry  steam,  expanded  re- 
ceiving sufficient  heat  to  pre- 
vent liquefaction. 

ROLB.— To  find  the  final  pressure  obtaining  with  any  ratio  of  expansion,  divide  the  initial 
pressure  by  the  number  opposite  the  ratio  of  expansion,  in  the  column  corresponding  with  the 

conditions  of  expansion. 


•5h»{ 


bio 


S 

£  S 


^  MANUAL   OF  THE   STEAM-ENGINE. 

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APPENDIX. 

BB8WR*a          &?  KISS'S 


811 


nil 


.  o.q..  .  o.o.o. 


«  «  move  q«o  - 
o  d-oJ  oo"  ti  ti\d  «" 


!  ..Ifel 


<c-ccccccc 


812 


A  MANUAL  OF  THE  STEAM-ENGINE. 


VI. 

COMPARISON  OF  THERMOMETERS. 


Celsius. 

Reaumur. 

Fahren- 
heit. 

Celsius. 

Reaumur. 

Fahren- 
heit. 

Celsius. 

Reaumur. 

Fahren- 
heit. 

—2O 

—  16 

—4 

25 

2O.  O 

77.0 

70 

56.0 

158.0 

—  19 

-15-2 

—2.2 

26 

20.8 

78.8 

71 

56.8 

159.8 

—  18 

-T4.4 

—0.4 

27 

21.6 

80.6 

72 

57-6 

161.6 

—  17 

-13.6 

1.4 

28 

22.4 

82.4 

73 

58.4 

163.4 

—  16 

-12.8 

3-2 

29 

23.2 

84.2 

74 

59-2 

165.2 

—  15 

—  12.0 

5-0 

30 

24.0 

86.0 

75 

60.0 

167.0 

—14 

—  II.  2 

6.8 

31 

24.8 

87.8 

76 

60.8 

168.8 

—13 

—  10.4 

8.6 

32 

25.6 

89.6 

77 

61.6 

170.6 

—  12 

-9.6 

10.4 

33 

26.4 

91.4 

78 

62.4 

172.4 

—  II 

-8.8 

12.2 

34 

27.2 

93-2 

79 

63-2 

174.2 

—  IO 

-8.0 

14.0 

35 

28.0 

95-o 

80 

64.0 

176.0 

—9 

-7-2 

15-8 

36 

28.8 

96.8 

81 

64.8 

177-8 

—8 

-6.4 

17-6 

37 

29.6 

98.6 

82 

65.6 

179.6 

—7 

-5-6 

19.4 

38 

30.4 

100.4 

83 

66.4 

181.4 

-6 

-4.8 

21.2 

39 

31.2 

IO2.2 

84 

67.2 

183.2 

-5 

-4.0 

23.0 

40 

32.0 

IO4.O 

85 

68.0 

185.0 

—4 

—3-2 

24.8 

4i 

32.8 

105.8 

86 

68.8 

186.8 

—3 

-2.4 

26.6 

42 

33-6 

107.6 

87 

69.6 

188.6 

—2 

—1.6 

28.4 

43 

34-4 

109.4 

88 

70.4 

190.4 

—  I 

-0.8 

30.2 

44 

35-2 

III.  2 

89 

71.2 

192.2 

0 

0 

32.0 

45 

36.0 

II3.0 

90 

72.0 

194.0 

I 

0.8 

33-8 

46 

36.8 

II4.8 

9i 

72.8 

195.8 

2 

1.6 

35-6 

47 

37-6 

II6.6 

92 

73-6 

197.6 

3 

2.4 

37-4 

48 

38.4 

II8.4 

93 

74-4 

199.4 

4 

3-2 

39-2 

49 

39-2 

I2O.2 

94 

75-2 

201.2 

5 

4.0 

41.0 

50 

40.0 

122.  0 

95 

76.0 

203.0 

6 

4.8 

42.8 

51 

40.8 

123.8 

96 

76.8 

204.8 

7 

5-6 

44.6 

52 

41.6 

125.6 

97 

77-6 

206.6 

8 

6.4 

46.4 

53 

42.4 

127.4 

98 

78.4 

208.4 

9 

7-2 

48.2 

54 

43-2 

129.2 

99 

79.2 

210.2 

10 

8.0 

50.0 

55 

44.0 

I3I.O 

IOO 

80.0 

212.  0 

ii 

8.8 

51.8 

56 

44-8 

132.8 

101 

80.8 

213.8 

12 

9.6 

53-6 

57 

45-6 

134.6 

102 

81.6 

215.6 

13 

10.4 

55-4 

58 

46.4 

136.4 

103 

82.4 

217.4 

14 

II.  2 

57.2 

59 

47.2 

138.2 

104 

83.2 

219.2 

15 

12.0 

59-o 

60 

48.0 

I4O.O 

105 

84.0 

221.  0 

16 

12.8 

60.8 

61 

48.8 

I4I.8 

106 

84.8 

222.8 

17 

13-6 

62.6 

62 

49.6 

143-6 

107 

85-6 

224.6 

IS 

14.4 

64.4 

63 

50.4 

145-4 

108 

86.4 

226.4 

19 

15.2 

66.2 

64 

51.2 

147-2 

109 

87.2 

228.2 

20 

16.0 

68.0 

65 

52.0 

149.0 

no 

88.0 

230.0 

21 

16.8 

69.8 

66 

52.8 

I5O.8 

III 

88.8 

231.8 

22 

17.6 

71.6 

67 

53-6 

152.6 

112 

89.6 

233-6 

23 

18.4 

73«4 

68 

54-4 

154-4 

"3 

90.4 

235.4 

24 

19.2 

75-2 

69 

55-2 

156.2 

114 

91.2 

237.2 

APPENDIX. 

COMPARISON  OF  THERMOMETERS — Continued. 


813 


Celsius. 

Reaumur. 

Fahren- 
heit. 

Celsius. 

Reaumur. 

Fahren-  1 
heit. 

Celsius. 

Reaumur. 

Fahren- 
heit. 

"5 

02.  0 

239.0 

127 

101.6 

260.6 

139 

III.  2 

282.2 

Il6 

92.8 

240.8 

128 

102.4 

262.4 

140 

112.  0 

284.0 

«7 

93.6 

242.6 

129 

103.2 

264.2 

141 

112.  8 

285.8 

iiS 

94-4 

244.4 

130 

104.0 

266.0 

142 

II3.6 

287.6 

119 

95.2 

246.2 

131 

104.8 

267.8 

143 

II4.4 

289.4 

1  20 

96.0 

248.0 

132 

105.6 

269.6 

144 

II5.2 

291.2 

121 

96.8 

249.8 

133 

106.4 

271.4 

145 

II6.O 

293.0 

122 

97-6 

251.6 

134 

107.2 

273.2 

146 

II6.8 

294.8 

123 

98.4 

253-4 

*35 

108.0 

275.0 

147 

II7.6 

296.6 

I24 

99.2 

255-2 

136 

108.8 

276.8 

I48 

Il8.4 

298.4 

125 

100.  0 

257.0 

137 

109.6 

278.6 

149 

Ilg.2 

300.2 

126 

100.8 

258.8 

138 

110.4 

280.4 

150 

I2O.O 

302.0 

8i4 


A  MANUAL   OF   THE   STEAM-ENGINE. 


VII. 

DENSITIES  AND  VOLUMES  OF  WATER. 
KOPP;  CORRECTED  BY  PORTER. 


Temperature. 

Volume,  Kopp. 

Corrected  Vol- 
ume. 

Differences. 

F. 

c. 

39-2 

4 

I.OOOOO 

.00000 

41.0 

5 

.OOOOI 

.OOOOI 

51.8 

10 

.00025 

.00025 

24 

c8 

34 

59-0 

15 

.00082' 

.00083 

58 
88 

30 

68.0 

20 

.00169 

.00171 

27 

77.0 

25 

.00284 

.00286 

JI5 

24 

86.0 

30 

.00423 

.00425 

139 

TA* 

22 

95  o 

35 

.00583 

.00586 

IOI 

181 

2O 

104.0 

40 

.00768 

.00767 

19 

113.0 

45 

.00967 

.00967 

200 

19 

122.0 

50 

.01190 

.01186 

219 

18 

I3I.O 
I4O.O 

55 
60 

.01423 
.01672 

.01423 
.01678 

237 

255 

18 
18 

149.0 
150.0 

65 
70 

.01943 
.02238 

.01951 

.02241 

273 
290 

17 
17 

167.0 

75 

.02554 

.02548 

3°7 

17 

I76.O 

80 

.02871 

.02872 

324 

185.0 

85 

.  03202 

.03213 

34  J 

16 

194.0 

90 

•03553 

•03570 

357 

16 

203.0 

95 

.03921 

•03943 

38 

16 

212.  O 

100 

1.04312 

1.04332 

WEIGHTS  AND  VOLUMES. 


Ratio  of 

Ratio  of 

Ratio  of 

1 

volume  to 
that  of 
equal 
weight  at 
maximum 

Weight 
of  a 
cubic 
foot 

B 

1 

volume  to 
that  of 
equal 
weight  at 
max  mum 

Weight 
of  a 
cubic 
foot. 

| 

v  lume  to 
hat  of 
equal 
weight  at 
maximum 

Weight 
of  a 
cubic 
foot. 

£ 

density. 

density. 

H 

density. 

Fahr. 

Lbs. 

Fahr. 

Lbs. 

Fahr. 

Lbs. 

32-° 

.OOOZ29 

62.417 

10  ° 

.04226 

59-894 

39o.° 

•  5S38 

54-030 

39.1 

.000000 

62.425 

12 

.04312 

59-707 

400. 

.  6366 

53-635 

40. 

.000004 

62.423 

2O 

.04668 

59.64 

410.  • 

.  7218 

53-255 

50. 

.000253 

62.409 

3° 

-05142 

59-37 

420. 

.  8090 

52.862 

60 

.000929 

62.367 

40 

•05633 

59-09 

430. 

.  8982 

52-466! 

& 

.001981 

.00332 

62  .  302 
62.218 

£ 

.06144 
.06679 

58.81 
58.51 

440. 
45°- 

•  0833 

52.065 
51.662 

90 

.00492 

62.119 

70 

•07233 

58.21 

460. 

•   J79° 

51.256 

100 

.00686 

62.000 

80 

.07809 

57-9°3 

470. 

.  2767 

50.848 

no 

.00902 

61.867 

290. 

.08405 

57-585 

.   3766 

50-438 

120 

.01143 

61.720 

300. 

.09023 

57-259 

49°- 

5O.O2O 

3° 

.01411 

61.556 

.09661 

56.925 

500. 

.   5828 

49.611 

40 

.01690 

61.388 

320. 

.  0323 

56.584 

510. 

.   6892 

49-195 

g 

.01995 
.02324 

61.204 
61.007 

330. 
340. 

:£S 

56-236 
55-883 

520- 

530- 

•   7975 
.   9080 

48.778 
48.360 

70 

.02671 

60.801 

350. 

•  2431 

55.523 

540. 

.30204 

47-941 

80 

.03033 

60.587 

360. 

•  3175 

55-158 

55°- 

•3'354 

47-52* 

90 

.03411 

60.366 

370- 

•  3042 

54.787 

200 

.03807 

60.136 

38o. 

•  4729 

54.411 

APPENDIX. 

VIII. 

TEMPERATURES  AND  PRESSURES,  SATURATED  STEAM. 
IN  METRIC  MEASURES  AND  FROM   REGNAULT. 


815 


1 

STEAM-PR 

ESSURE. 

a 

3 

STEAM-PR 

BS30KK. 

1 

In  Centimetres?' 

n  Atmospheres 

£ 

In  Centimetres. 

In  Atmospheres 

-  32C  C 

0.0320 

0.0004 

+  I4C  C. 

.1908 

0.016 

3i 

0.0352 

0.0005 

»5 

.2699 

0.017 

30 

0.0386 

0.0005 

16 

•3536 

O.OI8 

29 

0.0424 

O.OOO6 

17 

.4421 

O.OT9 

28 

0.0464 

O.OOO6 

18 

•5357 

0.020 

27 

0.0508 

0.0007 

19 

•6346 

0.022 

26 

0.0555 

0.0007 

20 

•7391 

O.O23 

25 

0.0605 

0.0008 

21 

.8495 

0.024 

24 

O.o66o 

0.0009 

22 

•059 

0.026 

23 

0.0719 

O.OOOg 

23 

.0888 

0.028 

22 

0.0783 

O.OOIO 

24 

.2184 

0.029 

21 

0.0853 

O.OOII 

25 

-3550 

0.031 

20 

0.0927 

0.0012 

26 

.4988 

0.033 

19 

O.IOOS 

0.0013 

27 

•5505 

0.034 

1  8 

0.1095 

0.0014 

28 

2.8101 

0.037 

17 

0.1189 

0.0015 

29 

2.9782 

0.039 

16 

0.1290 

0.0017 

30 

3.I54S 

0.043 

15 

0.1400 

0.0018 

31 

3.3406 

0.044 

14 

0.1518 

O.OO2O 

32 

3-5359 

0.047 

13 

0.1646 

0.0022 

33 

3-74" 

0.049 

12 

o.  1783 

0.0024 

34 

3-9565 

0.052 

II 

0.1933 

O.OO25 

35 

4.1827 

0.055 

10 

0.2093 

0.0027 

36 

4.4201 

0.058 

0.2267 

0.0030 

37 

4.6691 

0.061 

0-2455 

O.OO32 

38 

4-9302 

0.065 

7 

0.2658 

0.0035 

39 

5.2039 

0.068 

6 

0.2876 

0.003! 

40 

5-49o6 

0.072 

5 

0.3113 

0.0041 

4i 

5-7910 

0.076 

4 

0.3368 

0.0044 

42 

6.1055 

0.080 

3 

o.  3644 

0.0048 

43 

6.4346 

0.085 

2 

0.3941 

0.0052 

44 

6.7790 

0.089 

I 

0.4263 

O.OO56 

45 

7.1391 

0.094 

O 

0.4600 

0.0061 

46 

7-5I58 

0.099 

+   I 

0.4940 

0.0065 

47 

7.9093 

0.104 

2 

0.5302 

0.0070 

48 

8.3204 

0.109 

3 

0.5687 

o.ooTJ 

49 

8.7499 

0.115 

4 

0.6097 

0.0080 

50 

9.1982 

O.I2I 

5 

0.6534 

0.0086 

5i 

9.6661 

O.I27 

6 

0.6998 

0.0092 

52 

10.  1543 

0.134 

7 

0.7492 

0.0109 

53 

10.6636 

0.140 

8 

0.8017 

0.0107 

54 

11.1945 

0.147 

9 

0.8574 

O.OII 

55 

11.7478 

0.155 

10 

0.9165 

O.OI2 

56 

12.3244 

0.163 

II 
12 
13 

0.9792 

1.0457 
1.1162 

0.013 
O.OI4 
0.015 

9 

59 

12.9251 
13.5505 
14.2015 

O.I7O 
0.178 
0.187 

•X 


^   i  3.  5-9  ^ 


8l6  A  MANUAL  OF  THE  STEAM-ENGINE. 

TEMPERATURES  AND  PRESSURES,  SATURATED  STEAM—  Continued. 


Temperature. 

STEAM-PRESSURE. 

Temperature. 

STEAM-PRESSURE. 

In  Centimetres. 

In  Atmospheres 

In  Centimetres. 

In  Atmospheres 

+  60°  C. 

14.8791 

0.196 

-fl!0°C 

107.537 

I.4I5 

6l 

15.5839 

0.205 

III 

III.  209 

1.463 

62 

16.3170 

O.2I5 

112 

114.983 

I.5I3 

63 

17.0791 

0.225 

"3 

II8.86I 

1.564 

64 

17.8714 

0-235 

114 

122.847 

1.616 

65 

18.6945 

0.246 

115 

126.941 

1.670 

66 

19.5496 

0.257 

116 

I3LI47 

1.726 

67 

20.4376 

0.267 

"7 

135.466 

1.782 

68 

21.3596 

0.281 

118 

I39-902 

1.841 

69 

22.3165 

0.294 

119 

144-455 

1.  001 

70 

23-3093 

0.306 

120 

149.128 

1.962 

7i 

24  3393 

0.320 

121 

I53.925 

2.025 

72 

25-4073 

0.334 

122 

158.847 

2.091 

73 

26  5147 

0-349 

123 

163.896 

2.157 

74 

27.6624 

0.364 

124 

169.076 

2.225 

75 

28.8517 

0.380 

125 

I74.388 

2.295 

76 

30.0838 

0.396 

126 

I79-835 

2.366 

77 

31-3600 

0.414 

I2/ 

185.420 

2.430 

78 

32.6811 

0.430 

128 

191.147 

2.515 

79 

34-0488 

0.448 

I29 

197.015 

2.592 

So 

35-4643 

0.466 

130 

203.028 

2.671 

Bl 

36.9287 

0.486 

131 

209.194 

2.753 

82 

38-4435 

0.506 

132 

215.503 

2.836 

83 

40  oioi 

0.526 

133 

221.969 

2.921 

84 

41.6298 

0.548 

134 

228.592 

3.008 

85 

43.3041 

0.570 

135 

235-373 

3-097 

86 

45  0344 

0-593 

136 

242.316 

3.188 

87 

46.8221 

0.616 

137 

249.423 

3.282 

88 

48.6687 

0.640 

138 

256.700 

3-378 

89 

50.5759 

0.665 

139 

264.144 

3.476 

90 

52.5450 

0.691 

140 

271.763 

3.576 

91 

54-5778 

0.719 

141 

279-557 

3.678 

92 

56.6757 

0.746 

142 

287.530                   3.783 

93 

58.8406 

0.774 

143 

295.686                    3.890 

94 

61.0740 

0.804 

144 

304.026 

4.000 

95 

63.3778 

0.834 

145 

312.555 

4."3 

96 

65-7535 

0.865 

I46 

321.274 

4.227 

97 

68.2029 

0.897 

147 

330.187 

4-344 

98 

70.7280 

0.931 

I48 

339.298 

4-464 

99 

73-3305 

0.965 

149 

348.609 

4.587 

IOO 

76.000 

I.OOO 

150 

358.123 

4.712 

IOI 

76.7590 

1.036 

151 

367.843 

4.840 

102 

81.6010 

1.074 

152 

377-774 

4.971 

103 

84.5280 

1.  112 

153 

387.918 

5.104 

104 

87.5410 

I.I52 

154 

398.277 

5.240 

105 

90  6410 

I-I93 

155 

408.856 

5-380 

106 

93-8310 

I    235 

156 

419.659 

5-522 

107 

97.1140 

1.278 

157 

430.688 

5.667 

108 

100  4910 

1-322 

158 

441-945 

5.815 

109 

103.965 

1.368 

159 

453  436 

5.966 

APPEXDIX. 


8I7 


TEMPERATURES  AND  PRESSURES,  SATURATED  STEAM — Continued. 


a 

£ 

= 

Sn  '-•••.•• 

-i;  .  ;  F 

STEAM-PS 

CESSTU. 

I 

In  Centimetres. 

In  Atmospheres 

| 

In  Centimetres. 

taA»-*~ 

-t-i6o:C. 

465  .  162 

6.120 

+196'  C 

1074.595 

14-139 

161 

477-128 

6.278 

197 

1097.500 

14-441 

162 

459.336 

6.439 

198 

1120.982 

14-749 

163 

501.791 

6.603 

199 

1144.746 

15  062 

164 

514-497 

6.770 

200 

1163.896 

15-380 

165 

527-454 

6.940 

201 

"93-437 

I5-703 

1  66 

540.669 

7.114 

202 

1218.369 

16.031 

167 

554-143 

7.291 

203 

1243.700 

16.364 

1  63 

567.882 

7472 

204 

1269.430 

16.703 

169 

581.890 

7-656 

205 

1295.566 

17-047 

170 

596.166 

7.844 

206 

1322.112 

17-396 

171 

610.719 

8.036 

207 

1349-0/5 

17-751 

172 

625-543 

8.231 

208 

1376-453 

iS.ui 

173 

640.660 

S-430 

209 

1404.252 

18-477 

174 

656.055 

8.632 

210 

1432.480 

18.848 

175 

671.743 

5.839 

211 

1461.132 

19.226 

176 

687.722 

9.049 

212 

1490.222 

19.608 

177 

703-997 

9-263 

2I3 

1519.748 

19-997 

178 

720.572 

9-48i 

214 

1549-717 

20.391 

'79 

737-452 

9-703 

215 

1580.133 

20.791 

180 

754-639 

9-929 

216 

1610.994 

21.197 

181 

772-137 

10.150 

217 

1642.315 

21.690 

182 

789.952 

10.394 

215 

1674-090 

22.027 

'--:- 

806.084 

10.633 

2I9 

1706.329 

22.452 

rt| 

826.540 

10.876 

22O 

1739.036 

22.852 

:- 

845-323 

11.123 

221 

I77S-2I3 

23.319 

:'- 

864-435 

"-374 

222 

1805.864 

23.761 

--" 

--:--: 

11-630 

223 

1839994 

24.210 

;-- 

903.668 

::    --  = 

224 

1874-607 

24.666 

189 

923-795 

12.155 

225 

1909.704 

25.123 

190 

944-270 

12.425 

226 

1945-292 

25.596 

191 

965.093 

12.699 

227 

1981.376 

26.071 

192 

986.271 

12-977 

::- 

2017-961 

26.552 

193 

1007.504 

13.261 

229 

2055.048 

27.040 

194 

1029.701 

13-549 

230 

2092.640 

27-535 

195 

1051.963 

13.842 

8i8 


A  MANUAL   OF  THE  STEAM-ENGINE. 


IX. 

METRIC   STEAM   AND  WORK   TABLE. 


Absolute  pres- 
sures in  Atmos- 
phere. 

Specific  volumes 
v,  in  Cu.  meters. 

Product  p.v.. 

w_  26127.34 

~  1000  p.v. 

W  .  p.. 

O.  3 

14.504 

1.450 

18.010 

I.8or 

O.2 

7.525 

1.505 

17.418 

3.483 

0-3 

5.128 

1.540 

16.960 

5.088 

0.4 

3.908 

1.560 

16.750 

6.700 

0.5 

3.165 

1-580 

16.530 

8.265 

0.6 

.665 

1.600 

16.339 

9.803 

0.7 

•304 

1.610 

16.230 

11.361 

0.8 

.031 

1.620 

16.120 

12.896 

0.9 

.818 

1.630 

16.020 

14.418 

I.O 

.646 

1.646 

15.870 

15-870 

X.I 

•505 

1.655 

15.780 

I7-3S5 

1.2 

.386 

1.663 

15.710 

18.852 

1-3 

.285 

1.670 

15.640 

20.332 

1.4 

.199 

1.  680 

15-540 

21.756 

1-5 

.123 

1.684 

15-510 

23.265 

1.6 

•057 

1  .  691 

15.450 

24.720 

1-7 

0.999 

1.699 

15.370 

26.129 

1.8 

0.946 

1.703 

15.340 

27.612 

1.9 

0.899 

1.708 

15.290 

29.051 

2.0 

0.857 

1.714 

15.243 

30.486 

2.1 

0.819 

1.718 

15.208 

31-937 

2.2 

0.784 

I-725 

15.146 

33-321 

2-3 

0.751 

1.727 

15.128 

34-794 

2.4 

0.722 

1-733 

15-076 

36.182 

2-5 

0.695 

1.741 

15.002 

37.505 

2.6 

0.670 

1.742 

14.990 

38.974 

2.7 

0.646 

1.744 

14.970 

40.190 

2.8 

0.625 

1-750 

14.929 

41.801 

2.9 

0.604 

1-752 

14.921 

43.271 

3-0 

0.586 

1-758 

14.861 

44.583 

3-1 

0.568 

1.761 

14-838 

45-99* 

3-2 

0-551 

1.763 

14.818 

47.417 

3-3 

0-535 

1-765 

14.790 

48.807 

3-4 

0.521 

1.771 

14-749 

50.146 

3-5 

0.507 

1-774 

14.723 

5L330 

3-6 

0-493 

1-775 

14.720 

52.992 

3-7 

0.481 

1.780 

14.680 

54.3i6 

3-8 

0.469 

1.782 

14.660 

55.708 

3-9 

0.458 

1.786 

14-630 

57-057 

4.0 

0.447 

1.788 

14.61 

58.440 

4.1 

0-437 

1.792 

14.58 

59-778 

4-2 

0.427 

1-793 

I4-56 

61.152 

4-3 

0.418 

1.797 

14-53 

62.479 

4.4 

0.409 

1.799 

14.52 

63.888 

APPENDIX. 
METRIC  STEAM  AND  WOBLK  TABLE— Continued. 


8i9 


Absolute  pres- 
ure   pc   in   At- 

.  -  "  .  f 

Product  p.  T, 

~  JOOO  p.  T. 

W.p.. 

v.  in  Cu.  meters. 

4-5 

O-4OO 

1.  800 

14.51 

65.295 

4-6 

0-392 

1.803 

14-49 

66.654 

a 

0.384 
0-377 

1.805 
i.Sio 

M-45 

M  43 

67.915 
69.264 

4-9 

0.370 

i.Si3 

14.41 

70.609 

5-o 

0-363 

1.815 

M-39 

71-950 

5-i 

0.356 

1.816 

14-38 

73-338 

5-2 

0.350 

1.820 

14.36 

74-672 

5-3 

0-343 

1.821 

14-35 

76.055 

5-4 

0.337 

:   -:-. 

14-33 

"  383 

5-5 

0.332 

1.825 

14-31 

78.705 

5-6 

0.326 

1.826 

14.30 

80.080 

5-7 

0.321 

1.829 

14.26 

Si.  282 

5-8 

0.316 

1-833 

14.25 

82.650 

5-9 

0.311 

1.835 

14.24 

84.016 

6.0 

0.306 

1.836 

14-23 

85.380 

6.25 

0.294 

1.838 

14-21 

88.812 

6-5 

0.284 

1.845 

14.16 

92.040 

6.75 

0.273 

1.848 

14-13 

95-377 

7-o 

0.265 

14.10 

98.700 

7-25 

0.256 

i  .856 

14-07 

100.997 

-  - 

0.248 

i.  860 

14.04 

105.300 

7-75 
8.0 

0.241 
0.234 

1.867 

I  .  872 

13.99 
13.96 

108.422 
111.680 

8.25 

0.227 

1.873 

13-95 

114.077 

8-5 

O.22I 

1.878 

13.91 

118.235 

8-75 

O.2I5 

1.81}] 

13.89 

121  537 

9.0 

0.209 

1.883 

13.86 

124.740 

9.25 

0.204 

1.887 

13.84 

128.020 

9-5 

O.igg 

1.891 

13.81 

131.195 

9-75 

0.194 

1.893 

13.80 

134-550 

IO.O 

0.190 

1.900 

»3-75 

137-500 

820 


A   MANUAL   OF   THE  STEAM-ENGINE. 


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spunod  ui  'tunnoBA  E  aAoqe  ajnrsajj 

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In  British  Thermal  Units. 

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APPENDIX. 


821 


«,  MS 


a&a 
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?? 


lllilH 


bill 


S82-  s-s?£ 


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822 


A   MANUAL   OF   THE   STEAM-ENGINE. 


•tpui  a-iunbs  J3G 
pnnod  ui  'umnDBA  v  3Aoqe  aanssajj 


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jo    i  jSiaM   i^nbs  jo  auihioA 

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APPENDIX. 


823 


§  §5*?**wf2  =5?=r!  = 


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S3.  5-S 


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824 


A   MANUAL  Of   THE  STEAM-ENGINE. 


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APPENDIX. 

ssm-tsml 


825 


•r.  rx  «  «-.  ~  30    -.  ~  c  3: 

^El?f2??S 


----rc-r:-: 


IlilFlllliJUS 


lllflHIII 


Is&H 


nil 


ssi  ^RSSft:^?. 


H 

,25 


:??r  =  > 


SI 


a  = 


383. 

,,, 


msi 


.«»! 


ss 


8  ?-  2  5- 


iHH 


ilU 


826 


A   MANUAL   OF   THE   STEAM-ENGINE. 


The  column  headed  "  U"  in  the  table  cf  the  properties  of 
saturated  steam  is  useful  for  reducing  the  performance  of  differ- 
ent boilers  to  a  common  standard — this  standard  being  that 
most  generally  accepted  by  engineers :  the  equivalent  evapora- 
tion at  atmospheric  pressure  and  the  temperature  of  boiling 
water,  or,  as  it  is  frequently  called,  the  evaporation  from  and  at 
212°.  In  the  table  it  is  assumed  that  the  temperature  of  the 
feed-water  is  32°,  and  an  auxiliary  table  is  added,  giving 
corrections  for  any  temperature  of  feed  from  32°  to  2 12°. 

CORRECTION   FOR  TOTAL  HEAT  IN  UNITS  OF  EVAPORATION. 


Tempera- 
ture of 
feed,  Fah- 
renheit 
degrees. 

I 

Tempera- 
ture of 
feed.  Fah- 
renheit 
degrees.  . 

Correction. 

Tempera- 
ture of 
feed,  Fah- 
renheit 
degrees. 

Correction. 

Tempera- 
ture of 
feed,  Fah- 
renheit 
degrees. 

Correction. 

Tempera- 

feed.Fah- 
renheit 
degrees. 

Correction. 

33 

.001 

69 

.0383 

105 

.0756 

141 

.1129 

177 

.1504 

34 

.002 

70 

•°393 

106 

.0766 

142 

.1140 

178 

.1514 

35 

.003 

71 

.0404 

107 

.0777 

M3 

.1150 

179 

-1525 

36 

.004 

72 

.0414 

108 

.0787 

144 

.1160 

1  80 

•'535 

.005 

73 

.0424 

109 

.0797 

145 

.1171 

181 

•1545 

38 

.006 

74 

•°435 

.0808 

146 

.1181 

jS-2 

•155° 

39 
40 

.007 
.008 

9 

•0445 
•  °45° 

i  i 

I  2 

.0818 
.0829 

\% 

.1192 

.  1202 

J|3 

.1566 

•'577 

41 

.009 

77 

.0466 

1  3 

.0839 

149 

.1213 

185 

.1587 

42 

.   0 

78 

.0476 

1  4 

.0849 

150 

186 

.1598 

43 

79 

.0487  ; 

i  5 

.0860 

'51 

•  233 

187 

.1608 

44 

2 

80 

•0497  i 

i  6 

.0870 

•  244 

188 

.1618 

9 

•  35 
•  45 

81 
82 

.0507 

.0518  ! 

11 

.0880 
.0891 

J53 
'54 

190 

.1629 
.1639 

47 
48 

:  ii 

11 

.0528 

.0538  1 

119 

.0901 
.0911 

'55 
156 

-  27S 
.  285 

192 

.1650 
.1660 

49 

.  76 

85 

.0549  1 

121 

.0922 

157 

•  296 

iQ3 

.1670 

5° 

.  86 

86 

•0559 

122 

.0932 

158 

194 

.1681 

5' 

•  97 

87 

.0569 

123 

•0943 

159 

.    3l6 

1691 

52 

.0207 

88 

.0580  i 

124 

-0953 

160 

•  327 

196 

.1702 

S3 

.0217 

89 

.0590 

125 

.0963 

161 

•  337 

197 

.1712 

54 

.0228 

90 

.0601 

126 

.0974 

162 

.  348 

i98 

•  X723 

1 

23 

92 

.0611 
.0621 

3 

.0084 
.0994 

163 
164 

199 

200 

•'733 

.0259 

93 

.0632  • 

129 

.1005 

165 

'•  379 

201 

•'754 

58 

.0269 

94 

.0642  ! 

1  66 

•  389 

202 

.1764 

59 

.0279 

95 

.0652 

J3* 

.  IO25 

167 

.  400 

203 

•1775 

60 

.0290 

96 

.0663 

132 

.  IO^6 

168 

410 

204 

•1785 

61 

.0300 

97 

.0673 

133 

.  046 

,69 

420 

205 

.1796 

62 

.031 

98 

.0683 

'34 

•  °57 

170 

•  431 

206 

.1806 

63 

.032 

99 

.0694 

135 

.  067 

171 

•  44' 

207 

•1817 

64 

•°33 

100 

.0704 

136 

•  °77 

172 

•  452 

65 

•034 

101 

.0714 

*37 

.  088 

173 

.  462 

209 

•1837 

66 

•035 

102 

.0725 

138 

.  098 

174 

•  473 

210 

.1848 

67 

.0362 

103 

•0735 

139 

.  109 

175 

.  483 

211 

.1858 

68 

.0372 

104 

.0746 

140 

.  119 

176 

•  493 

212 

.1869 

APPENDIX. 


827 


mm 


.  --  -  -  : 


?  5     -  ~  - 


2?H*  <---=*='* 


Ail 


HtH 


rl2os«! 


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i 


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Hii 


r  ?          . 


828 


A   MANUAL   OF   THE   STEAM-ENGINE. 

C^         J.    ~ 


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APPEXDIX. 


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sa 


Z 


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"*i?un  (Euu^tp  qsnug 
01  aims  jo  paitod  jaj 


830 


A   MANUAL   OF   THE  STEAM-ENGINE. 


1          m 

f 

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equal  weig 
imum  dens 

ii 

ii 

I! 

- 

g" 

C. 

c 

"o  rt 

r° 

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S 

8 

5 

5 

11 

b'l 

jj 

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n  latent  heat  of  evapo: 

Of  a  cubic  foot  of 

ic  foot  of  distilled  wat< 

Of  a  pound  of  ste 

rolume  of  steam  to  vol 
water  at  temperature 

'olume  of  distilled  wat 
jual  weight  at  tempers 

£ 

| 

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0 

0  ° 

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0 

1 

1 

1 

f 

1 

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APPENDIX. 


831 


m 

\  ih  ?i:l^]v**** 

^  — 

*    2  el  ?ls  =  5g  8f¥v!  1^^-  Jr§«?  ?=  =  ?s  1f?f  1 1 

?  srr1??  'i.^s^j;  iL^ss^^n?  gr2?s 

I      x    '     »     **  I  *    «  •  •  S  «    -  -  -  -  -    _  _  _  -  «    __«_'_    «  »  •  S  3T 

S  'i 

I  I   s.,'?n.5?«  !H*.H???? ??-??=  ==??f  HnifirHI 

i  |T?i 

<     =    

y       5   .    a_  t«.  I  • 

»-^  >     "3    

SX  i^ 

~        ^  * 

I!  ?  L «! =  =i§?i?|Kif  ??f?5 5§n=  2i?y§ nm  fifti i 

B .,,.,,, ..HRmimn 

~l  ,   =  IffSf  ifSfl  ?????  r  =  S  =  ?  fffff  f  Stfl  III??  ? 
|Js:|nsfH*??f??????1  =  =  =  |SfK« 

i  -   -  1 1  8??55 

IFs^fl 
_!: 
K(  - 

E=  : 


832 


A  MANUAL   OF  THE  STEAM-ENGINE. 


XIV. 
COMPOSITION   OF  VARIOUS    FUELS   OF  THE   UNITED  STATES. 


C. 

H.      0. 

N. 

S. 

Mois- 
ture. 

Ash. 

Spec. 
Grav. 

Pennsylvania  Anthracite  
Rhode  Island          "          

78.6 
85.8 

2.5     1.7 
,0.5 

0.8 

3-7 

... 

14.8 

!-45 

•2 

61 

7  8 

2.0 

.78 

Welsh                      "          

84.2 

Maryland  Semi-bituminous  

80.5 

!-7 

8-3 

•33 

.i                                         4( 

*9-4 

38.8 

.8 

i  24 

Illinois  Bituminous  .Y.Y.T~""II 

"       (Block)  Bituminous  

52.0 
62.6 
58.2 

39-o 
35  5 
37-i 
Vd  6 

•9 

•27 
•3° 

Kentucky  (Cannel)  Bituminous  
Tennessee  Bituminous  

48.4 
71.0 

48.8 
17.0 
56  5 

.8 

•25 

•45 

Alabama               *" 

42  6 

o 

I 

^ 

Virginia              " 

* 

18.6 

California  and  Oregon  Lignite  

50.1 

3-9  '3-7 

0.9 

i-5 

16.7 

13.2 

1.32 

THEORETIC 

AL  VALUE. 

STATE. 

COAL. 
KIND  OF  COAL. 

Per  Cent,  of 
Ash. 

In  Heat 
Units. 

In  Pounds 
of  Water 
Evaporated. 

Pennsylvania  . 

Anthracite    

3-49 
6.13 

14,199 
3,535 

14.70 
14.01 

i« 

' 

;;       ! 

Connelsville  
Semi-bituminous  
Stone's  Gas  
Youghiogheny.   ..  

6.50 
10.77 

is 

M& 

3.'55 
4.021 
4.265 

3:8 

3S 

Kentucky  

Caking  
Cannel 

a.  75 

4-39« 
s  108 

^89 

16  76 

M 

'384 

Illinois...;'.'.'.! 

Lignite  
Bureau  County  

7.00 
5.20 
5  60 

9,326 
13.025 

9.65 
13-48 
13  58 

1C 

Indiana  

Block  
Caking 

5*11 

13,588 

ll'll 

«i 

Cannel  

Maryland  
Arkansas  
Colorado  

Cumberland  
Lignite  

13.98 
S.oo 
9.25 

2,226 
9,2'5 

3.562 
3866 

12.65 
9-54 
14.04 

Texas 

it 

so 

tt 

3  lo 

II    QO 

Pennsylvania  . 

Petroleum  

20,746 

21.47 

APPENDIX. 


833 


ANALYSES  OF  ASH. 


Specific 
Grav. 

Color 

of  Ash. 

Silica 

Alum- 
ina. 

Oxide 

Iron. 

Lime. 

at 

Loss. 

0.48 
0.40 

Acids 
S.&P. 

Pennsylvania  Anthracite  
Bituminous  
Welsh  Anthracite  
Scotch  Bituminous  

•559 

.373 

Reddish 
Buff. 
Gray. 

45-6 
76.0 
40.0 
37-6 

42.75 
44-8 

9-43 
2.60 

5*8 

1-4* 
3-7 

°-33 
trace 
26 

2.97 

5-0» 
33-8 

7 

3 

3  7 

834 


A   MANUAL   OF    THE   STEAM-ENGINE. 


XV. 

HORSE-POWER   PER   POUND   MEAN   PRESSURE. 


SPEED  OF  PISTON  IN  FEET  PER  MINUTE 


j3U«    100 

240 

300 

350 

400 

450 

500 

550 

600 

650 

750 

4 

.038 

.091 

.114 

•  133 

•  152 

.171 

.19 

.209 

.228 

•  247 

.285 

4i 

.048 

.115 

.144 

.168 

.192 

.216 

-24 

.264 

.288 

.312 

.360 

.06 

.144 

.18 

.21 

'288 

•  27 

'36 

336 

•36 

•  450 

6 

.086 

.205 

.256 

.299 

-342 

.324 
•  385 

& 

•471 

-432 

•555 

64° 

6} 

O2 

.245 

•  3°7 

.391 

.409 

•464 

.512 

•563 

.614 

.698 

.800 

7 

;  16 

.279 

•  348 

.408 

.466 

•524 

•  583 

699 

.756 

•  874 

7i 

•  34 

.321 

.401 

.468 

•534 

.602 

.669 

.802 

.869 

1.002 

8 

-   52 

.365 

•  456 

•532 

.608 

.685 

.761 

.912 

.989 

1.  121 

84 

•  72 

•  4'3 

.516 

.602 

.688 

•774 

.86 

.. 

.118 

1.200 

9 

•  92 

.462 

.674 

.770 

.866 

•963 

•059 

•J54 

•251 

1.444 

•   '5 

•  5'5 

.644 

•751 

•859 

.966 

1.074 

.181 

.288 

•395 

10 

.   38 

•57' 

.714 

.831 

•  952 

1.071 

1.190 

•3«9 

.428 

•547 

I  .  785 

.262 

-63 

•  787 

.919 

1.050 

1.181 

•444 

•575 

.706  1  1.969 

22 

.288 

.691 

.864 

I.OOS 

1.152 

1.296 

1.44 

•584 

.728 

.872  '2.160 

IlJ. 

.314 

•754 

•943 

I.I 

1.257 

1.414 

1-572 

•729 

.886 

.043  i  2.357 

12 

•342 

1.025 

1.  195 

i  .  366 

1.540        1.708 

.880 

.050 

2.222    .    2.564 

J3 

.402 

^64 

1.206 

i.  608 

1.809     ;        2.01 

.211 

2.412 

2.613  ;  3.015 

*4 

.466 

1.119 

1.398 

I.63I 

1.864 

2.097     '        2-33' 

•564 

•797 

3.029    3.495 

15 

•535 

1.285 

i.  606 

1.873 

2.131 

2.409 

2-677 

•945 

.212 

3.479  1  4.004 

16 

.609 

1.461 

1.827 

2.131 

2.436 

2.741 

3.045 

•349 

•654 

3.958    4.567 

17 

.685 

1.643 

2.054 

2-739 

3.o8l 

3-424 

.766 

4-450    5.135 

18 

•77' 

1.849 

2.312 

2.697 

3-083 

3.468 

3-854 

•239 

:e°4 

5.009  i  5.780 

'9 

•859 

2.061 

2-577 

3.006 

3-436 

3.865 

4-295 

.724 

•  154 

5.583    6.442 

20 

•952 

2.292 

2.855 

3-331 

3-807 

4.28S 

4-759 

•234 

5-731 

6.186    7.138 

21 

1.049 

8.518 

3.148 

3.672 

4-I97 

4.722 

5.247        5.771 

6.296 

6.820  i  7.869 

22 
23 

1.152 

1.259 

2-764 
3.021 

3-455 
3-776 

4.031 
4-405 

4.607 
5-035 

5.183     '        5.759            6.334 
5.664            6.294            6.923 

6.911 

7-552 

7.486    8.638 

8.181  i  9.44 

24 

1.370 

3.289 

4.  HI 

4-797 

5-482 

6.167    '        6.853            7.538 

8.223 

8.908    10.279 

25 

1.487 

4.461 

5-105 

5-948 

6.692            7.436 

8.179 

8.923 

9.566    11.053 

26 

1.609 

3.861 

4.826 

5.630 

6-435 

7.239            8.044 

8.848 

9.652 

27 

!-733 

4-159 

5.199 

6.066 

6.932 

7.799  ;    8.666 

9-532 

10.399 

1.26      12.998 

28 

1.865 

4-477 

5.596 

6.529 

7.462 

8.395       9.328     10.261 

11.193 

2.12          I3-99I 

29 

2.002 

4.805 

6.006 

7.007 

8.008 

9.009         10.01       '•       I.  OH 

12.012 

3-01          15.015 

30 

2.142 

5.141 

6.426 

7-497 

8.568 

9.639         I0.7I       i       1.781        12.852 

3.92         16.065 

31 

2.288 

5.486 

6.865 

8.001 

9.144 

10.287      11-43     j     2.573 

13.716 

4.86         17.145 

3» 
33 

2.436 
2    590 

5.846 
6.216 

7.308 
7.770 

8.526 
9.065 

9-744 
0.360 

10.962      12.  18         3.398 
1.655      12-959       4-245 

4.616 

5-54 

is!  a?    1  9  '.425 

34 

2.746 

6-59 

8.238 

9.6n 

0.984 

2-357       '3-73          5-«>3  i     6.476 

7.84      20  595 

P 

2.914 
3.084 

6-993 
7.401 

8.742 
9.252 

10.199 
10.794 

1.656 
2.336 

3.113       14.57          6.027        7.484 
3.878       15.42          6.962        8.504 

8-94      =1855 
0.04      23.130 

P 

3-253 
3-436 

7.8.9 
8.246 

9-774 
0.308 

11.403 
12.026 

3-032 
3-744 

4.861       16.29          7.919        9.548 
5.462      17.18          8.898      20.616 

1.17       24  435 
2-33      25  770 

39 

3.620 

8.648 

0.86 

2.67 

4-48 

6.29     18.1    ;  9-91 

21.62 

3-53      27.150 

40 

3.808 

9.139 

1.424 

3.328 

5-232 

7.136    19.04 

0-944 

22.848 

24-75     128.560 

41 

4.002 

9.604 

2.006 

4.007 

6.008 

8.009        20.00 

26.01      130  015 

42 

0.065 

2-594 

4-693 

6.792 

8.901         20.99 

3.089      25.188 

27.287 

31.485 

43 
'44 

4.40 
4.606 

0.56 
1.046 

3-20 

3-818 

3:!,, 

7-6 
8.424 

9.8 
0.727 

22.00 
23.03 

4.2 
25-333 

26.4 

27.636 

28.6 
29-939 

33.00 

34-545 

45 

4.818 

1.563      4-454 

6.863 

9.272 

1.681 

24.09 

26.399      28.908 

3I-3I7 

36.135 

46 
47 

5.043 

5.256 

2.o86|     5.128 
2.614'     5-768 

7.626 
8.396 

0.144 

2.662 
3.652 

25.18 
26.28 

27.698 
28.908 

30.216 

32-754 
34.164 

37-770 
39  •  420 

48 

5.482 

2.846:     6.446 

9.187 

4.669 

27.41 

30-151 

3'-  152 

35-633 

4i-"5 

49 

5-7I4 

2.913 

7.142 

9-999 

5-713 

28.57 

34.284 

37  -H1 

42.855 

5° 

5-950 

4.28 

7-85 

20.825 

3-8 

26.775 

29-75 

32-725 

35-7 

38-675 

44-625 

6.180 

4.832 

8-54 

1.665 

4-76 

27-855 

30.95 

34.045     37.08 

40-205 

46-425 

52 

6.432 

5-437 

19.296 

2.512 

5.728 

28.944 

32.16 

35-376 

38.592 

i.  808 

53 

6.684 

6.041 

20.052 

3-394 

6-736 

30.078 

33-42 

36.762 

40.104 

3-446 

50.130 

54 

6.940 

6.656 

20.82 

4.29 

7-76 

31-23 

34-7 

38-17 

41.64 

52.05 

55 

7.198 

7-275 

21-594 

5-193 

8.792 

32.  391 

35-99 

39-589 

43-188 

'.787 

53.985 

56 

7.462 

7.909 

22.386 

26.117         9  848 

33-579 

37-31 

41.041 

44.772  j     8.503 

55  •  965 

57 

7-732 

8-557 

23-196 

27.062  !  30.928 

34-794 

38.66 

42  .  526 

46.392  |  50.258 

57-99 

58 

8.006 

9  214 

24.018 

28.021   j  32.024 

36-027 

44-033 

48.036  |   52.039 

60.045 

59 

8.284 

9.902!   24.852 

28.964  |  33.136 

37.278 

41.42 

45  •  562 

48.704      53.846 

62.  .3 

60 

8.566 

20.558'   25.698 

64.24J 

APPENDIX. 


835 


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836 


A   MANUAL   OF   THE   STEAM-ENGINE. 


LOG  OF  TRIAL  BY  MECHANICAL  LABORATORY,  DEPARTMENT  OF  ENGINEERING. 

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APPENDIX. 


«    ~    d    d    d    CO  I 


in  C<co  *-  O  T  co  T 
O«nOco3inOd 
O  O  Ci  in  in  —  inco 

O  d"  co'  coco  co  r^.  ~ 


inco  r>r^  w  00  t^  O 
r^C^r^**  co  O  co  -• 
C  O  O  O  O  r^  «  T 

co  ;>  T  O  «n  O  T=o 


•n  co -co  =000  OO   -  co  m  r^  =- r^  m  co 

sssss^sssssRsteH 


OOrvt^d-rr;-0>e«  moo  6  co  mco   ~  ci  TO 
i2£?l!OS'f-<   ""'*  «  ""-co   ci   inco   -   inos  -   T 


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s 

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i     co  i^.  O  T  r^  —  TOO  -   ^f-j-J  ^  Cnoo   -   S^.cc'^   TCO  2"*T  S  — 

«  «  w  N  w  cococOTTT<nm  mo  O  O  r^  r^  r^*co  coco   ^Cso^5O"O 

co  u-iTcot--cocoT—  OO^Sco  moo  o  co  co  O^C^coO  •TcocOTTi  co 
O  co  O  T  m  coco  »*cocoO*^oir^O"-OC>r^T»-'r^c*oaoOcicoei 
d  oo  T  ^*  T  O*  coco  «  O  O  cot^-O  Tf^O  CI  moo  «  coo  oo  O  co  in  r^  O* 
coo  O  co  t^  O  T  r^  -  TOO  -  TOO  -  TOO  ~  T  r>.  ~  -tt^O  T  r-  C  c-.O 
«  -.  d  d  d  coeocOTt-^-Tinrn  mo  O  O  r^  r»  t-»co  oooo  C-C>J>O  OO 


O  Ocor^—  NO>fe«  —  C^co  O  «  C^r^c~.ooooin«H  o  «  1-O  co  ~  £- 1~~ 
O  moo  O^  t~*  r^oo  «  O  ^  0s  co  co  •-  mo  C"QO  *-*-oO't'OO"T«coOt' 
•*  t^  'Too  O  co  co  I-  &  C>0  co  <?•  rt  r^co  1^0  «n  n  oo  •*  5  4o  oo  O  -  O 


r^r^^i-oO  —  Otn  r^O  oo  co  co  >n  r>.eo 
«  co  1-1  mo  O  Too  oo  «  w  o  r^o  coo  ^ 
I^  «  C>  CO  in  T  C-  N  T  m  co  S>  in  5  T  in  T 

T  —  O  N  r^no  **  in^  coo  O  T  r^  C  coO  ^  "^  T  r^  C*  w  TO  QO  O  ct 
cT  o  J-coO  0  ?^r^  O  cor>.5  T  r-  O  T  r- O  co  r^  O  coo  O  coo  O  coo 
««~WWCOCOCOTT  Tminino  OO  l»  r^  t^oo  coco  »<*&<>O  O 


m  O»  C«  CO  m 


q  m  co  ^)  q*  ocrc?1q  -  o  S  d  t^.  -  "d  d  c  r  : 

i-i  r^  c^.oo  Tco  cor^dO  o^cor^O  Tf^O  co  mco  •-*  coo  co  *-  co  m  r^  & 
M  rnOdO  ocoo  CcooOcor^Ocor-0  coo  O  «o<>  "3*  J^b  O>  JJ  jp 
M  -  «  d  d  d  cocOTTT>nininooo  r^r^.  t^-co  oococo  CT>  O>  CT-  O  O 


goooooogoo oo 0^00080230^008580 

coco  r^  ci  in  T  O  TO  r^  m  M  oo  co  r^  C-  S>oo  oco  —  Ooi^O>'"comT 

r^-co^inO  >n6  -**>  NO  6  cor>-d  coo  O  «  mco  O  co  in  r^  6  «  t-O 
-  inco  00  C>?--=  CM-.O  O  coo  O  coo  O  COO  C7>  COO  5>  M  O  C-c;  in 
_  „  M  M  ci  CI  cococOTTmminOOOO  l^t^  l^co  oo  CO  C^  CT>  C^  O  O 


co  <*  mO  I>-CO  C>  O  *•  w  co  f  «nO  t^oo  C>  O  «  «  co  T  >"O  r^oo   O  O  — 

MMMMMMI-IMMndCldddCICIdddCOCO 


842 


A   MANUAL   OF   THE   STEAM-ENGINE. 


a 


I 


N    TtvO  OO    CO  CO  CO.CO  CO  CO  COCO  O    T  N    OcOO    TN    OcOO    r^cOOmw    1^ 

mi-^  t^  in  moo   wTr-O  comTmoo   co  Ooo   ON   r^coN   COTOO  f^OO 
M  Ooo  in  T  N   OO   »-*  o    Omt-*o   O   TO  co    O  O    Oco  O  CO   O   *-"   N   co  N 


N  CO   TOO    Nco   TO   co  in  r-^  O  i-i   CO 
i  O  N   in  i^co   Ooo  r^mr^OO   "   N  »-< 


Too  NO  TTTTTTT 
inco  O  OO  O  TOO  N  o  O 
Oco  r~  co  N  i-i  co  TO  Too 


\C  r»cc  O^O  "-<  w  to-i-u-jr^QO  ^ 
-  -t  f^  O  -^-  r^  O  cno  o  w  moo 
\oOiO  r^.t^.r^.oocoooao  c^OC^ 


«  Oooo   *t  *1-  f  -*  *fr  »t  -to  co   O  w  Tj-o  co   O   w   -to  c 

in'—   ^oco   -^fOO  wco   -to   r^'-iO  cow   cor^M   OCXD 

miocoooo  r^innn  t^*-.  u^oo   NO  O  co  mo  r^o   m 

-  1 ; 


OOOOcococococococoOOOOOOOOOOOOcocococococ 
in  M  r^  5   OO   coOt^-t'-iONOCMOOcJONOOc-icoocO't  Oc 


NCN   f^"co  O  co'R  S"  co  T  m  m 
co   O  «  N   T  m  r^oo'   O  6  >-> 


f^co    O 

^-Tr^ 

OOO 


NO  O  Tr^r^r^r^r^r*.  r^o  NCO  TOO  ^NOO  TO  r^N  TO  co  o  N  T 

T  co  «  O  O  Ooo  t-»O  in  TO  O  m  co  co  Too  coi-i~NOcofiOcoOO 
O  Oco  in  co  M  OO  N  I^M  inN  r^NO  Ow  COTTCO^  O  co  ino  O  O 

I-- O  «  comr^co  6  N  co  mo  co  O  "  N  co  mo  t-^-co  O  O  >-'  N  co  T  mo 
ONO  ON  inco  N  inco  •-*  TI^O  Tr^O  coo  ON  inooi  inco  «  Tf^ 
0  i-,  _  w  N  o)  N  cococoTTTinininoooO  r^r^r^cococo  OOO 


cOTNOMtH*HMMWMOTOOO>-<ONi-)w   coco  in  O    O  N  co    O 
r^-r^O  COHH   Oco  inMO  O  cooo   O   Tco   O  N  COCON   O   ON   cominm 

TO  COO'N   Tmr^oONco  mo  oo   O  6   N   co  T  -no   i>.  r»  O  C i  >-<   N   co 
ON  m  ON   moo   wTcoi-i-tr^OcooOcooONmcoi-iTco«Tr-~ 


oTNJ^r^r^t^r^r^r^OPJTOrr  NTOcoONOcot^«inO 
TTN  M  N  cOTinO  rococo  inTu"jOT*H  o  w  tnO  NCD  r^»-<co  O 
in  T  N  Oco  OCOOTCONCOTOCOO  OwMNMOooONTTT 


I-H   CO  in  r^  co   O 


OOOOOOOOOOOOOOOOOOOOOOOOOOOOO 
NinoinNTOcoONTONOONONOONONOOOOcoc5 
co  co  N  O  r^O  TMCO  cor^o  t^coco  N  moo  O  M  M  O  ot^O"  cocoT 


oo   O   N  T^nr^O>-<  N   Tm  r^c 
co   N   inoo   «    T  t^  «   T  r^  O   co 


N  coTmO  r^co   OO  M 


*-<   co  T  m  r^co   O  O   O   »-'  N   T  ino   r^ 

c<-»o    O  N   mco   n   moo   «    T  r^  p^  coo 


~co    O  O    w   N   co  T  >nO  r^oo    O  ( 


APPENDIX.  843 

XX. 

HIRN'S   ANALYSIS. 


DATA  AND  RESULTS. 

Test  of  Steam-engine  made  by at. 

Kind  of  engine  . .  .Diam.  cylinder Length  stroke 

Diam.  piston-rod Vol.  cylinder,  crank  end Vol.  head  end 

Vol.  clearance,  cu.  ft.,  head Clearance  in  per  cent  of  stroke 

"  "  "       crank "  "  "     

Boiler-pressure  by  gauge Barometer 

Boiler-pressure  absolute Boiling  temp.,  atmos.  pressure 

Revolutions  per  hour Steam  used  during  run,  Ibs 

Quality  of  steam  in  steam  pipe Quality  of  steam  in  steam-chest 

Quality  of  steam  in  compression Quality  of  steam  in  exhaust 

Weight  of  condensed  steam  per  hour 

Pounds  of  wet  steam  per  stroke Head Crank. . .   

Temperatures  condensed  steam 

Temperatures  condensing  water,  cold Hot 

Pounds  of  condensing  water,  per  hour Per  stroke 

SYMBOLS. 

To  denote  different  portions  of  the  stroke,  the  following  subscripts  are 
used  : 

Admission  (a);  expansion  (6);  exhaust  (c)\  compression  (</). 

To  denote   different    events    of    the    stroke,    th6   following   sub-numbers 
are  used  : 

Cut-off  (i);   release  (2);   compression,  beginning  of  (3);   admission,  begin- 
ning of  (o);  in  exhaust  (5). 

Quality  of  steam  denoted  by  X. 

Cut-off,  crank  end  per  cent  of  stroke Release,  crank  end 

Cut-off,  head  end  per  cent  of  stroke Release,  head  end 

Compression,  crank  end  per  cent  of  stroke Lbs.  steam  per  I.  H.  P 

Compression,  head  end  per  cent  of  stroke Lbs.  steam  per  brake  H.  P 

I.  H.  P Brake  horse-power 


844 


A    MANUAL    OF   THE   STEAM-ENGINE. 

XX. — (Continued?) 

DATA   AND    RESULTS. 

PER  100  STROKES. 
Engine.  Date 


.189 


QUANTITIES. 

SYMBOL. 

FORMULA. 

RESULTS 

1 

u 

Weight  steam  per  100  strokes,  Ibs  
Weight  of  steam  in  clearance,  Ibs  
Weight  of  steam,  total  ,  

Condensing  water,  Ibs  
Heat  given  to  condensing  water,  B.T.U. 

M 

c, 

K 
Q 
ft 

ft 

K.(Wt.  percu.ft.) 

M(XL  -\-  S) 

Heat  retained  by  compression,  B.T.U  .  . 
External  heat  steam  at  cut-off,  B.T.U... 
Internal  heat  steam  at  cut-off,  B.T.U.  .  . 

Cylinder  loss  during  admission,  B.T.U. 
Loss  sensible  heat  during  expansion  

Internal  heat  after  expansion  
Cylinder  loss  during  expansion,  B.T.U. 

M0S0  -|  —  -. 
(M  -f-  Mt))Sl 

H 

MS 

H, 

JM.'*£ 

Heat  delivered  from  condenser  

Heat  carried  off  in  exhaust  ...  

ft 
ft 

H' 

ft 

Q 
B 

D' 

M(XLt-(-Ss)  (per  calorimeter).... 

778 

Cylinder  loss,  exhaust,  B.T.U  

Sensible  heat,  gain  during  compression. 
I  nternal  heat  at  admission  

«£«-•-£ 

Cylinder  loss  during  compression,  B.T.U. 

Heat  admitted  
Heat  discharged  and  external  work  
Loss  

#.  +  *•+  total  W+Tfl  

Q         Q 

Loss  

APPENDIX. 


845 


•>       -c     r»  oo 


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A   MANUAL   OF   THE   STEAM-ENGINE. 


APPENDIX. 


XXI. — (  Continued. ) 


855 


NON-CONDENSING   ENGINES,   UNJACKETED  CYLINDERS,  STEAM 
SUPERHEATED  SUFFICIENTLY  TO  PREVENT  CONDENSATION. 


(/} 

POINT  OF  CUT-OFF. 

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% 

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366 

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26.1 

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hourly,  calculated  by  \  *}"  "' 
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l^  ri  .  r  .  . 

9 

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148.8 
3963 

26.6 

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33^8 

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32«  |  3627 

22  I  24.2 

Pounds  of  steam 

Point   of 
Cut-off. 

Pounds  of 
steam  hourly. 

Effective 
horse-power. 

hourly,  per 
effective 

hcrse-power. 

Full  stroke. 

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'77 

33.2 

94 

5582 

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57 
3-9 

XXII. 

NOTE  TO  §   112. — The  transformation  of  the  first  of  the 
equations  of  Rankine  into  the  second  may  be  thus  effected  : 


/"^'  C*1     —  i  T  dp\ 

udp  =         dpd^(J  log,  _'  +  P,  ^J 
-  ,'»  •//»        dT 


T,  T,  > 

T;  (r,  -  ra)  -/(r,  log,  r,  -  T;  log, 


,  -  r,  +  71,) 


=  /  [rt  -  T,  +  T,  (log,  T;  -  log,  7,)  +  «', 


INDEX. 


Absolute  Limits  to  Expansion m    201  786 

Action  of  the  Jacket 153  627 

Actual  Cases,  Construction  of  Efficiency-diagrams 189  762 

.  Unavoidable  Thermodynamic  Waste  in 124  482 

Actual  Efficiencies  and  Economy  of  Proposed  Steam-engine 137  572 

Actual  Engine  Efficiency,  Limit  of n3  466 

Actual  Engines,  Method  of  Waste  in 122  471 

Actual  Thermodynamic  Lines  and  -  Carres  of  Efficiency". 180  718 

Adiabaiic  Condensation 112  431 

Agricultural  Engines 38  179 

Algebraic  Expressions  in  Energetics 79  307 

Amelioration  of  Wastes  by  Jacketing 140  590 

by  Superheating 140  590 

Application  of  Computations,  Ideal  Engine  Efficiencies 117  454 

Back-pressure arts.  123,171,  pp.  477,  683 

and  Clearance in  430 

as  modifying  Economy 196  776 

in  Actual  Engines 123  476 

Balance  of  Forces 151  620 

Binary-vapor  Engines. 172  697 

Boiling  and  Fusing  Points 89  322 

Calonmetry ...92  333 

Capital,  Efficiency  of 182  741 

Carnot's  Work 58  2=5 

Character  ot  Energy.  Transformations,  Sources,  etc 47  245 

Chemical  Principles  involved  in  Transformations  of  Energy 48  245 

Clansins' Work 59  2fel 

Clearance  and  Back-pressure «i  43° 

and  Compression 171  683 

Compound  and  Single  Engines 34  93 

Compound  Engine,  Waste  of  the 139  58° 

,  Early .-    19  27 

.  Screw  Engines 42  217 

857 


858  INDEX. 


ART. 


Compounding,  First  Step  in 143  596 

,  Problems  of 141  592 

,  Three  Fundamental  Principles  of 142  593 

Compression  and  Clearances 171  603 

Computation  of  Efficiency  and  Economy  of  Real  Engines 137  572 

,  Examples  of.  137  572 

Latent  and  Total  Heat  of  Steam 93  336 

Efficiency,  Examples  of 149  611 

Ideal  Engine  Efficiencies,  Examples  of  Applications 

of "7  454 

Conclusions  relative  to  Maximum  Efficiency 200  785 

Condensation,  Adiabatic 112  431 

,  Cylinder 65-70  271-281 

,  Magnitude  of 128  488 

,  Restriction  of 131  534 

,  Status  of  Theory  of,  in  1850 68  217 

,  Variation  of 198  783 

Condensation,  Internal,  and  Waste,  Theory  of 130  517 

,  Laws  governing  Loss  by 129  499 

Condition  of  Internal  Surfaces  of  Engine 161  659 

Maximum  Efficiency .115  449 

of  Fluids 125  483 

Conduction  and  Radiation,  Heat-wastes  by 126  483 

,  Methods  of  Reduction  of  Losses  by 127  487 

Constitution  of  Matter  and  Thermodynamics 88  326 

Construction,  General  Principles  of 31  86 

Construction  of  Thermodynamic  Lines 103  400 

Consumption  of  Steam , 1 28  488 

Corliss  and  Greene  Engines,  Simple  and  Compound  Forms 34  95 

Costs  and  Profits,  Relation  of 193  772 

,  Deduction  from  the  Investigation  of 197  776 

,  Estimation  of 191  766 

Cotterill's  Work 67  275 

Critical  Physical  Condition  and  Temperature  of  Steam 94  350 

Curves  of  Efficiency  for  Real  Engines 186  756 

Real  Efficiency,  Thurston's 187  757 

Cycles  of  Real  Engines ,    119  467 

Cyclical  Operations,  Efficiency  of 114  447 

Thermodynamic  Operations 104  410 

Cylinder-condensation 65  271 

,  Clark's  Researches  on ..  65  271 

,  Hirn's  Investigations  on.    . . . , . .   66  274 

,  Magnitude  of 128  488 

,  Restriction  ol     131  531 

,  Status  of  Theory  of,  in  1850 68  277 


INDEX.  859 

ART.  PACE 

Cylinder-condensation,  Three  Periods  of  Philosophy  of 69  279 

,  Variation  of . .    igS  783 

,  Work  to  be  done  on 70  281 

Cylinder-wastes  vs.  Jacket-wastes 154  532 

Cylinders  in  Series,  Numbers  of 146  602 

De  Pambour's  Problem 58  258 

Design,  Principles  of 30  85 

Designer's  Aim   30  85 

Details  of  Action  of  the  Jacket 153  627 

Diagram  of  Ideal  Efficiency,  Rankine's 184  749 

,  Construction  of  Efficiency,  for  Actual  Cases 189  762 

,  Method  of  Use  of  Efficiency 190  765 

Distribution  and  Magnitude  of  Losses  in  Actual  Engines 123  475 

Variation  of  Internal  Engine  Friction 134  .  565 

Distribution  of  Energy  in  Real  Steam-engines 120  467 

Pressures  and  Efficiency  of  Mechanism 151  620 

Double-acting  Engine,  Watt's 17  23 

Dwelshauvers-Dery,  Work  of 66  274 

Dynamic  Wastes,  Mechanical  or ill  430 

Economical  Expansion,  Extent  of 144  597 

Economy,  Back-pressure  as  modifying 196  776 

and  Efficiency  of  Real  Engines,  Computation  of.    137  572 

,  Examples  of 187  757 

,  Computation  of .187  757 

and  Efficiencies.  Actual,  of  Proposed  Steam-engines 137  570 

Efficiency,  Actual,  of  the  Working  Substance 177  712 

,  Conditions  of  Maximum,  of  Fluids ....  125  483 

.Curvesof     180  718 

,  for  Real  Engines 186  756 

Diagrams,  Construction  of,  for  Actual  Cases 189  762 

,  Method  of  Use  of     190  765 

,  Examples  of  Computations  of — 149  6n 

,  Ideal,  Rankine's  Diagram  of 184  749 

,  Limit  of  Actual  Engine. . 118  466 

Problems,  solved  by  Inspection 199  784 

,  Real  Maximum,  of  Engine;  Conditions  of ...135  57O 

,  Real,  Thurston's  Curves  of ..187  757 

,  Solution  of  Practical  Problems  of ...........    .    «SS  759 

,  Thermodynamic 1/5  709 

and  Economy  of  Real  Engines,  Computation  of...     .        .137  5Q2 

Examples  of 187  757 

and  Jacket-waste,  Computation  of 155  636 

,  Maximum,  Conditions  of 115  449 

,  of  Jacket-action 156  648 


86O  INDEX. 


Efficiency  of  Capital 182 

of  Cyclical  Operations 114  447 

of  Engine  and  the  Jacket 106  66S 

of  Ideal  Engines,  Th?ory  of 1 16  450 

of  Mechanism 151  620 

of  Steam,  Conditions  of  Maximum  Total 136  571 

of  the  Machine  and  Engine  Friction 132  540 

and  the  Engine 179  683 

Efficiencies,  Application  of  Computations  of,  for  Real  Engines 117  455 

,  Computations  of,  in  Ideal  Engines 117  454 

for  Real  Engines,  Theories  of 185  752 

,  Mathematical  Treatment  of  Engine 173  705 

,  Maximum,  Conclusions  relative  to 200  785 

of  the  Engine,  The  Several 174  705 

of  the  Ideal  Engine 183  741 

,  Ratios  of  Expansion  at  Maximum. 181  725 

and  Economy,  Actual,  of  Proposed  Steam-engines 137  572 

Energetics  and  Thermodynamics 51  249 

Algebraic  Expressions  in 79  307 

denned  and  discussed 75  298 

Fundamental  Law  of 75  298 

Laws  of 77  304 

Newton 's  Laws  and 78  305 

,  Thermodynamics  a   Restricted  Case  of 80  309 

,  Thermodynamics  as  a  Branch  of 74  297 

Energy 76  299 

,  Character,  Source,  and  Transformation  of 47  24; 

Chemical  Principles  of  Transformation  of 48  245 

,  Distribution  of,  in  Real  Steam-engines 120  367 

,  Mechanical  Principles  of  Transformation  of. .......    50  247 

,  Physical  Principles  of  Transformation  of  .    49  246 

,  stored,  in  Steam 100  383 

,  Thermodynamics  of  Work  and   .. 97  365 

,  Transformation,  General  Methods  of 2  i 

Engine,  Compound,  Waste  of  the 139  586 

.Screw 42  217 

,  Conditions  of  Real  Maximum  Efficiency  of ...  .135  570 

,  Cost  of,  as  effecting  Best  Ratio  of  Expansion 195  775 

Efficiency,  Actual,  Limit  of nS  466 

and  the  Jacket . 166  668 

of  the  Machine  and  the.    179  714 

Efficiencies,  Mathematical  Treatment  of .    .   173  705 

ri  ction  and  Efficiency  of  the  Machine 132  540 

,  Internal,  Investigation  of 133  558 

.  Variation  and  Distribution  of 134  565 


INDEX.  86 1 

ART.  PAGE 

Engine    Heat-,  Purpose  of  the ,  , 

,  The  Steam-engine  as  a 1O5  ^22 

.Hero's 6 

,  Ideal,  distinguished  from  the  Real 107  423 

,  Efficiencies  of  the 1g3  -40 

,  Ideal  and  Real 52  -o 

Progress  of  the  Philosophy  of  the 54  251 

,  Influence  of  Size  of 147  50, 

,  Marquis  of  Worcester's g  g 

,  Newcomen's 12  12 

,  its  Merits  and  Demerits 13  jfc 

,  Performance  of  Savery's u  jj 

,  Real,  distinguished  from  the  Ideal 107  423 

,  Several  Efficiencies  of  the  Steam 174  705 

-  speed,  Influence  of 145  ggg 

,  Steam,  Actual,  Efficiencies  of  proposed 137  572 

,  as  a  Heat-engine 106  422 

,  Origin  of  the 5  3 

,  Peculiar  Types  of 44  331 

,  Philosophical  Study  of  Development  of 26  77 

,  Process  of  Development  of 25  73 

,  Structure  and  Use  of 27  82 

,  Thermodynamics  of 105  42 1 

,  Superheated  Steam  and  the  Steam- i6S  671 

,  The  Locomotive- 21  34 

,  The  Mill-  or  Factory- 34  95 

,  The  Stationary 20  33 

Older  Forms  of 33  87 

,  Thermodynamics  of  the  Steam- 72  296 

,  Watt's  Double-acting 17  23 

,  Watt's  Single-acting 16  22 

with  Jackets,  Proportions  of 163  661 

Engines,  Actual,  Methods  of  Waste  in 122  471 

,  Classification  of,  into  Types 28  82 

,  Corliss  and  Greene,  Simple  and  Compound  Forms 34  95 

,  Distribution  of  Energy  in  Real 120  467 

,  Early  Compound 19  72 

,  Experimental 44  231 

,  Heat-,  Classified   .     3  2 

,  High-speed,  Jackets  on 159  656 

,  Simple  and  Compound  Forms 35  116 

,  Ideal,  Computations  of  Efficiencies  of 117  454 

,  Theory  of  Efficiency  of. . 116  449 

,  Jackets  on  Multiple-cylinder 157  654 

.Jacketed 113  444 


862  INDEX. 

ART.  P^  GK 

Engines,  Low-speed,  Simple  and  Compound  Forms 35  116 

,  Marine 41  211 

.Early 22  45 

-Later 23  57 

,  Standard  Forms 42  217 

,  Multiple-cylinder,  Recent  Use  of 24  68 

,  Portable 38  179 

.Pumping 37  163 

.Later 18  25 

,  Real,  and  their  Cycles 116  467 

,  Computations  of  Efficiency  and  Economy  of 137  572 

,  Curves  of  Efficiency  for 186  756 

,  Examples  of  Computations  of  Economy  and  Effi- 
ciency of 137  572 

,  Theory  of  Efficiencies  for.. 185  752 

,  Single-acting  and  H  igh-speed  36  150 

,  Size  of 182  741 

,  Steam-,  Classed 29  83 

.Defined 4  2 

.Steam  Fire- ...   21  34 

,  Steam-jackets  on  Multiple-cylinder  152  622 

on  Simple  Cylinder. 152  622 

,  The  Locomotive 40  103 

,  The  Scope  of  the  Philosophy  of  the  Heat- 45  243 

,  Theory  of,  General 57  257 

,  Theory  of  Multiple-cylinder,  General 138  584 

Equations,  General  Fundamental  Thermodynamic. 86  319 

Equivalent,  Mechanical,  of  Heat.    .. 82  312 

Estimate  of  Costs 191  766 

of  Fuel ,., 178  713 

of  Heat 178  713 

of  Steam...    178  713 

Evaporation,  Factors  of  89  332 

,  Tables  of  Factors  of . 99  376 

Examples  of  Computations  of  Efficiencies 149  61 1 

Expansion,  Absolute  Limits  to 201  786 

,  Best  Ratio  of 64  271 

,  Cost  of  Engine  as  affecting 195  775 

,  Extent  of  Economical 144  597 

,  Profits  at  a  fixed 194  774 

,  Ratios  of,  at  Maximum  Efficiencies 181  725 

,  Thermal  Lines  of,  for  Steam 102  394 

,  for  Vapors 102  394 

Experiment,  General  Results  of ,.      150  614 

Experimental  Engines 44  2-" 


INDEX.  863 

AJTT.  FACE 

Experimental  Results.  Experience  with  Jackets , 165  664 

External  and  Internal  Work 99  ygf 

Factory  or  Mill  Engine 34  95 

Fire-engine.  Sarerys ,o  n 

Fire-engines,  Steam 2I  34 

First  Law  of  Thermodynamics 82  312 

Fluid,  Superheated  Steam  as  a  Working 167  671 

Fluids,  Conditions  of  Maximum  Efficiency  of 125  453 

Force 76  299 

Forces,  Balance  of 151  620 

Friction,  Internal  Engine.  Investigation  of 133  55$ 

,  Variation  and  Distribution  of 134  565 

Friction  of  Engine,  and  Efficiency  of  the  Machine 132  540 

Fuel,  Heat,  Steam,  Estimates  of 178  713 

,  Thermodynamk  Demand  for 176  709 

Function,  Thermodynamic 101  319 

Fundamental  Principles  of  Compounding. 142  595 

Thermodynamic  Equations,  General 86  319 

Fusing  and  Boiling  Points 89  322 

Gas,  Definition  of  Perfect 95  354 

Equation  for  the  Perfect 95  354 

Thermodynamics  of  the  Perfect 96  355 

Gases 89  322 

and  Vapors,  Thermodynamics  of  the  Imperfect 95  373 

Greene  and  Corliss  Engines,  Simple  and  Compound  Forms 34  95 

Heads  and  Piston,  Jacketing  the 162  661 

Heat  and  Temperature.  Absolute  Scale 91  328 

,  Mechanical  Equivalent  of 82  312 

,  Mechanical  Theory,  Origin  and  Form  of 55  253 

of  Steam,  Computation  of  Latent  and  Total 93  336 

.  Quantities  of .....92  333 

,  Steam,  Fuel,  Estimates  of .*. .   ..178  713 

,  Thermodynamic  Demand  for 176  709 

Heal.  Transformed 112  431 

Heats,  Specific.  Latent  and  Total 93  336 

Heat-engine,  Purpose  of I  I 

.  The  Steam-engine  as  a 106  422 

H  rat -engines,  Classification  of. 3  2 

.First  Law  of 83  515 

.  The  Scope  of  the  Philosophy  of 45  243 

Heat-wastes  by  Conduction  and  Radiation 126  483 

Hero's  Engine 6  3 

High-speed  and  the  Steam-engine 131  534 

and  Single-acting  Engines 36  150 

Engines,  Jackets  on 159  656 


804  INDEX. 

ART.  PAGE 

Hirn's  Investigations  on  Cylinder-condensation 66  274 

Ideal  Efficiency,  Rankine's  Diagram  of 184  749 

Thermodynamic  Cases 112  431 

,  Special.    113  444 

Ideal  Engine  distinguished  from  Real  94  350 

,  Efficiencies  of 183  746 

Ideal  Engines  and  Real 52  250 

,  Progress  of  Philosophy  of 54  251 

,  Scientific  Problem  of 53  251 

Ideal  Engines,  Application  of  Computation  of  Efficiencies  of 117  454 

,  Computation  of  Efficiencies  of 117  454 

Theory  of  Efficiency  of 116  450 

Imperfect  Gases  and  Vapors,  Thermodynamics  of „ 98  375 

Internal  Condensation  and  Waste,  Theory  of 130  5 1 7 

,  Laws  governing  loss  by 129  499 

Internal  Engine-friction,  Investigation  of 133  558 

,  Variation  and  Distribution  of 134  565 

Internal  Work 90  327 

Investigation  of  Costs,  Deductions  from 197  776 

Ishenvood's  Work 67  275 

Jacket,  Action  of  the,  in  Detail 153  627 

and  Engine  Efficiency 166  668 

Jacket-action,  Limitations  of 156  648 

,  Maximum  Efficiency  of 156  648 

Jacket-waste,  Computation  of  Efficiency  and 155  636 

Jacket-wastes  v.  Cylinder-wastes ,    154  632 

Jackets,  Air  in « 164  663 

,  Experimental  Results  of  Experience  with, 165  664 

,  on  High-speed  Engines   159  650 

on  Multiple-cylinder  Engines 157  654 

,  Temperatures  and  Pressures  in 160  658 

,  Proportions  of  Engine  with 163  661 

Jackets,  Steam 131  534 

,  on  Simple  and  Multiple-cylinder  Engines . .  152  622 

Jacketed  Engines 113  444 

Jacketing,  Amelioration  of  Wastes  by 140  590 

,  Conclusions  relative  to 166  668 

,  Defective 164  663 

.Influence  of 145  598 

the  Heads  and  Piston ,.162  661 

and  Superheating 158  656 

Kinetic  Theory  of  Gases < 89  322 

Latent  Heat  of  Steam,  Computation  of r 93  336 

Heats,  Specific,  Total  and 73  291 

Law,  First,  of  Heat-engines    83  315 


INDEX.  -C: 

XKT.  PAG* 

Law,  First,  of  Thermodynamics. ..........„..".  82  312 

,  Fundamental,  of  Energetics. 75  ,98 

*4  315 

and  the  Steam-engine 85  319 

Laws  and  Basis  of  Thermodynamics 8l  310 

governing  Loss  by  Internal  Condensation 129  409 

,  Newton's,  and  Energetics 78  305 

of  Energetics. 77  304 

of  Thermodynamics,  Relation  of  the  two 87  321 

Limit  of  Actual  Engine  Efficiency 118  466 

in  Superheating.. 169  675 

Limits,  Absolute,  to  Expansion .201  787 

Limitations  of  Jacket-action.. 136  648 

of  Thermodynamic  Theory 62  267 

Lines,  Actual  Tbermodynamk,  and  Corves  of  Efficiency 180  718 

Liquids 89  322 

21  34 

40  193 

Locomotives,  Road- - 39  187 

Loss  by  Internal  Condensation,  Laws  governing 129  499 

Losses  by  Conduction  and  Radiation,  Methods  of  Reduction  by....  127  487 

in  Actual  Engines.  Magnitude  and  Distribution  of 122  4?! 

Machine,  Efficiency  of  the  Engine  as  a . 179  714 

.  Friction  of  the  Engine  and  Efficiency  of  the 132  540 

Magnhnde  of  Cylinder-condensers 128  488 

and  Distribution  of  Losses  in  Actual  Engines 123  476 

Marine  Engines 41  211 

.Early 22  45 

.Later 23  57 

,  Standard  Forms  of 42  217 

Mathematical  Treatment  of  Engine  Efficiencies 173  705 

Matter 76  299 

,  Thermodynamics  and  Constitution  of SS  326 

Efficiency,  Conclusions  relative  to 200  788 

,  Conditions  of 115  449 

of  Engine.  Conditions  of  Real 135  570 

of  Fluids,  Conditions  of 125  483 

of  Jacket-action .156  627 

Efficiencies,  Ratio  of  Expansion  at 181  725 

Total  Efficiency  of  Steam,  Conditions  of. 136  571 

il  Equivalent  of'rleat 82  3" 


or  Dynamic  Wastes in        430 

Theory  of  Heat,  Origin  and  Form  of 55        253 

,  Efficiency  of 151        620 


Methods  of  Operation  of  Real  Engines 121        470 


866  INDEX, 

ART.  PAGE 

Methods  of  Waste  in  Actual  Engines 122  471 

Mill  or  Factory  Engine 34  95 

Model,  The  Newcomen 15  19 

Multiple-cylinder  and  Simple  Engines,  Jackets  on 152  622 

Multiple-cylinder  Engines,  General  Theory  of 138  584 

,  Jackets  on 157  654 

,  Recent  Use  of 24    .      68 

Newcomen  Engine,  The 12  12 

,  its  Merits  and  Demerits 13  16 

Newcomen  Model 15  19 

Newton's  Laws  and  Energetics 78  305 

Operations,  Efficiency  of  Cyclical 114  447 

,  of  Real  Engines,  Methods  of 121  470 

Origin  and  Form  of  Mechanical  Theory  of  Heat 55  253 

Perfect  Gas,  Definition  of 95  354 

,  Equation  of 95  354 

,  Thermodynamics  of  the 96  355 

Performance  of  Engine,  Solution  of  Problems  relating  to 148  604 

Philosophy  of  Cylinder-condensation,  Three  ^tiods  of 69  279 

Heat-engines,  Scope  of  the 45  243 

Ideal  and  Real  Engines,  Progress  of 54  25 1 

Physical  Condition,  Critical,  and  Temperature  of  Steam 94  350 

or  Thermal  Wastes no  429 

Principles  of  Transformation  of  Energy 49  246 

Piston,  jacketing  the  Heads  and 162  661 

Points,  Fusing  and  Boiling 89  322 

Portable  Engines 38  179 

Pressure,  Back- 171  683 

,  as  modifying  Economy 196  776 

,  and  Clearance in  430 

Pressure,  Steam,  Adaptation  of  Structure  to  Increasing 43  229 

Pressures,  Distribution  of ...  151  620 

and  Temperatures  in  Jackets 160  658 

Princip''.s  of  Construction,  General 31  86 

of  Design   30  85 

of  Transformation  of  Energy,  Chemical 48  245 

.Mechanical 50  247 

.Physical 49  246 

Three  Fundamental,  of  Compounding 142  593 

Problem,  Scientific,  of  Real  and  Ideal  Engines 53  251 

Problems,  Efficiency,  solved  by  Inspection 199  784 

of  Compounding 141  592 

,  Practical  Solution  for  Efficiency 188  759 

relating  to  Performance,  Solution  of 148  604 

Processes,  Nature  of  the  Thermal 46  243 


INDEX.  867 

ART.  J-AGE 

Profits  and  Costs,  Relation  of 103  j-j2 

at  a  Fixed  Expansion IQ^  -74 

Progress  of  Philosophy  of  Ideal  and  Real  Engines 54  251 

Pumping-engines 37  ,63 

.Later XS  25 

Quality  of  Steam  in  Steam-jackets 161  659 

Radiation  and  Conduction,  Heat- wastes  by 126  483 

,  Method  of  Reduction  of  Losses  by 127  487 

Rankine's  Work 60  263 

Diagram  of  Ideal  Efficiency 184  750 

Ratio  of  Expansion,  Best 64  271 

Ratios  of  Expansion  at  Maximum  Efficiencies 181  725 

Cost  of  Engine  as  affecting 195  775 

Real  Efficiency,  Thurston's  Curves  of 187  757 

Real  Engine  distinguished  from  Ideal 04  350 

and  Ideal 52  250 

,  Progress  of  Philosophy  of 54  251 

,  Scientific  Problem  of 52  250 

Real  Engines  and  their  Cycles 119  467 

,  Computation  of  Economy  and  Efficiency  of 137  572 

,  Curves  of  Efficiency  for 186  7^6 

,  Distribution  of  Energy  in 120  467 

,  Examples  of  Computation  of  Economy  and  Efficiency 

of 137 

,  Methods  of  Operation  of 121  471 

,  Theory  of  Efficiencies  for 185  752 

Real  Maximum  Efficiency  of  Engine,  Conditions  of 135  570 

Reduction  of  Losses  by  Conduction  and  Radiation,  Methods  of 127  487 

Results  of  Experiment,  General 150  614 

,  Statement  of 192  768 

Road  Locomotives  and  Rollers 39  187 

Rollers,  Steam 39  i:~ 

Rollers,  Steam  Road 39  187 

Savery's  Engine,  Performance  of n  n 

"Fire-engine" 10 

Science  of  Thermodynamics 46  243 

Scientific  Problem  of  Real  and  Ideal  Engines 53  251 

Screw-engine,  Compound... 42  217 

Second  Law  of  Thermodynamics 84  315 

and  the  Steam-engine 85  319 

Several  Efficiencies  of  the  Steam-engine 174  705 

Simple  and  Compound  Forms,  Corliss  and  Greene  Engines 34  95 

Multiple-cylinder  Engines,  Steam-jackets  on 152  622 

Single-acting  Engine,  Watt's 16  22 

Engines  and  High-speed  Engines 36  150 


868  INDEX. 

ART.  PAGE 

Size  of  Engine,  Influence  of. , 147  604 

Smeaton's  and  Watt's  Discoveries 63  268 

Solids 09  326 

Solution  of  Practical  Problems  of  Efficiency 188  759 

Problems  relating  to  Performance 148  604 

Source  of  Energy,  Transformations,  Character  of,  and 47  245 

Special  Ideal  Thermodynamic  Cases 113  444 

Speed,  High 131  534 

Stationary  Engine,  The 20  33 

,  Older  Forms  of 33  87 

Status  of  Theory  of  Cylinder-condensation  in  1850 68  277 

Steam,  Conditions  of  Maximum  Total  Efficiency  of 136  571 

,  Consumption  of 128  488 

,  Critical  Physical  Conditions  and  Temperature  of 94  350 

,  Early  Knowledge  of 7  5 

,  General  Thermodynamic  Equation  for 101  389 

,  Thermodynamic  Demand  for 176  709 

in  the  Middle  Ages 8  5 

-power 100  383 

-pressure,  Adaptation  of  Structure  to  increasing 43  229 

,  Quality  of 161  659 

Road  Rollers 39  187 

,  Saturated,  Use  of 113  444 

,  Stored  Energy  in 100  383 

,  Superheated,  and  the  Steam-engine 168  671 

,  Superheated,  as  a  Working  Fluid 167  671 

,  Thermal  Lines  for  Expansion  of 102  394 

Steam-engine  as  a  Heat-engine  106  422 

,  Peculiar  Types  of  the 44  231 

,  Philosophical  Study  of  Development  of  the 26  77 

,  Process  of  Development  of  the 25  73 

,  Structure  and  Uses  of  the , 27  82 

,  Thermodynamics  of  the 105  421 

,  Wastes  of  the 108  426 

Steam-engines,  Actual  Efficiencies  01  Proposed 137  572 

classed 29  83 

defined 4  2 

,  Economy  of  Proposed 137  572 

,  General  Theory  of 57  257 

,  Origin  of 5  3 

,  Real,  Distribution  of  Energy  in 120  467 

,  Thermodynamics  of 72  296 

Steam  Fire-engine 21  34 

Steam-jackets 131  534 

on  Multiple-cylinder  Engines 152  622 


INDEX.  869 

ART.  PACE 

Steam-jackets  on  Single-cylinder  Engines 152  622 

Stored  Energy  in  Steam 100  383 

Structure,  Adaptation  of,  to  increasing  Steam-pressure. 43  229 

Superheated  Steam  and  the  Steam-engine 168  671 

as  a  Working-fluid 167  671 

Superheating 131  534 

and  Jacketing 158  656 

,  Amelioration  of  Wastes  by 140  590 

,  Conclusions  relative  to 170  680 

,  Experience  and  Testimony 170  6So 

,  Influence  of 145  598 

,  Limit  in 169  675 

Surfaces,  Condition  of 161  659 

Tables  of  Factors  of  Evaporation 99  376 

Temperature  and  Critical  Physical  Condition  of  Steam 94  350 

and  Heat,  Absolute  Scale 91  320 

Temperatures  and  Pressures  in  Jackets 60  263 

Testimony  and  Experience  in  Superheating 170  680 

Theory,  General,  of  Multiple-cylinder  Engines 138  584 

,  of  Steam-engines 57  217 

,  Kinetic,  of  Gases 89  322 

of  Cylinder-condensation,  Status  of,  in  1850 68  277 

Efficiency  of  Ideal  Engines 116  450 

for  Real  Engines 185  752 

Heat,  Mechanical,  Origin  and  Form  of 55  253 

Internal  Condensation  and  Waste 130  517 

Thermodynamics,  Limitations  of 62  262 

Thermal  Lines,  Actual 180  718 

,  Construction  of 103  400 

for  Expansion  of  Steam 102  394 

Vapors 102  394 

Processes,  Nature  of  the 46  243 

Wastes,  Physical  or no  429 

Thermodynamic  Cases,  Ideal 112  431 

Demand  for  Heat 176  709 

Steam 176  709 

Fuel 176  709 

Efficiency 175  709 

Equation,  General  Fundamental  86  319 

,  General,  for  Steam 100  383 

Thermodynamic  Function 101  389 

Operations,  Cyclical 104  410 

Theory,  Limitations  of 62  267 

Wastes 109  427 

,  Unavoidable,  in  Actual  Cases 124  482 


8/0  INDEX. 

ART.  PAGE 

Thermodynamics , 49  246 

and  Energetics 45  243 

and  the  Constitution  of  Matter 88  322 

as  a  Branch  of  Energetics. . -••'A 74  29? 

,  Basis  and  Laws  of Si  310 

,  Definition  of 73~8o  291-309 

,  First  Law  of 82  3-2 

of  Imperfect  Gases 98  373 

Vapors 98  373 

of  Steam 99  376 

of  To-day 61  267 

Work  and  Energy 97  365 

the  Steam-engine 72-105  296-421 

Perfect  Gas 96  355 

,  Relation  of  the  Two  Laws  of 87  321 

,  Restricted  Case  of  Energetics So  309 

,  Science  of 56  256 

,  Second  Law  of 84  315 

Total  Efficiency  of  Steam,  Conditions  of  Maximum 135  570 

Total  and  Latent  Heat  of  Steam,  Computations  of 93  336 

Total,  Latent  and  Specific  Heats 93  336 

Transformations  of  Energy,  Character,  Source,  and 47  245 

,  Chemical  Principles  of 48  245 

,  Mechanical  Principles  of 50  247 

,  Physical  Principles  of 49  246 

Types,  Classification  of  Engines  into 28  82 

,  Peculiar,  of  Steam-engines 44  217 

Vapor  System,  Binary 172  697 

Vapors  and  Gases,  Theory  of  Imperfect 98  373 

,  Thermal  Lines  for  Expansion  of 102  394 

Variation  and  Distribution  "of  Internal  Engine-friction 134  565 

Waste  and  Internal  Condensation,  Theory  of 130  517 

,  Computation  of,  in  Actual  Engines 122  491 

,  Unavoidable,  in  Thermodynamic  Cases  124  482 

Wastes,  Amelioration  of 140  590 

,  by  Jacketing 140  590 

,  by  Superheating 140  590 

,  Mechanical  or  Dynamic in  430 

Wastes  of  Heat,  by  Conduction  and  Radiation 126  ^83 

Jacket  vs.  Wastes  of  Cylinder 154  632 

the  Compound  Engine . 139  586 

Steam-engine 108  426 

Wastes,  Physical  or  Thermal ito  429 

,  Thermodynamic 109  427 

Watt,  James 14  18 


INDEX. 


Watt's  and  Smeaton's  Discoveries 63  266 

Double-acting  Engine 17  223 

Single-acting  Engine 16  22 

Worcester's  Engine,  Marquis  of 9  5 

Work 76  209 

and  Energy,  Thermodynamics  of 97  365 

External  and  Internal 90  327 

RegnanU's. loo  383 

Working  Fluid,  Superheated  Steam  as  a 167  671 

Substance,  Actual  Efficiency  of  the 177  712 


END  OF   PART  L 


IHIflll      I 


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